library(readxl)
dat <- read_xlsx("sem_example.xlsx")SEM: Demonstrate Maximum Likelihood Estimation
Goal
Try doing the minimization ourselves (using nlm()).
Notes
The code is styled for readability, even if this means longer code. Names will be reused to avoid having too many names.
For learning, whenever possible, only functions covered before will be used.
The functions are just for demonstration. In real research, error catching is needed in the them.
Read the Data
Use the following to show the data
head(dat)# A tibble: 6 × 21
case_id x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 case_1 5.37 3.36 5.43 4.65 6.48 5.20 6.46 6.56 5.93 7.11 4.93
2 case_2 4.93 4.77 4.93 6.34 4.93 4.74 4.42 4.47 5.83 6.47 3.88
3 case_3 5.48 5.36 5.64 7.11 4.42 6.70 5.44 4.81 5.34 4.27 4.92
4 case_4 6.63 5.42 4.93 6.47 5.46 4.61 3.38 3.68 4.76 5.27 5.71
5 case_5 4.78 3.97 5.06 4.64 5.24 5.55 5.37 4.57 5.73 6.18 5.06
6 case_6 3.53 5.06 5.21 3.23 4.93 5.87 5.66 4.76 6.05 5.18 4.72
# ℹ 9 more variables: x12 <dbl>, x13 <dbl>, x14 <dbl>, x15 <dbl>, x16 <dbl>,
# s1 <dbl>, s2 <dbl>, s3 <dbl>, s4 <dbl>A Path Analysis Model
mod_pa <-
"
s3 ~ s1 + s2
s4 ~ s3
"Write a Function to Create the Model Matrices
# Parameters in thetas, in this order (as in lavaan)
# (b31, b32, b43, sigma33, sigma44, sigma11, sigma12, sigma22)
matrices_pa <- function(thetas) {
vnames <- c("s3", "s4", "s1", "s2")
# Create the 4x4 beta matrix
beta <- matrix(c( 0, 0, thetas[1], thetas[2],
thetas[3], 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 0),
byrow = TRUE,
nrow = 4,
ncol = 4)
colnames(beta) <- vnames
rownames(beta) <- vnames
# Create the 4x4 psi matrix
psi <- diag(thetas[c(4, 5, 6, 8)])
psi[4, 3] <- psi[3, 4] <- thetas[7]
colnames(psi) <- vnames
rownames(psi) <- vnames
# Return the matrices as a list
out <- list(beta = beta,
psi = psi)
return(out)
}Test the function by using arbitrary numbers:
matrices_pa(thetas = 1:8)$beta
s3 s4 s1 s2
s3 0 0 1 2
s4 3 0 0 0
s1 0 0 0 0
s2 0 0 0 0
$psi
s3 s4 s1 s2
s3 4 0 0 0
s4 0 5 0 0
s1 0 0 6 7
s2 0 0 7 8Write a Function to Compute the Implied Covariance Matrices
implied_cov_pa <- function(thetas) {
# Create the matrices
m <- matrices_pa(thetas)
beta <- m$beta
psi <- m$psi
# Compute the implied covariance matrix
a <- solve(diag(4) - beta)
sigma_implied <- a %*% psi %*% t(a)
sigma_implied
}Write the ML Discrepancy Function
It will have three arguments.
thetasis the vector or parameters.data_covis the (ML) sample covariance matrix.impliedis the function to be used to compute the implied covariance matrix.
Only thetas will change in the minimization. data_cov and implied are fixed and will not change.
f_ml <- function(thetas,
data_cov,
implied) {
# Compute the implied covariance matrix
sigma_implied <- implied(thetas)
# Compute the discrepancy function value
p <- ncol(data_cov)
fx <- log(det(sigma_implied)) - log(det(data_cov)) +
sum(diag(data_cov %*% solve(sigma_implied))) - p
fx
}Find the Solution
Prepare the ML estimate sample covariance matrix first:
n <- nrow(dat)
# Variables ordered as in lavaan
my_data_cov <- cov(dat[, c("s3", "s4", "s1", "s2")])
my_data_cov <- my_data_cov * (n - 1) / n
round(my_data_cov, 3) s3 s4 s1 s2
s3 0.568 0.356 0.207 0.201
s4 0.356 0.603 0.223 0.228
s1 0.207 0.223 0.556 0.157
s2 0.201 0.228 0.157 0.443Set the starting values:
- Positive numbers for variances or error variances.
- Some nonzero numbers for regression coefficients just for identifying them in the minimization.
# Parameters in thetas, in this order (as in lavaan)
# (b31, b32, b43, sigma33, sigma44, sigma11, sigma12, sigma22)
start <- c(`s3~s1` = .03,
`s3~s2` = .08,
`s4~s3` = .06,
`s3~~s3` = .50,
`s4~~s4` = .08,
`s1~~s1` = .50,
`s1~~s2` = .08,
`s2~~s2` = .50)Put the starting values into the model matrices:
matrices_pa(thetas = start)$beta
s3 s4 s1 s2
s3 0.00 0 0.03 0.08
s4 0.06 0 0.00 0.00
s1 0.00 0 0.00 0.00
s2 0.00 0 0.00 0.00
$psi
s3 s4 s1 s2
s3 0.5 0.00 0.00 0.00
s4 0.0 0.08 0.00 0.00
s1 0.0 0.00 0.50 0.08
s2 0.0 0.00 0.08 0.50Use nlm() to minimize the discrepancy function value by trying different values for the parameters.
The argument f is the discrepancy function. The first argument of f should be the vector of parameters, thetas in our case.
From the help page, ... are other arguments to be used by f. In our case, it is data_cov, set to my_data_cov created above.
Set print.level = 2 just for illustration.
f_ml_min <- nlm(f = f_ml,
p = start,
data_cov = my_data_cov,
implied = implied_cov_pa,
print.level = 2)iteration = 0
Step:
[1] 0 0 0 0 0 0 0 0
Parameter:
[1] 0.03 0.08 0.06 0.50 0.08 0.50 0.08 0.50
Function Value
[1] 4.805795
Gradient:
[1] -0.7120980 -0.6427548 -8.0496758 -0.1107065 -75.3963364 -0.1255387
[7] -0.6667372 0.3374183Warning in log(det(sigma_implied)): NaNs producedWarning in nlm(f = f_ml, p = start, data_cov = my_data_cov, implied =
implied_cov_pa, : NA/Inf replaced by maximum positive valueiteration = 1
Step:
[1] 0.07120980 0.06427548 0.80496758 0.01107065 7.53963364 0.01255387
[7] 0.06667372 -0.03374183
Parameter:
[1] 0.1012098 0.1442755 0.8649676 0.5110707 7.6196336 0.5125539 0.1466737
[8] 0.4662582
Function Value
[1] 2.269081
Gradient:
[1] -0.50227093 -0.47362142 0.03552988 0.08927538 0.12413816 -0.15883677
[7] -0.06198200 0.14165884
iteration = 2
Step:
[1] 0.050078710 0.047221963 -0.003469182 -0.008899016 -0.011693173
[6] 0.015835851 0.006185128 -0.014125271
Parameter:
[1] 0.1512885 0.1914974 0.8614984 0.5021716 7.6079405 0.5283897 0.1528589
[8] 0.4521329
Function Value
[1] 2.221056
Gradient:
[1] -0.370771781 -0.367363025 0.035066339 0.141090172 0.124334128
[6] -0.104174492 0.003731536 0.054745474
iteration = 3
Step:
[1] 0.1662352505 0.1638664157 -0.0150606778 -0.0596918125 -0.0519308470
[6] 0.0473225350 0.0006865728 -0.0269075094
Parameter:
[1] 0.3175238 0.3553639 0.8464377 0.4424798 7.5560096 0.5757123 0.1535454
[8] 0.4252254
Function Value
[1] 2.155561
Gradient:
[1] 0.113185260 0.029252321 0.033042427 0.006412762 0.125207584
[6] 0.073813866 -0.026130126 -0.099142456
iteration = 4
Step:
[1] -0.023917899 -0.016597775 -0.001520645 0.005084623 -0.006277815
[6] -0.010304208 0.002567834 0.010481756
Parameter:
[1] 0.2936059 0.3387661 0.8449171 0.4475644 7.5497318 0.5654080 0.1561133
[8] 0.4357071
Function Value
[1] 2.151591
Gradient:
[1] 0.040840492 -0.020726151 0.032841029 0.035884136 0.125312396
[6] 0.035435971 -0.009459744 -0.040196060
iteration = 5
Step:
[1] -0.0146895117 -0.0002947197 -0.0068493921 -0.0041016616 -0.0262374885
[6] -0.0101859081 0.0039498329 0.0116341496
Parameter:
[1] 0.2789163 0.3384714 0.8380677 0.4434628 7.5234943 0.5552221 0.1600631
[8] 0.4473413
Function Value
[1] 2.147388
Gradient:
[1] 0.004181962 -0.031908022 0.031921057 0.016428689 0.125753947
[6] -0.009370230 0.020639260 0.014920088
iteration = 6
Step:
[1] -0.025744278 0.016035230 -0.024168920 -0.013582700 -0.093049780
[6] -0.018562396 0.005033178 0.023476196
Parameter:
[1] 0.2531721 0.3545066 0.8138988 0.4298801 7.4304445 0.5366597 0.1650963
[8] 0.4708175
Function Value
[1] 2.138048
Gradient:
[1] -0.05055505 -0.01866278 0.02862471 -0.05643992 0.12733703 -0.09382561
[7] 0.05145596 0.11845304
iteration = 7
Step:
[1] -0.025255155 0.030699802 -0.039315694 -0.012858786 -0.153551351
[6] -0.013975086 0.002753964 0.020404602
Parameter:
[1] 0.2279169 0.3852064 0.7745831 0.4170213 7.2768932 0.5226847 0.1678502
[8] 0.4912221
Function Value
[1] 2.125658
Gradient:
[1] -0.09632902 0.02698756 0.02308942 -0.13869487 0.13000924 -0.16167559
[7] 0.06160524 0.19718183
iteration = 8
Step:
[1] -0.04817245 0.07052932 -0.10031621 -0.01324530 -0.39833897 -0.01521041
[7] 0.00226082 0.02938658
Parameter:
[1] 0.1797445 0.4557357 0.6742669 0.4037760 6.8785542 0.5074742 0.1701111
[8] 0.5206087
Function Value
[1] 2.096504
Gradient:
[1] -0.177282891 0.145213868 0.007854577 -0.260812245 0.137319414
[6] -0.238557886 0.052103844 0.294353976
iteration = 9
Step:
[1] -0.078154555 0.117765579 -0.204051700 0.001656068 -0.826658501
[6] -0.008477836 0.002154524 0.032005102
Parameter:
[1] 0.1015899 0.5735013 0.4702152 0.4054321 6.0518957 0.4989964 0.1722656
[8] 0.5526138
Function Value
[1] 2.038059
Gradient:
[1] -0.29966903 0.34151582 -0.02938573 -0.36511542 0.15448033 -0.28128154
[7] 0.02202108 0.37902259
iteration = 10
Step:
[1] -0.149744023 0.220496197 -0.475788814 0.040539139 -1.974706444
[6] 0.003602872 0.004789534 0.037724194
Parameter:
[1] -0.048154119 0.793997492 -0.005573658 0.445971204 4.077189274
[6] 0.502599284 0.177055111 0.590337965
Function Value
[1] 1.894928
Gradient:
[1] -0.49048718 0.64321092 -0.17622105 -0.46176815 0.20873942 -0.25777129
[7] -0.02701692 0.45373044Warning in log(det(sigma_implied)): NaNs produced
Warning in log(det(sigma_implied)): NA/Inf replaced by maximum positive valueiteration = 11
Step:
[1] -0.041024321 0.058351341 -0.146148475 0.017879966 -0.627793765
[6] 0.002606861 0.001695773 0.006633764
Parameter:
[1] -0.08917844 0.85234883 -0.15172213 0.46385117 3.44939551 0.50520614
[7] 0.17875088 0.59697173
Function Value
[1] 1.843027
Gradient:
[1] -0.53040972 0.70213249 -0.25643845 -0.47112365 0.22902705 -0.24468285
[7] -0.03383878 0.46378835Warning in log(det(sigma_implied)): NaNs produced
Warning in log(det(sigma_implied)): NA/Inf replaced by maximum positive valueiteration = 12
Step:
[1] -0.063987025 0.090779724 -0.243858932 0.035705706 -1.098699380
[6] 0.006071645 0.002546934 0.005807260
Parameter:
[1] -0.1531655 0.9431286 -0.3955811 0.4995569 2.3506961 0.5112778 0.1812978
[8] 0.6027790
Function Value
[1] 1.751026
Gradient:
[1] -0.57784475 0.77277551 -0.49417651 -0.46110674 0.24916816 -0.21469324
[7] -0.04318859 0.47183422
iteration = 13
Step:
[1] -6.167199e-03 1.010437e-02 -3.719340e-02 1.008094e-02 -1.941685e-01
[6] 3.985615e-03 -7.453559e-05 -4.081634e-03
Parameter:
[1] -0.1593327 0.9532329 -0.4327745 0.5096378 2.1565276 0.5152634 0.1812233
[8] 0.5986974
Function Value
[1] 1.72667
Gradient:
[1] -0.57364298 0.77126083 -0.55826892 -0.42628517 0.24484654 -0.19360960
[7] -0.04872908 0.46653694
iteration = 14
Step:
[1] 0.047457217 -0.033421983 -0.156786645 0.122336686 -1.292352181
[6] 0.075708411 -0.006432229 -0.120930204
Parameter:
[1] -0.1118754 0.9198109 -0.5895611 0.6319745 0.8641754 0.5909718 0.1747911
[8] 0.4777672
Function Value
[1] 1.648411
Gradient:
[1] -0.39571571 0.59867215 -1.59930695 0.09359044 -0.47722425 0.09611893
[7] -0.02970559 0.14979896
iteration = 15
Step:
[1] 0.21258227 -0.25727371 0.31076251 0.09734556 0.99602626 0.09938995
[7] -0.02159180 -0.16414707
Parameter:
[1] 0.1007068 0.6625372 -0.2787986 0.7293201 1.8602017 0.6903618 0.1531993
[8] 0.3136201
Function Value
[1] 1.415956
Gradient:
[1] -0.1295998 0.2976624 -0.5531426 0.4661481 0.2931105 0.2831564 0.3393709
[8] -1.5499410
iteration = 16
Step:
[1] -0.051409087 0.022348147 0.010793167 -0.063827265 -0.004152265
[6] -0.051192015 -0.020977778 0.166565388
Parameter:
[1] 0.04929774 0.68488539 -0.26800543 0.66549279 1.85604940 0.63916975
[7] 0.13222148 0.48018547
Function Value
[1] 1.320859
Gradient:
[1] -0.2173705 0.3317157 -0.5477723 0.3908053 0.2964227 0.2744989 -0.3929188
[8] 0.2481374
iteration = 17
Step:
[1] 0.033925789 -0.047455842 0.033251698 -0.015008635 -0.335330043
[6] -0.005843206 0.017444284 -0.002727245
Parameter:
[1] 0.08322353 0.63742954 -0.23475373 0.65048416 1.52071936 0.63332654
[7] 0.14966576 0.47745823
Function Value
[1] 1.16321
Gradient:
[1] -0.1873088 0.2910909 -0.6437137 0.4072581 0.3109076 0.2483561 -0.2849857
[8] 0.2155659
iteration = 18
Step:
[1] 0.0323268230 -0.0453052435 0.0422427851 -0.0159391337 -0.3484778194
[6] -0.0031358818 0.0082443848 -0.0005313852
Parameter:
[1] 0.1155503 0.5921243 -0.1925109 0.6345450 1.1722415 0.6301907 0.1579101
[8] 0.4769268
Function Value
[1] 0.9978276
Gradient:
[1] -0.1577929 0.2511240 -0.7941253 0.4169171 0.2989929 0.2317528 -0.2280929
[8] 0.1987516Warning in log(det(sigma_implied)): NaNs produced
Warning in log(det(sigma_implied)): NA/Inf replaced by maximum positive valueWarning in log(det(sigma_implied)): NaNs producedWarning in nlm(f = f_ml, p = start, data_cov = my_data_cov, implied =
implied_cov_pa, : NA/Inf replaced by maximum positive valueWarning in log(det(sigma_implied)): NaNs producedWarning in nlm(f = f_ml, p = start, data_cov = my_data_cov, implied =
implied_cov_pa, : NA/Inf replaced by maximum positive valueiteration = 19
Step:
[1] 2.748040e-02 -3.846410e-02 3.897487e-02 -1.351488e-02 -2.877911e-01
[6] -2.174070e-03 6.001111e-03 -9.166806e-05
Parameter:
[1] 0.1430307 0.5536602 -0.1535361 0.6210301 0.8844505 0.6280166 0.1639113
[8] 0.4768352
Function Value
[1] 0.8670452
Gradient:
[1] -0.1314784 0.2155935 -1.0024517 0.4213172 0.2026061 0.2183379 -0.1844378
[8] 0.1858914Warning in log(det(sigma_implied)): NaNs produced
Warning in log(det(sigma_implied)): NA/Inf replaced by maximum positive valueiteration = 20
Step:
[1] 0.027813473 -0.038844479 0.038832693 -0.012303058 -0.179397852
[6] -0.002757953 0.007959515 -0.001057004
Parameter:
[1] 0.1708442 0.5148157 -0.1147034 0.6087271 0.7050526 0.6252586 0.1718708
[8] 0.4757782
Function Value
[1] 0.7834943
Gradient:
[1] -0.10337395 0.17774485 -1.19493573 0.42343267 0.02547692 0.19826567
[7] -0.12031085 0.16186963
iteration = 21
Step:
[1] 0.037759396 -0.052805113 0.049463702 -0.017109666 -0.106139005
[6] -0.005363493 0.012877285 -0.002460648
Parameter:
[1] 0.20860361 0.46201060 -0.06523968 0.59161742 0.59891363 0.61989514
[7] 0.18474806 0.47331752
Function Value
[1] 0.7066857
Gradient:
[1] -0.0634310275 0.1238245435 -1.3128539269 0.4185013704 -0.1482909564
[6] 0.1564331775 0.0009947456 0.1105806335
iteration = 22
Step:
[1] 0.27983952 -0.39344671 0.35594937 -0.14026982 -0.35570604 -0.04513897
[7] 0.08810711 -0.01742984
Parameter:
[1] 0.4884431 0.0685639 0.2907097 0.4513476 0.2432076 0.5747562 0.2728552
[8] 0.4558877
Function Value
[1] 0.6689277
Gradient:
[1] 0.3324554 -0.4155562 -1.5699124 -0.1571814 -3.3982178 -0.6807551 1.9687060
[8] -0.8729821
iteration = 23
Step:
[1] 0.0269971006 -0.0407773571 0.0034120772 -0.0060472082 0.3635922459
[6] -0.0003468831 -0.0037455148 -0.0055933228
Parameter:
[1] 0.51544024 0.02778654 0.29412176 0.44530039 0.60679984 0.57440929 0.26910966
[8] 0.45029436
Function Value
[1] 0.5136082
Gradient:
[1] 0.3756204 -0.4833178 -0.6228370 -0.2549913 0.4450850 -0.6601690 1.9470013
[8] -0.8923928
iteration = 24
Step:
[1] -0.133234186 0.171392719 -0.152298080 0.097908325 -0.005773572
[6] 0.068485329 -0.160602556 0.028351396
Parameter:
[1] 0.3822061 0.1991793 0.1418237 0.5432087 0.6010263 0.6428946 0.1085071
[8] 0.4786458
Function Value
[1] 0.4994174
Gradient:
[1] 0.1343002 -0.1935954 -0.9167592 0.3077296 0.2418719 0.2898635 -0.5135702
[8] 0.2566006
iteration = 25
Step:
[1] 0.062085617 -0.086613189 0.106862947 -0.058376654 -0.052347589
[6] -0.030764164 0.043892872 0.003516036
Parameter:
[1] 0.4442917 0.1125661 0.2486866 0.4848321 0.5486787 0.6121305 0.1524000
[8] 0.4821618
Function Value
[1] 0.3928664
Gradient:
[1] 0.23674700 -0.33501824 -0.78291022 0.06385864 0.29037660 0.19822149
[7] -0.24991027 0.22713175
iteration = 26
Step:
[1] 0.030246449 -0.050139838 0.168710601 -0.078422618 -0.135026461
[6] -0.078482397 0.085585077 -0.001395748
Parameter:
[1] 0.47453812 0.06242623 0.41739723 0.40640945 0.41365221 0.53364806 0.23798505
[8] 0.48076604
Function Value
[1] 0.3216416
Gradient:
[1] 0.32643493 -0.48563327 -0.57501766 -0.46118850 0.05079746 -0.53894876
[7] 1.15730896 -0.27792979
iteration = 27
Step:
[1] -0.027115860 0.043462220 -0.020191475 0.039802460 -0.005727412
[6] 0.028634311 -0.041408941 -0.007577520
Parameter:
[1] 0.4474223 0.1058885 0.3972058 0.4462119 0.4079248 0.5622824 0.1965761
[8] 0.4731885
Function Value
[1] 0.2598242
Gradient:
[1] 0.26033889 -0.37507410 -0.63933659 -0.12592314 -0.01243889 -0.09222820
[7] 0.31481071 0.01943653
iteration = 28
Step:
[1] -0.047185369 0.070441669 0.051808888 0.022069232 -0.064347119
[6] -0.001955107 -0.020373099 -0.013844239
Parameter:
[1] 0.4002369 0.1763301 0.4490146 0.4682811 0.3435777 0.5603273 0.1762030
[8] 0.4593443
Function Value
[1] 0.203389
Gradient:
[1] 0.18327643 -0.25572411 -0.58772707 0.05415320 -0.46109297 -0.03258666
[7] 0.13968552 0.02811634
iteration = 29
Step:
[1] -0.077075368 0.114928014 0.049887207 0.013850854 -0.002253844
[6] -0.006883718 -0.024058838 -0.014028193
Parameter:
[1] 0.3231615 0.2912581 0.4989018 0.4821320 0.3413238 0.5534435 0.1521442
[8] 0.4453161
Function Value
[1] 0.1498197
Gradient:
[1] 0.075126449 -0.087318574 -0.425526089 0.170916751 -0.412217236
[6] 0.004469409 -0.053270627 0.028763411
iteration = 30
Step:
[1] -0.049454401 0.075027668 0.080201216 -0.010752597 0.012880283
[6] -0.005378323 -0.014251470 -0.010259626
Parameter:
[1] 0.2737071 0.3662858 0.5791031 0.4713794 0.3542041 0.5480652 0.1378927
[8] 0.4350565
Function Value
[1] 0.1176638
Gradient:
[1] 0.010176035 0.018805397 -0.152759799 0.140587098 -0.216400932
[6] 0.013654119 -0.159525596 0.006599024
iteration = 31
Step:
[1] -0.0075948108 0.0075505398 0.0331071248 -0.0173500088 0.0175529919
[6] -0.0005279322 0.0066493885 0.0030046314
Parameter:
[1] 0.2661123 0.3738363 0.6122102 0.4540294 0.3717571 0.5475373 0.1445421
[8] 0.4380611
Function Value
[1] 0.109549
Gradient:
[1] -0.002810790 0.029009712 -0.044351387 0.067033431 -0.060984110
[6] -0.002747095 -0.096738061 0.005867120
iteration = 32
Step:
[1] 0.006741810 -0.014464285 0.017003313 -0.012306723 0.006988320
[6] 0.002783217 0.008505320 0.003035337
Parameter:
[1] 0.2728541 0.3593721 0.6292135 0.4417227 0.3787454 0.5503205 0.1530474
[8] 0.4410964
Function Value
[1] 0.1077617
Gradient:
[1] 0.003797592 0.005590408 0.007480535 0.008320647 -0.009228494
[6] -0.012434965 -0.021019211 -0.001599203
iteration = 33
Step:
[1] 0.0002132757 -0.0023411804 -0.0026056635 -0.0014880322 0.0026610672
[6] 0.0017544991 0.0025483864 0.0012110566
Parameter:
[1] 0.2730674 0.3570309 0.6266078 0.4402346 0.3814065 0.5520750 0.1555958
[8] 0.4423075
Function Value
[1] 0.1076861
Gradient:
[1] 0.0026791724 0.0010483880 -0.0003346621 0.0007152110 0.0092167820
[6] -0.0118521095 -0.0018364776 -0.0020292781
iteration = 34
Step:
[1] 6.283655e-05 -9.614507e-04 3.324193e-04 -3.301696e-04 -7.608527e-04
[6] 1.511936e-03 7.561164e-04 1.867761e-04
Parameter:
[1] 0.2731302 0.3560694 0.6269403 0.4399045 0.3806456 0.5535869 0.1563519
[8] 0.4424943
Function Value
[1] 0.1076659
Gradient:
[1] 0.0021537119 -0.0008429275 0.0006570176 -0.0009899974 0.0040023345
[6] -0.0077600681 0.0016041746 -0.0027825813
iteration = 35
Step:
[1] -8.703511e-04 4.057357e-04 -3.565468e-04 -2.791057e-05 -7.015238e-04
[6] 1.878279e-03 6.149503e-04 3.321524e-04
Parameter:
[1] 0.2722599 0.3564752 0.6265837 0.4398766 0.3799441 0.5554652 0.1569669
[8] 0.4428264
Function Value
[1] 0.1076548
Gradient:
[1] 0.0002436611 -0.0006468195 -0.0004081091 -0.0011313102 -0.0008423697
[6] -0.0017698376 0.0018885356 -0.0019330528
iteration = 36
Step:
[1] -2.329246e-04 3.194533e-04 9.904804e-06 9.173229e-05 2.399946e-05
[6] 3.412691e-04 1.835542e-05 1.108619e-04
Parameter:
[1] 0.2720270 0.3567946 0.6265936 0.4399683 0.3799681 0.5558065 0.1569852
[8] 0.4429373
Function Value
[1] 0.107654
Gradient:
[1] -0.0001169935 -0.0001694396 -0.0003784635 -0.0006566196 -0.0006760246
[6] -0.0003995790 0.0007273488 -0.0011277965
iteration = 37
Step:
[1] -3.524305e-05 1.099009e-04 7.826852e-05 8.079796e-05 7.611920e-05
[6] 1.082278e-04 -8.845612e-06 9.691744e-05
Parameter:
[1] 0.2719917 0.3569045 0.6266719 0.4400491 0.3800442 0.5559147 0.1569764
[8] 0.4430342
Function Value
[1] 0.1076538
Gradient:
[1] -1.275922e-04 2.677858e-05 -1.443672e-04 -2.391189e-04 -1.486811e-04
[6] 1.067191e-04 -2.156320e-05 -4.317879e-04
iteration = 38
Step:
[1] 3.394972e-05 -1.378029e-05 3.994488e-05 3.296234e-05 2.593966e-05
[6] -2.604601e-06 7.217757e-06 5.402323e-05
Parameter:
[1] 0.2720257 0.3568907 0.6267118 0.4400820 0.3800702 0.5559121 0.1569836
[8] 0.4430882
Function Value
[1] 0.1076538
Gradient:
[1] -5.164758e-05 2.324896e-05 -2.493117e-05 -6.887824e-05 3.091838e-05
[6] 1.029736e-04 -1.264979e-04 -1.188667e-04
iteration = 39
Step:
[1] 2.345284e-05 -1.929043e-05 1.053614e-05 1.180536e-05 3.514316e-07
[6] -1.401769e-05 1.111974e-05 2.580433e-05
Parameter:
[1] 0.2720491 0.3568714 0.6267224 0.4400938 0.3800705 0.5558981 0.1569947
[8] 0.4431140
Function Value
[1] 0.1076538
Gradient:
[1] -6.161294e-06 1.136868e-06 6.568968e-06 -7.920775e-06 3.335110e-05
[6] 2.843059e-05 -5.583711e-05 -3.106848e-06
iteration = 40
Step:
[1] 3.366556e-06 -2.762619e-06 -1.393623e-06 1.343481e-06 -3.733148e-06
[6] -3.773389e-06 4.311391e-06 3.883401e-06
Parameter:
[1] 0.2720525 0.3568687 0.6267210 0.4400952 0.3800668 0.5558943 0.1569990
[8] 0.4431179
Function Value
[1] 0.1076538
Gradient:
[1] 3.721468e-07 -2.025047e-06 2.401634e-06 -9.841017e-07 7.508660e-06
[6] 3.096190e-06 -1.139888e-05 4.107825e-06
iteration = 41
Step:
[1] -3.153262e-07 7.854673e-07 -7.746248e-07 1.203274e-07 -1.039596e-06
[6] -1.803319e-07 8.922505e-07 1.735312e-08
Parameter:
[1] 0.2720522 0.3568695 0.6267202 0.4400953 0.3800658 0.5558941 0.1569999
[8] 0.4431179
Function Value
[1] 0.1076538
Gradient:
[1] 1.367795e-07 -6.679102e-07 8.704149e-08 -3.623768e-07 3.126388e-07
[6] -1.421085e-07 -1.110223e-06 9.592327e-07
iteration = 42
Parameter:
[1] 0.2720520 0.3568698 0.6267201 0.4400954 0.3800657 0.5558942 0.1570000
[8] 0.4431178
Function Value
[1] 0.1076538
Gradient:
[1] -8.881784e-09 -1.101341e-07 -6.750156e-08 -1.048051e-07 -1.172396e-07
[6] -4.973799e-08 -9.769963e-08 1.278977e-07
Relative gradient close to zero.
Current iterate is probably solution.We can safely ignore the warning messages in this case. Even in real data and model, it is possible that some attempts yield invalid results. What matters is the final solution.
Check the code first to see if the minimization terminated normally (see the help page for the meaning of different code):
f_ml_min$code[1] 1The result of nlm() is a list. The solution is in the element estimate.
round(f_ml_min$estimate, 3)[1] 0.272 0.357 0.627 0.440 0.380 0.556 0.157 0.443start s3~s1 s3~s2 s4~s3 s3~~s3 s4~~s4 s1~~s1 s1~~s2 s2~~s2
0.03 0.08 0.06 0.50 0.08 0.50 0.08 0.50 Compare with lavaan Output
library(lavaan)This is lavaan 0.6-19
lavaan is FREE software! Please report any bugs.mod_pa <-
"
s3 ~ s1 + s2
s4 ~ s3
"
fit_pa <- sem(model = mod_pa,
data = dat,
fixed.x = FALSE)
summary(fit_pa)lavaan 0.6-19 ended normally after 1 iteration
Estimator ML
Optimization method NLMINB
Number of model parameters 8
Number of observations 400
Model Test User Model:
Test statistic 43.062
Degrees of freedom 2
P-value (Chi-square) 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Regressions:
Estimate Std.Err z-value P(>|z|)
s3 ~
s1 0.272 0.047 5.801 0.000
s2 0.357 0.053 6.794 0.000
s4 ~
s3 0.627 0.041 15.325 0.000
Covariances:
Estimate Std.Err z-value P(>|z|)
s1 ~~
s2 0.157 0.026 6.032 0.000
Variances:
Estimate Std.Err z-value P(>|z|)
.s3 0.440 0.031 14.142 0.000
.s4 0.380 0.027 14.142 0.000
s1 0.556 0.039 14.142 0.000
s2 0.443 0.031 14.142 0.000Compare the parameter estimates from the two methods:
round(f_ml_min$estimate, 3)[1] 0.272 0.357 0.627 0.440 0.380 0.556 0.157 0.443coef(fit_pa) s3~s1 s3~s2 s4~s3 s3~~s3 s4~~s4 s1~~s1 s1~~s2 s2~~s2
0.272 0.357 0.627 0.440 0.380 0.556 0.157 0.443 Compute the differences:
f_ml_min$estimate - coef(fit_pa) s3~s1 s3~s2 s4~s3 s3~~s3 s4~~s4 s1~~s1 s1~~s2 s2~~s2
0 0 0 0 0 0 0 0 Compare the values of the discrepancy function:
lavInspect(fit_pa, "optim")$fx[1] 0.05382688f_ml_min$minimum / 2[1] 0.05382688Note that lavaan divides the value by 2.
A Confirmatory Factor Analysis Model
mod_cfa <-
"
f1 =~ x1 + x2 + x3 + x4
f2 =~ x5 + x6 + x7 + x8
f3 =~ x9 + x10 + x11 + x12
f4 =~ x13 + x14 + x15 + x16
"Write a Function to Create the Model Matrices
# Parameters in thetas in this order (as in lavaan)
# (lambda1 .... lambda12, ev1 .... ev16, v1 .. v4, v21, v31, v41, v32, v42, v43)
# ev?? is the error variance of an item
# v? is the variance of a factor
# v?? is the covariance between two factors
# - 1:12: lambda1 .... lambda12,
# - 13:28: ev1 .... ev16,
# - 29:32: v1 .. v4,
# - 33:38: v21, v31, v41, v32, v42, v43
matrices_cfa <- function(thetas) {
vnames <- paste0("x", 1:16)
fnames <- c("f1", "f2", "f3", "f4")
# Create the 16x4 lambda matrix
lambda <- matrix(c( 1, 0, 0, 0,
thetas[1], 0, 0, 0,
thetas[2], 0, 0, 0,
thetas[3], 0, 0, 0,
0, 1, 0, 0,
0, thetas[4], 0, 0,
0, thetas[5], 0, 0,
0, thetas[6], 0, 0,
0, 0, 1, 0,
0, 0, thetas[7], 0,
0, 0, thetas[8], 0,
0, 0, thetas[9], 0,
0, 0, 0, 1,
0, 0, 0, thetas[10],
0, 0, 0, thetas[11],
0, 0, 0, thetas[12]),
byrow = TRUE,
nrow = 16,
ncol = 4)
rownames(lambda) <- vnames
colnames(lambda) <- fnames
# Create the 16x16 theta matrix
theta <- diag(thetas[13:28])
rownames(theta) <- vnames
colnames(theta) <- vnames
# Create the 4x4 psi matrix
psi <- diag(thetas[29:32])
psi[2, 1] <- psi[1, 2] <- thetas[33]
psi[3, 1] <- psi[1, 3] <- thetas[34]
psi[4, 1] <- psi[1, 4] <- thetas[35]
psi[3, 2] <- psi[2, 3] <- thetas[36]
psi[4, 2] <- psi[2, 4] <- thetas[37]
psi[4, 3] <- psi[3, 4] <- thetas[38]
rownames(psi) <- fnames
colnames(psi) <- fnames
# Return the matrices as a list
out <- list(lambda = lambda,
theta = theta,
psi = psi)
return(out)
}Test the function by using arbitrary numbers:
matrices_cfa(thetas = 1:38)$lambda
f1 f2 f3 f4
x1 1 0 0 0
x2 1 0 0 0
x3 2 0 0 0
x4 3 0 0 0
x5 0 1 0 0
x6 0 4 0 0
x7 0 5 0 0
x8 0 6 0 0
x9 0 0 1 0
x10 0 0 7 0
x11 0 0 8 0
x12 0 0 9 0
x13 0 0 0 1
x14 0 0 0 10
x15 0 0 0 11
x16 0 0 0 12
$theta
x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16
x1 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
x2 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0
x3 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 0
x4 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0
x5 0 0 0 0 17 0 0 0 0 0 0 0 0 0 0 0
x6 0 0 0 0 0 18 0 0 0 0 0 0 0 0 0 0
x7 0 0 0 0 0 0 19 0 0 0 0 0 0 0 0 0
x8 0 0 0 0 0 0 0 20 0 0 0 0 0 0 0 0
x9 0 0 0 0 0 0 0 0 21 0 0 0 0 0 0 0
x10 0 0 0 0 0 0 0 0 0 22 0 0 0 0 0 0
x11 0 0 0 0 0 0 0 0 0 0 23 0 0 0 0 0
x12 0 0 0 0 0 0 0 0 0 0 0 24 0 0 0 0
x13 0 0 0 0 0 0 0 0 0 0 0 0 25 0 0 0
x14 0 0 0 0 0 0 0 0 0 0 0 0 0 26 0 0
x15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 27 0
x16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28
$psi
f1 f2 f3 f4
f1 29 33 34 35
f2 33 30 36 37
f3 34 36 31 38
f4 35 37 38 32Write a Function to Compute the Implied Covariance Matrices
implied_cov_cfa <- function(thetas) {
# Create the matrices
m <- matrices_cfa(thetas)
lambda <- m$lambda
theta <- m$theta
psi <- m$psi
# Compute the implied covariance matrix
sigma_implied <- lambda %*% psi %*% t(lambda) + theta
sigma_implied
}Write the ML Discrepancy Function
No need. The discrepancy can be used again. We only need to tell it how to compute the implied covariance matrix by setting implied.
Find the Solution
Prepare the ML estimate sample covariance matrix first:
n <- nrow(dat)
# Variables ordered as in lavaan
my_data_items_cov <- cov(dat[, paste0("x", 1:16)])
my_data_items_cov <- my_data_items_cov * (n - 1) / n
round(my_data_items_cov, 3) x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12
x1 1.112 0.445 0.491 0.418 0.023 0.420 0.091 0.009 0.195 0.223 0.155 0.134
x2 0.445 0.961 0.396 0.340 0.041 0.339 0.039 -0.002 0.143 0.166 0.173 0.121
x3 0.491 0.396 0.935 0.344 0.237 0.531 0.227 0.161 0.377 0.325 0.361 0.295
x4 0.418 0.340 0.344 1.019 0.044 0.264 -0.005 0.093 0.193 0.170 0.143 0.143
x5 0.023 0.041 0.237 0.044 1.104 0.290 0.297 0.193 0.162 0.184 0.183 0.150
x6 0.420 0.339 0.531 0.264 0.290 1.067 0.287 0.174 0.314 0.223 0.296 0.310
x7 0.091 0.039 0.227 -0.005 0.297 0.287 1.038 0.176 0.140 0.196 0.207 0.176
x8 0.009 -0.002 0.161 0.093 0.193 0.174 0.176 1.048 0.134 0.181 0.146 0.214
x9 0.195 0.143 0.377 0.193 0.162 0.314 0.140 0.134 0.988 0.441 0.497 0.425
x10 0.223 0.166 0.325 0.170 0.184 0.223 0.196 0.181 0.441 1.087 0.410 0.390
x11 0.155 0.173 0.361 0.143 0.183 0.296 0.207 0.146 0.497 0.410 0.935 0.396
x12 0.134 0.121 0.295 0.143 0.150 0.310 0.176 0.214 0.425 0.390 0.396 0.964
x13 0.208 0.175 0.346 0.200 0.275 0.294 0.174 0.172 0.383 0.398 0.369 0.319
x14 0.203 0.137 0.308 0.140 0.229 0.322 0.228 0.073 0.325 0.309 0.321 0.301
x15 0.236 0.204 0.360 0.183 0.202 0.337 0.256 0.168 0.482 0.453 0.374 0.363
x16 0.256 0.126 0.353 0.139 0.183 0.314 0.256 0.166 0.349 0.340 0.309 0.304
x13 x14 x15 x16
x1 0.208 0.203 0.236 0.256
x2 0.175 0.137 0.204 0.126
x3 0.346 0.308 0.360 0.353
x4 0.200 0.140 0.183 0.139
x5 0.275 0.229 0.202 0.183
x6 0.294 0.322 0.337 0.314
x7 0.174 0.228 0.256 0.256
x8 0.172 0.073 0.168 0.166
x9 0.383 0.325 0.482 0.349
x10 0.398 0.309 0.453 0.340
x11 0.369 0.321 0.374 0.309
x12 0.319 0.301 0.363 0.304
x13 0.950 0.451 0.505 0.462
x14 0.451 0.955 0.480 0.432
x15 0.505 0.480 0.967 0.536
x16 0.462 0.432 0.536 1.048Set the starting values:
- Positive numbers for variances or error variances.
# Parameters in thetas in this order (as in lavaan)
# - 1:12: lambda1 .... lambda12,
# - 13:28: ev1 .... ev16,
# - 29:32: v1 .. v4,
# - 33:38: v21, v31, v41, v32, v42, v43
start <- rep(0, 38)
start[13:28] <- .60
start[29:32] <- .50Put the starting values into the matrices:
matrices_cfa(thetas = start)$lambda
f1 f2 f3 f4
x1 1 0 0 0
x2 0 0 0 0
x3 0 0 0 0
x4 0 0 0 0
x5 0 1 0 0
x6 0 0 0 0
x7 0 0 0 0
x8 0 0 0 0
x9 0 0 1 0
x10 0 0 0 0
x11 0 0 0 0
x12 0 0 0 0
x13 0 0 0 1
x14 0 0 0 0
x15 0 0 0 0
x16 0 0 0 0
$theta
x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16
x1 0.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x2 0.0 0.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x3 0.0 0.0 0.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x4 0.0 0.0 0.0 0.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x5 0.0 0.0 0.0 0.0 0.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x6 0.0 0.0 0.0 0.0 0.0 0.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x7 0.0 0.0 0.0 0.0 0.0 0.0 0.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x10 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.6 0.0 0.0 0.0 0.0 0.0 0.0
x11 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.6 0.0 0.0 0.0 0.0 0.0
x12 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.6 0.0 0.0 0.0 0.0
x13 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.6 0.0 0.0 0.0
x14 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.6 0.0 0.0
x15 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.6 0.0
x16 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.6
$psi
f1 f2 f3 f4
f1 0.5 0.0 0.0 0.0
f2 0.0 0.5 0.0 0.0
f3 0.0 0.0 0.5 0.0
f4 0.0 0.0 0.0 0.5We use nlm() again. The call is nearly the same. We use the item level covariance this time, and use implied_cov_cfa() to compute the implied covariance matrix.
f_ml_min <- nlm(f = f_ml,
p = start,
data_cov = my_data_items_cov,
implied = implied_cov_cfa,
print.level = 2)iteration = 0
Step:
[1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Parameter:
[1] 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.6 0.6 0.6 0.6 0.6 0.6 0.6
[20] 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.5 0.5 0.5 0.5 0.0 0.0 0.0 0.0 0.0 0.0
Function Value
[1] 6.489492
Gradient:
[1] -0.674462015 -0.744306881 -0.632870979 -0.439096453 -0.449578653
[6] -0.293082458 -0.668117252 -0.753363707 -0.643684221 -0.682805293
[11] -0.765247865 -0.700732812 -0.009616187 -1.002028281 -0.930702445
[16] -1.164852499 -0.003714963 -1.296281621 -1.216053153 -1.243618684
[21] 0.092923841 -1.352113063 -0.929761889 -1.010357842 0.124316209
[26] -0.985004107 -1.019454420 -1.245495287 -0.009616187 -0.003714963
[31] 0.092923841 0.124316209 -0.037374829 -0.321513998 -0.343362537
[36] -0.267621179 -0.454878524 -0.633029952
iteration = 1
Step:
[1] 0.323237656 0.356710987 0.303305045 0.210438105 0.215461726
[6] 0.140460522 0.320196912 0.361051495 0.308487319 0.327236193
[11] 0.366747008 0.335828003 0.004608582 0.480224631 0.446041541
[16] 0.558258557 0.001780405 0.621246301 0.582796602 0.596007453
[21] -0.044533990 0.648003664 0.445590777 0.484216595 -0.059578863
[26] 0.472065752 0.488576153 0.596906821 0.004608582 0.001780405
[31] -0.044533990 -0.059578863 0.017911983 0.154086410 0.164557379
[36] 0.128258138 0.218001703 0.303381233
Parameter:
[1] 0.32323766 0.35671099 0.30330504 0.21043810 0.21546173 0.14046052
[7] 0.32019691 0.36105149 0.30848732 0.32723619 0.36674701 0.33582800
[13] 0.60460858 1.08022463 1.04604154 1.15825856 0.60178041 1.22124630
[19] 1.18279660 1.19600745 0.55546601 1.24800366 1.04559078 1.08421659
[25] 0.54042114 1.07206575 1.08857615 1.19690682 0.50460858 0.50178041
[31] 0.45546601 0.44042114 0.01791198 0.15408641 0.16455738 0.12825814
[37] 0.21800170 0.30338123
Function Value
[1] 3.024356
Gradient:
[1] -0.25771368 -0.33133232 -0.23838968 -0.20385209 -0.18204715 -0.13709700
[7] -0.31010944 -0.34844788 -0.31135700 -0.34939216 -0.41009126 -0.32772738
[13] 0.17476300 0.23261247 0.28337308 0.20662918 0.06976203 0.15503165
[19] 0.15498828 0.12733034 0.27751928 0.22071253 0.28989008 0.23735501
[25] 0.31218631 0.26168429 0.30511921 0.24027405 -0.18395020 -0.02560500
[31] -0.05696112 -0.04717197 -0.09408111 -0.12378398 -0.18806761 -0.06225652
[37] -0.15369321 -0.47894365
iteration = 2
Step:
[1] 0.155255085 0.193454212 0.144063501 0.118079192 0.108326090
[6] 0.079300632 0.179634814 0.201975456 0.178999228 0.198886881
[11] 0.231627117 0.189572716 -0.081895430 -0.059462106 -0.086960951
[16] -0.039060035 -0.032697276 -0.008156636 -0.012154153 0.002263331
[21] -0.135466426 -0.036320127 -0.090079934 -0.061280417 -0.153379400
[26] -0.074018122 -0.092766463 -0.050880310 0.087189137 0.012255332
[31] 0.022195668 0.016009235 0.046218258 0.074449245 0.105844454
[36] 0.042748367 0.095226482 0.257459998
Parameter:
[1] 0.47849274 0.55016520 0.44736855 0.32851730 0.32378782 0.21976115
[7] 0.49983173 0.56302695 0.48748655 0.52612307 0.59837412 0.52540072
[13] 0.52271315 1.02076252 0.95908059 1.11919852 0.56908313 1.21308967
[19] 1.17064245 1.19827078 0.41999958 1.21168354 0.95551084 1.02293618
[25] 0.38704174 0.99804763 0.99580969 1.14602651 0.59179772 0.51403574
[31] 0.47766168 0.45643037 0.06413024 0.22853566 0.27040183 0.17100651
[37] 0.31322818 0.56084123
Function Value
[1] 2.660275
Gradient:
[1] -0.14571819 -0.18482321 -0.13717283 -0.12819005 -0.11943730 -0.08797800
[7] -0.15566028 -0.07967297 -0.08699618 -0.06800173 -0.18715576 -0.08209583
[13] 0.10913588 0.27042062 0.34853439 0.23961619 -0.11127714 0.17558057
[19] 0.17313306 0.13996757 -1.61324724 0.24906764 0.27329565 0.23119511
[25] -2.27030948 0.24273364 0.35365186 0.23547452 -0.15995787 -0.21859445
[31] -2.90948317 -3.97638890 -0.27593241 -0.59511759 0.68269942 -1.37187993
[37] 1.56582537 6.61021327
iteration = 3
Step:
[1] 0.210660529 0.263373149 0.195521882 0.161648516 0.148041039
[6] 0.108670407 0.243922030 0.269410391 0.239772101 0.265201218
[11] 0.314551941 0.253284846 -0.115481364 -0.100956093 -0.141277714
[16] -0.073235874 -0.038259120 -0.029507942 -0.034149101 -0.013330093
[21] -0.099315943 -0.071435157 -0.141642931 -0.101470199 -0.089820874
[26] -0.118956045 -0.149988182 -0.089486720 0.125015799 0.027492024
[31] 0.177903331 0.223899683 0.075714669 0.127647198 0.104857384
[36] 0.124876254 0.045029509 0.005759473
Parameter:
[1] 0.6891533 0.8135383 0.6428904 0.4901658 0.4718289 0.3284316 0.7437538
[8] 0.8324373 0.7272586 0.7913243 0.9129261 0.7786856 0.4072318 0.9198064
[15] 0.8178029 1.0459626 0.5308240 1.1835817 1.1364933 1.1849407 0.3206836
[22] 1.1402484 0.8138679 0.9214660 0.2972209 0.8790916 0.8458215 1.0565398
[29] 0.7168135 0.5415278 0.6555650 0.6803301 0.1398449 0.3561829 0.3752592
[36] 0.2958828 0.3582577 0.5666007
Function Value
[1] 1.666174
Gradient:
[1] 0.053725774 0.089510380 0.035233729 -0.072040827 -0.052640011
[6] -0.043042469 -0.009984415 0.062732553 0.030217780 0.058102255
[11] 0.066910580 0.008343882 -0.196848362 0.278036609 0.382017888
[16] 0.249427456 -0.133728502 0.205307869 0.190746801 0.150885614
[21] -0.518675371 0.298258970 0.369605605 0.293282270 -0.598606853
[26] 0.336926298 0.458470666 0.327587423 0.030992034 -0.088604303
[31] -0.314470736 -0.210950645 -0.229838882 0.105981062 0.098104397
[36] 0.086049493 0.081712464 0.599094840
iteration = 4
Step:
[1] 0.07250889 0.07755282 0.07519367 0.11558397 0.09889653 0.07466102
[7] 0.12293222 0.10092693 0.10262336 0.10141491 0.11515174 0.12191966
[13] 0.05590824 -0.17762386 -0.25030177 -0.14873250 0.04762529 -0.10559947
[19] -0.10078928 -0.07045466 0.14314305 -0.17227625 -0.24788459 -0.18824121
[25] 0.15486998 -0.22015297 -0.29509399 -0.19875284 0.03622146 0.04970942
[31] 0.09799579 0.00563107 0.14734468 -0.02450368 0.03890378 -0.05817722
[37] 0.06769988 0.04602481
Parameter:
[1] 0.7616622 0.8910912 0.7180841 0.6057498 0.5707254 0.4030926 0.8666860
[8] 0.9333643 0.8298820 0.8927392 1.0280778 0.9006052 0.4631400 0.7421826
[15] 0.5675011 0.8972302 0.5784493 1.0779823 1.0357041 1.1144860 0.4638267
[22] 0.9679721 0.5659833 0.7332248 0.4520908 0.6589386 0.5507275 0.8577870
[29] 0.7530350 0.5912372 0.7535608 0.6859611 0.2871896 0.3316792 0.4141630
[36] 0.2377055 0.4259576 0.6126255
Function Value
[1] 1.058867
Gradient:
[1] 0.085879055 0.096752480 0.085704990 -0.057347410 -0.016634679
[6] 0.006192064 0.068567132 0.133133863 0.094950224 0.078537123
[11] 0.081302742 0.046546059 -0.183449561 0.173437389 0.247984740
[16] 0.180101953 -0.174034621 0.205993089 0.164968365 0.119480537
[21] 0.049363823 0.265844442 0.169548724 0.189274324 -0.044519151
[26] 0.184303392 0.320442695 0.275626260 0.198257961 -0.045959482
[31] 0.166553022 -0.295590887 -0.038402373 -0.319734784 0.159538782
[36] -0.686363993 0.648131024 0.570708451Warning in log(det(sigma_implied)): NaNs producedWarning in nlm(f = f_ml, p = start, data_cov = my_data_items_cov, implied =
implied_cov_cfa, : NA/Inf replaced by maximum positive valueiteration = 5
Step:
[1] 0.0073969126 0.0076657203 0.0078006331 0.0245312098 0.0187618078
[6] 0.0128188737 0.0174761219 0.0097963113 0.0124729854 0.0137107587
[11] 0.0155757063 0.0193428769 0.0223748282 -0.0414477005 -0.0590769318
[16] -0.0368380101 0.0195339936 -0.0312165041 -0.0275953172 -0.0192077225
[21] 0.0113407951 -0.0467532627 -0.0535946750 -0.0446140284 0.0162411135
[26] -0.0498377421 -0.0718731074 -0.0522602723 -0.0077235304 0.0107393320
[31] -0.0102358235 0.0004042219 0.0270751894 0.0157849658 0.0002975933
[36] 0.0311869747 -0.0242724697 0.0060421100
Parameter:
[1] 0.7690591 0.8987569 0.7258847 0.6302810 0.5894872 0.4159115 0.8841621
[8] 0.9431606 0.8423550 0.9064500 1.0436535 0.9199481 0.4855149 0.7007349
[15] 0.5084242 0.8603921 0.5979833 1.0467657 1.0081087 1.0952783 0.4751675
[22] 0.9212189 0.5123886 0.6886107 0.4683320 0.6091009 0.4788544 0.8055267
[29] 0.7453115 0.6019765 0.7433250 0.6863653 0.3142648 0.3474641 0.4144606
[36] 0.2688925 0.4016851 0.6186676
Function Value
[1] 0.9195202
Gradient:
[1] 0.081297056 0.056462380 0.087943498 -0.057828665 -0.007420326
[6] 0.010710000 0.071762191 0.113842329 0.090983200 0.073860601
[11] 0.058090236 0.047822756 -0.172728214 0.124459927 0.177774425
[16] 0.150238961 -0.123069121 0.209344130 0.156865058 0.112225633
[21] 0.054624078 0.247557590 0.063240797 0.139413643 0.008977239
[26] 0.115969243 0.226442488 0.252585451 0.194468758 0.069945187
[31] 0.148911319 -0.176185871 0.029177052 -0.309078970 0.121871459
[36] -0.489883881 0.292018619 0.532590825
iteration = 6
Step:
[1] -0.006458921 0.001811006 -0.007521914 0.024438385 0.012448665
[6] 0.007272535 0.001957588 -0.005709244 -0.003159811 -0.001195174
[11] 0.004286706 0.006036420 0.040099391 -0.040102507 -0.056880692
[16] -0.042834163 0.021145851 -0.051043661 -0.040015911 -0.028399618
[21] 0.009327681 -0.064276824 -0.033391484 -0.044494760 0.007288229
[26] -0.043216117 -0.068933431 -0.068685192 -0.028565062 -0.021319842
[31] -0.026739001 -0.019729118 0.008052155 0.035655642 -0.005796896
[36] 0.026399139 0.026222376 -0.030163850
Parameter:
[1] 0.7626001 0.9005679 0.7183628 0.6547194 0.6019359 0.4231840 0.8861197
[8] 0.9374513 0.8391952 0.9052548 1.0479402 0.9259845 0.5256142 0.6606324
[15] 0.4515435 0.8175580 0.6191291 0.9957221 0.9680928 1.0668787 0.4844952
[22] 0.8569420 0.4789972 0.6441160 0.4756202 0.5658848 0.4099210 0.7368415
[29] 0.7167464 0.5806567 0.7165860 0.6666362 0.3223169 0.3831198 0.4086637
[36] 0.2952917 0.4279075 0.5885038
Function Value
[1] 0.7903282
Gradient:
[1] 0.056127714 -0.020572113 0.070410994 -0.076911416 -0.019142004
[6] 0.004826568 0.066362279 0.086205109 0.077440003 0.057038196
[11] 0.020636691 0.040587405 -0.124718575 0.057426917 0.087051113
[16] 0.105446805 -0.157452277 0.197946729 0.133308244 0.094601464
[21] 0.071479299 0.211397598 -0.030787309 0.070094842 0.018709141
[26] 0.029060978 0.039226528 0.198555728 0.153470889 0.013522122
[31] 0.135976673 -0.224783722 0.025317501 -0.114477078 -0.006267431
[36] -0.560299856 0.498136629 0.493988935
iteration = 7
Step:
[1] -0.013829297 0.010123055 -0.017002273 0.026923873 0.009516180
[6] 0.003760345 -0.011223255 -0.015218775 -0.014794783 -0.012239565
[11] -0.001203570 -0.005522504 0.043625124 -0.025254541 -0.036506589
[16] -0.037968053 0.035939642 -0.062722077 -0.044009187 -0.031874877
[21] 0.007007463 -0.069177024 -0.002561191 -0.030142671 0.003968161
[26] -0.021115906 -0.024265273 -0.068342056 -0.034039028 -0.020668276
[31] -0.042062510 -0.025366145 0.001024544 -0.008318544 0.021368824
[36] 0.045653632 -0.013239951 -0.034409126
Parameter:
[1] 0.7487709 0.9106909 0.7013605 0.6816433 0.6114520 0.4269443 0.8748964
[8] 0.9222326 0.8244004 0.8930152 1.0467366 0.9204620 0.5692394 0.6353778
[15] 0.4150369 0.7795899 0.6550688 0.9330000 0.9240837 1.0350038 0.4915026
[22] 0.7877650 0.4764360 0.6139733 0.4795884 0.5447688 0.3856557 0.6684994
[29] 0.6827074 0.5599884 0.6745235 0.6412701 0.3233415 0.3748012 0.4300325
[36] 0.3409453 0.4146675 0.5540946
Function Value
[1] 0.6894281
Gradient:
[1] 0.021621442 -0.076986776 0.039182844 -0.091143519 -0.032111814
[6] -0.010293466 0.041397332 0.050024962 0.039464680 0.032560948
[11] -0.005775644 0.016070572 -0.066797323 -0.007539093 0.006254236
[16] 0.050396764 -0.117387561 0.177715929 0.105205935 0.076767434
[21] 0.081061732 0.155286422 -0.040767748 0.017624608 0.022148836
[26] -0.030928678 -0.045667509 0.117974718 0.034399619 0.066758211
[31] 0.146345553 -0.245271014 -0.095667893 -0.283463436 0.444348355
[36] -0.206162923 0.212434891 0.309722719
iteration = 8
Step:
[1] -0.0057512730 0.0119276343 -0.0082307399 0.0177739853 0.0067577493
[6] 0.0030918997 -0.0061293369 -0.0075156269 -0.0069671847 -0.0061888609
[11] 0.0010121440 -0.0023509727 0.0204027597 -0.0074631913 -0.0122819284
[16] -0.0169382622 0.0216834805 -0.0365160963 -0.0238417921 -0.0174786875
[21] -0.0005890019 -0.0364849757 0.0021560841 -0.0115086788 0.0005829839
[26] -0.0045477066 -0.0016405760 -0.0329308134 -0.0109333450 -0.0129912247
[31] -0.0289152325 -0.0036667624 0.0114828705 0.0088612757 -0.0266943869
[36] 0.0129190340 -0.0067212512 -0.0127642258
Parameter:
[1] 0.7430196 0.9226186 0.6931298 0.6994172 0.6182098 0.4300362 0.8687671
[8] 0.9147169 0.8174332 0.8868264 1.0477488 0.9181110 0.5896421 0.6279146
[15] 0.4027550 0.7626517 0.6767523 0.8964839 0.9002419 1.0175251 0.4909136
[22] 0.7512800 0.4785921 0.6024646 0.4801713 0.5402211 0.3840151 0.6355686
[29] 0.6717740 0.5469972 0.6456082 0.6376033 0.3348243 0.3836625 0.4033381
[36] 0.3538643 0.4079463 0.5413304
Function Value
[1] 0.6432148
Gradient:
[1] 0.012044360 -0.078008163 0.027408657 -0.109813058 -0.034986524
[6] -0.014009036 0.016281881 0.025506179 0.015825698 0.027589572
[11] 0.005240478 0.009420692 -0.040195207 -0.028625625 0.006812737
[16] 0.023221993 -0.114203559 0.169807109 0.083553196 0.063598872
[21] 0.064827013 0.114797821 -0.051388099 -0.014546995 0.032189394
[26] -0.036511789 -0.021089043 0.070730408 0.061147411 0.062052425
[31] 0.033202380 -0.061524542 -0.032009009 -0.064665507 0.130804221
[36] -0.106850543 0.097350775 0.250591789
iteration = 9
Step:
[1] -0.007744072 0.096355812 -0.023286021 0.150343804 0.058501365
[6] 0.031043047 0.003046649 -0.011498573 -0.001284365 -0.018366539
[11] 0.007038675 0.008995238 0.073771264 -0.009358715 -0.068696859
[16] -0.063150739 0.142277814 -0.223662943 -0.121561284 -0.091762896
[21] -0.038671315 -0.175002141 0.005891144 -0.027629459 -0.024550370
[26] -0.012699986 -0.044399804 -0.132868173 -0.073312202 -0.068049218
[31] -0.060337613 -0.079755210 0.055544571 -0.021127342 -0.047696966
[36] 0.026275782 -0.007383119 -0.105723896
Parameter:
[1] 0.7352755 1.0189744 0.6698438 0.8497610 0.6767112 0.4610793 0.8718137
[8] 0.9032184 0.8161489 0.8684598 1.0547875 0.9271063 0.6634134 0.6185559
[15] 0.3340581 0.6995009 0.8190301 0.6728210 0.7786806 0.9257622 0.4522423
[22] 0.5762779 0.4844832 0.5748352 0.4556210 0.5275212 0.3396153 0.5027004
[29] 0.5984618 0.4789479 0.5852706 0.5578481 0.3903689 0.3625352 0.3556412
[36] 0.3801401 0.4005632 0.4356065
Function Value
[1] 0.5968366
Gradient:
[1] -0.0128772726 -0.0791233450 -0.0209957314 -0.1686150135 -0.0044312536
[6] -0.0026992950 -0.0405664657 0.0090545846 0.0003716387 -0.0214900986
[11] -0.0531408450 -0.0629936956 0.0078764444 -0.1072037001 -0.0620238119
[16] -0.1326929784 -0.0889337457 0.0235429063 -0.1012232183 -0.0350995251
[21] -0.0607984880 -0.2280756100 -0.0402361486 -0.0784814169 -0.0768741089
[26] -0.0865265619 -0.2461858415 -0.2701566082 -0.0621226661 -0.2114172375
[31] 0.0620864604 -0.0267394711 0.1316641480 0.0670192257 0.1040282243
[36] 0.2887802637 0.3471796610 -0.4232142672
iteration = 10
Step:
[1] -0.022005707 -0.007865380 -0.019408536 0.036839450 -0.013986402
[6] -0.011481185 -0.015342800 -0.034326583 -0.026960162 -0.025653638
[11] -0.022759794 -0.011492520 0.014334775 0.034234332 0.018739807
[16] 0.035581058 0.029762582 -0.023608693 0.018766873 0.001301570
[21] 0.018610879 0.053411439 0.026241780 0.027323115 0.024006171
[26] 0.029956784 0.053705248 0.069112370 -0.017312881 0.032086055
[31] -0.009437495 -0.002726046 -0.061177819 -0.001764654 -0.028247422
[36] -0.066624649 -0.074641854 0.019014264
Parameter:
[1] 0.7132698 1.0111090 0.6504353 0.8866005 0.6627248 0.4495981 0.8564709
[8] 0.8688918 0.7891887 0.8428062 1.0320277 0.9156138 0.6777482 0.6527903
[15] 0.3527979 0.7350820 0.8487927 0.6492123 0.7974474 0.9270638 0.4708532
[22] 0.6296893 0.5107250 0.6021583 0.4796271 0.5574779 0.3933206 0.5718128
[29] 0.5811489 0.5110340 0.5758331 0.5551221 0.3291911 0.3607705 0.3273937
[36] 0.3135155 0.3259213 0.4546208
Function Value
[1] 0.5516504
Gradient:
[1] -0.030386946 -0.057580342 -0.036583462 -0.099812954 -0.018507340
[6] -0.007684186 -0.033031547 -0.022787869 -0.016804925 -0.038247737
[11] -0.029080846 -0.026134909 0.040883137 -0.029480677 0.027431586
[16] -0.060908334 0.024575161 0.037965883 -0.032181269 -0.024139805
[21] 0.004794529 -0.087512870 0.009584330 -0.027833927 0.039111757
[26] -0.001140172 0.039462904 -0.048353677 0.007081784 0.250546446
[31] -0.082358714 0.079368988 -0.153823930 0.288453087 -0.053847543
[36] -0.037850956 -0.172890552 0.028519455
iteration = 11
Step:
[1] 0.017774574 0.032731886 0.021517971 0.063059585 0.010513214
[6] 0.004925714 0.024080593 0.010982879 0.009982727 0.027230323
[11] 0.030207577 0.028033648 -0.012591357 0.011245380 -0.018640396
[16] 0.032021651 -0.002190983 -0.017048116 0.023360934 0.012953724
[21] -0.003355154 0.058588262 -0.013077846 0.005745427 -0.010206220
[26] -0.002636359 -0.004586869 0.043499193 0.003321227 -0.068481427
[31] 0.014287718 0.015002429 0.040356654 -0.063962125 -0.022864046
[36] 0.020675551 -0.004295437 0.016784768
Parameter:
[1] 0.7310444 1.0438409 0.6719532 0.9496601 0.6732380 0.4545238 0.8805515
[8] 0.8798747 0.7991714 0.8700365 1.0622352 0.9436474 0.6651568 0.6640356
[15] 0.3341575 0.7671036 0.8466017 0.6321642 0.8208084 0.9400175 0.4674980
[22] 0.6882776 0.4976471 0.6079037 0.4694209 0.5548416 0.3887337 0.6153120
[29] 0.5844702 0.4425526 0.5901208 0.5701245 0.3695478 0.2968084 0.3045297
[36] 0.3341910 0.3216259 0.4714056
Function Value
[1] 0.5345426
Gradient:
[1] -0.0098258361 -0.0245945092 -0.0007855760 -0.1422890357 -0.0049498219
[6] -0.0089545686 0.0213205134 -0.0209065583 -0.0114594094 -0.0061180430
[11] 0.0152530610 0.0242691485 0.0203017692 -0.0041786095 -0.0079519857
[16] -0.0114816565 -0.0454414995 0.0536568585 -0.0415933208 -0.0214833769
[21] -0.0027329961 0.0281757870 -0.0153969282 -0.0010508110 0.0019814976
[26] -0.0005832952 0.0440146266 0.0513002867 0.1036054655 -0.0008627943
[31] -0.0006772609 0.1595010986 0.2424679337 -0.3673942821 -0.0123164234
[36] 0.3013019594 -0.3511010682 0.1294010659
iteration = 12
Step:
[1] 0.020319323 0.052067794 0.018250379 0.113995290 0.022750788
[6] 0.013781788 0.016083595 0.017208351 0.014286905 0.026000993
[11] 0.026979559 0.020246005 -0.007671125 0.002934445 -0.026329459
[16] 0.014457093 0.043643281 -0.057948230 0.012637473 0.003613077
[21] -0.009512231 0.007562697 -0.012876117 -0.004637580 -0.007443723
[26] -0.008835830 -0.016784355 -0.006307516 -0.033277014 -0.033666716
[31] -0.006778072 -0.023567012 -0.022256242 0.033373501 0.001075577
[36] -0.019053648 0.012556964 -0.028285046
Parameter:
[1] 0.7513637 1.0959087 0.6902036 1.0636554 0.6959888 0.4683056 0.8966351
[8] 0.8970830 0.8134583 0.8960375 1.0892148 0.9638934 0.6574857 0.6669701
[15] 0.3078281 0.7815607 0.8902450 0.5742159 0.8334459 0.9436306 0.4579858
[22] 0.6958403 0.4847710 0.6032661 0.4619772 0.5460057 0.3719493 0.6090045
[29] 0.5511931 0.4088859 0.5833428 0.5465575 0.3472915 0.3301819 0.3056053
[36] 0.3151374 0.3341828 0.4431205
Function Value
[1] 0.4969242
Gradient:
[1] 6.352963e-05 -2.728735e-02 8.950561e-03 -1.061811e-01 -5.237400e-03
[6] -4.971941e-03 3.890034e-02 -1.184886e-02 4.028649e-03 1.327081e-04
[11] 1.440398e-02 2.130554e-02 -2.450777e-02 -1.205524e-02 -4.660305e-02
[16] 1.260688e-03 -7.112682e-03 -6.056776e-03 -2.745865e-02 -2.175931e-02
[21] -1.797077e-02 4.247724e-02 -3.658101e-02 -1.038169e-02 -4.294951e-02
[26] -1.530015e-02 -2.723590e-02 4.243937e-02 9.114054e-02 1.245105e-02
[31] 9.949555e-02 1.553227e-01 5.119066e-02 4.888440e-02 -1.820352e-01
[36] -6.305925e-03 1.297107e-01 -1.518773e-01
iteration = 13
Step:
[1] 3.469521e-03 3.325541e-02 3.543623e-05 8.901180e-02 1.202806e-02
[6] 6.774119e-03 -7.085550e-03 1.015150e-03 -1.721034e-03 3.729999e-03
[11] 2.696643e-03 -3.792904e-05 1.062462e-02 8.495598e-03 -2.473505e-03
[16] 6.707840e-03 2.925206e-02 -4.426428e-02 4.243574e-03 -5.901312e-04
[21] 9.493971e-03 -1.204909e-02 5.456832e-03 1.905051e-03 2.112775e-02
[26] 3.000955e-03 -1.970023e-04 -1.375746e-02 -4.044942e-02 -3.801331e-02
[31] -2.144728e-02 -3.097138e-02 -6.430068e-03 6.716382e-03 -1.974405e-03
[36] -1.351957e-02 -2.363962e-02 -1.631444e-02
Parameter:
[1] 0.7548332 1.1291641 0.6902390 1.1526672 0.7080168 0.4750797 0.8895496
[8] 0.8980982 0.8117373 0.8997675 1.0919114 0.9638555 0.6681103 0.6754657
[15] 0.3053546 0.7882686 0.9194970 0.5299517 0.8376894 0.9430405 0.4674798
[22] 0.6837912 0.4902278 0.6051712 0.4831049 0.5490067 0.3717523 0.5952470
[29] 0.5107437 0.3708726 0.5618955 0.5155861 0.3408614 0.3368983 0.3036309
[36] 0.3016178 0.3105432 0.4268061
Function Value
[1] 0.481821
Gradient:
[1] -0.010977551 -0.046048705 -0.003094044 -0.101555859 -0.001382212
[6] -0.002980009 0.015869027 -0.016830171 -0.006166843 -0.011053864
[11] -0.015705973 -0.002714032 -0.033394063 -0.013938774 -0.023865027
[16] -0.001387196 0.001587868 -0.058450127 -0.037582520 -0.028653055
[21] -0.003116817 0.019354918 -0.030213354 -0.012014940 0.014842321
[26] -0.011141719 -0.032876500 0.010548451 -0.104768702 -0.100258497
[31] -0.007646079 0.043281148 0.230211313 0.236250656 -0.121950574
[36] -0.006104557 0.163398276 -0.108495016
iteration = 14
Step:
[1] 8.481934e-03 4.214398e-02 3.847726e-03 1.031407e-01 1.357812e-02
[6] 8.351260e-03 -5.848872e-03 6.955672e-03 2.638854e-03 9.830126e-03
[11] 1.011236e-02 4.155335e-03 1.424515e-02 7.099208e-03 -3.555728e-03
[16] 4.918516e-03 2.351231e-02 -3.269279e-02 9.371850e-03 4.274947e-03
[21] 5.714251e-03 -1.643536e-02 4.680708e-03 1.639931e-05 1.256646e-02
[26] 5.786760e-04 -4.697658e-03 -1.917502e-02 -1.427287e-02 -2.944395e-02
[31] -1.540213e-02 -2.423490e-02 -4.027345e-02 -1.342795e-02 -1.002259e-02
[36] -1.277573e-02 -2.633534e-02 -1.283205e-02
Parameter:
[1] 0.7633152 1.1713081 0.6940868 1.2558079 0.7215949 0.4834310 0.8837007
[8] 0.9050538 0.8143761 0.9095976 1.1020238 0.9680108 0.6823555 0.6825649
[15] 0.3017988 0.7931871 0.9430093 0.4972589 0.8470613 0.9473154 0.4731940
[22] 0.6673558 0.4949086 0.6051876 0.4956714 0.5495854 0.3670547 0.5760720
[29] 0.4964709 0.3414286 0.5464934 0.4913512 0.3005880 0.3234703 0.2936083
[36] 0.2888421 0.2842079 0.4139740
Function Value
[1] 0.4703989
Gradient:
[1] -0.012382337 0.019792018 -0.008332368 -0.064934827 -0.012461516
[6] -0.011075780 -0.003240711 -0.009372005 -0.011254929 -0.011830014
[11] -0.031172277 -0.022462554 -0.005620958 0.001914366 0.018151578
[16] 0.006084182 0.031705984 -0.079434717 -0.020868985 -0.022124699
[21] 0.002056808 -0.014832594 -0.018874900 -0.011042641 0.040706134
[26] -0.013244549 -0.054829417 -0.037073459 0.076784445 0.034419944
[31] -0.065243281 -0.044952973 -0.217677432 0.146383467 0.034695326
[36] 0.207805702 0.095982518 -0.078821490
iteration = 15
Step:
[1] 1.373799e-02 4.536657e-02 7.624513e-03 1.396772e-01 1.872707e-02
[6] 1.196357e-02 -4.226056e-03 1.069995e-02 6.071632e-03 1.690031e-02
[11] 2.146584e-02 1.163214e-02 1.683822e-02 4.909443e-03 -1.448472e-02
[16] 4.626451e-03 2.361678e-02 -2.451780e-02 1.728976e-02 1.063042e-02
[21] -1.924170e-03 -1.387550e-02 7.254594e-03 -6.472931e-04 -4.588508e-03
[26] -7.948656e-05 -1.586336e-03 -1.609506e-02 -3.717702e-02 -4.047996e-02
[31] -4.630043e-03 -1.575755e-02 -1.884660e-02 -2.629726e-02 -1.402811e-02
[36] -5.009295e-02 -4.469314e-02 -1.468233e-02
Parameter:
[1] 0.7770531 1.2166746 0.7017113 1.3954851 0.7403220 0.4953945 0.8794747
[8] 0.9157538 0.8204478 0.9264979 1.1234896 0.9796430 0.6991937 0.6874743
[15] 0.2873141 0.7978135 0.9666261 0.4727411 0.8643510 0.9579458 0.4712699
[22] 0.6534803 0.5021632 0.6045403 0.4910829 0.5495059 0.3654684 0.5599770
[29] 0.4592938 0.3009486 0.5418633 0.4755937 0.2817414 0.2971731 0.2795802
[36] 0.2387491 0.2395147 0.3992917
Function Value
[1] 0.4568537
Gradient:
[1] -1.218212e-02 1.525857e-02 -1.027328e-02 -3.829893e-02 -1.066814e-02
[6] -7.763123e-03 -1.298300e-02 1.663772e-02 -2.478728e-05 2.306841e-03
[11] -8.440971e-03 -2.640293e-02 2.115332e-03 -1.354490e-03 -8.300034e-03
[16] 1.923919e-03 4.267060e-02 -2.532173e-02 -1.090977e-02 -1.647957e-02
[21] 1.168928e-02 -3.791383e-02 1.553889e-02 -7.354981e-03 2.071799e-02
[26] -1.248940e-02 -4.654092e-02 -7.627744e-02 -1.917983e-02 1.449473e-01
[31] 5.387780e-02 -6.339256e-03 1.084176e-02 2.615808e-02 1.704179e-01
[36] -3.370576e-02 -1.345237e-01 -7.911652e-02
iteration = 16
Step:
[1] 0.0086913674 0.0198104313 0.0057432225 0.0858293001 0.0106302133
[6] 0.0067560687 -0.0009181824 0.0012885073 0.0017831401 0.0077067142
[11] 0.0097682970 0.0088567013 0.0057829071 0.0045420306 -0.0060795812
[16] 0.0066110943 0.0096021487 -0.0100945160 0.0161443002 0.0110021808
[21] 0.0010411756 0.0066482751 0.0005668279 0.0028452716 0.0006861977
[26] 0.0023557831 0.0070223413 0.0102519907 -0.0241796464 -0.0419757377
[31] -0.0066500472 -0.0082179018 -0.0205118025 -0.0188244257 -0.0184827309
[36] -0.0152223829 -0.0141020071 -0.0060551169
Parameter:
[1] 0.7857445 1.2364851 0.7074545 1.4813144 0.7509522 0.5021506 0.8785565
[8] 0.9170423 0.8222309 0.9342046 1.1332579 0.9884997 0.7049766 0.6920164
[15] 0.2812345 0.8044246 0.9762283 0.4626466 0.8804953 0.9689480 0.4723110
[22] 0.6601286 0.5027300 0.6073856 0.4917691 0.5518617 0.3724907 0.5702289
[29] 0.4351142 0.2589729 0.5352133 0.4673758 0.2612296 0.2783486 0.2610974
[36] 0.2235267 0.2254127 0.3932366
Function Value
[1] 0.4490497
Gradient:
[1] -0.0129486111 0.0054773565 -0.0107534639 -0.0449094780 -0.0180367365
[6] -0.0127496342 -0.0129309932 0.0164857177 0.0012465051 0.0052564673
[11] 0.0057361166 -0.0171224741 0.0061456760 0.0048563109 -0.0248432919
[16] 0.0080486160 0.0415894341 -0.0632015613 -0.0019526674 -0.0087694900
[21] 0.0153985233 -0.0261339643 0.0184593070 0.0004671215 0.0210587636
[26] -0.0029451215 -0.0116506200 -0.0478355560 -0.0327583614 -0.0641570814
[31] 0.0585816089 0.0103142774 0.1511257679 -0.0409170902 0.0566570115
[36] -0.0023217446 -0.0128417739 -0.0654422045
iteration = 17
Step:
[1] 0.0271841243 0.0239288616 0.0211272989 0.1606458323 0.0291556113
[6] 0.0199363110 0.0054229501 0.0013570859 0.0068986629 0.0156037724
[11] 0.0141465055 0.0223228235 -0.0067453182 0.0021081009 0.0097242754
[16] 0.0068508973 -0.0298363992 0.0446036166 0.0332172398 0.0309844428
[21] 0.0008686627 0.0287637853 -0.0065594667 0.0067230838 -0.0020124489
[26] 0.0054384515 0.0111183172 0.0383407994 -0.0522704345 -0.0514927193
[31] -0.0174291266 -0.0092168523 -0.0537944144 -0.0199743502 -0.0250218418
[36] -0.0269361665 -0.0239854582 -0.0057980444
Parameter:
[1] 0.8129286 1.2604139 0.7285818 1.6419603 0.7801078 0.5220869 0.8839794
[8] 0.9183994 0.8291296 0.9498084 1.1474044 1.0108225 0.6982313 0.6941245
[15] 0.2909588 0.8112755 0.9463919 0.5072502 0.9137126 0.9999325 0.4731797
[22] 0.6888924 0.4961705 0.6141087 0.4897566 0.5573001 0.3836090 0.6085697
[29] 0.3828438 0.2074802 0.5177842 0.4581589 0.2074352 0.2583743 0.2360756
[36] 0.1965906 0.2014273 0.3874385
Function Value
[1] 0.4457614
Gradient:
[1] -0.0179925479 -0.0292971783 -0.0182922690 -0.0028477399 -0.0333925243
[6] -0.0219673382 -0.0063311312 0.0001523297 0.0041719410 0.0157386815
[11] 0.0235647049 0.0161705364 -0.0065518648 0.0144400119 -0.0015340049
[16] 0.0217657181 0.0168438454 0.0536453015 0.0342443833 0.0214134737
[21] 0.0090712895 0.0230253043 -0.0061914243 0.0119393988 0.0135730787
[26] 0.0157119473 0.0361283057 0.0410179481 -0.0571546508 0.1228466004
[31] -0.0123726345 0.0337399797 -0.2619894133 0.0796469273 -0.0168646785
[36] -0.0484523603 0.0567886254 0.0092169223
iteration = 18
Step:
[1] 0.0128782745 0.0238802769 0.0112914025 0.0355756714 0.0195539529
[6] 0.0131540785 0.0110201198 0.0034290727 0.0043979971 0.0013026170
[11] 0.0020814435 0.0064792752 0.0033369413 -0.0054885865 -0.0014267912
[16] -0.0082725061 0.0004791922 -0.0195557023 -0.0105917091 -0.0072865525
[21] -0.0023224749 -0.0065947098 -0.0025385269 -0.0064047211 -0.0032604300
[26] -0.0063341911 -0.0112213611 -0.0070877807 0.0223187760 -0.0095888071
[31] -0.0014839690 -0.0112270222 0.0146300915 0.0045684967 0.0012787287
[36] -0.0002315687 -0.0111828380 -0.0055074034
Parameter:
[1] 0.8258069 1.2842942 0.7398732 1.6775359 0.7996618 0.5352410 0.8949995
[8] 0.9218284 0.8335276 0.9511110 1.1494859 1.0173018 0.7015682 0.6886359
[15] 0.2895320 0.8030030 0.9468711 0.4876945 0.9031209 0.9926459 0.4708572
[22] 0.6822977 0.4936320 0.6077039 0.4864962 0.5509659 0.3723876 0.6014820
[29] 0.4051625 0.1978914 0.5163002 0.4469319 0.2220653 0.2629428 0.2373543
[36] 0.1963590 0.1902444 0.3819311
Function Value
[1] 0.4413681
Gradient:
[1] -0.0014666917 0.0391889651 -0.0044670223 -0.0231926009 -0.0276903336
[6] -0.0191002378 0.0039020520 0.0021505464 0.0046189790 0.0069114350
[11] -0.0010995962 0.0130905067 -0.0032371190 0.0054176255 0.0262835655
[16] 0.0094832018 0.0062577321 0.0002646310 0.0154498494 0.0122852306
[21] -0.0028819009 0.0136832341 -0.0151845860 0.0001033946 -0.0023445956
[26] -0.0041595456 -0.0081547675 0.0264342930 0.0245983927 -0.1470668884
[31] -0.0149765071 0.0077347657 0.1381277706 -0.0144713717 -0.0457865497
[36] 0.0708939574 -0.1043804367 0.0373019091
iteration = 19
Step:
[1] -0.0021541523 -0.0151792801 -0.0001977334 -0.0185529118 0.0117879523
[6] 0.0075352310 -0.0010084897 -0.0048466052 -0.0052270426 -0.0093597600
[11] -0.0048973173 -0.0085306170 0.0066164388 -0.0049787628 -0.0111491485
[16] -0.0104911792 0.0013578487 -0.0194376706 -0.0204172213 -0.0152424069
[21] -0.0012877421 -0.0144272017 0.0058189315 -0.0037307915 0.0020322772
[26] -0.0005302865 0.0034053552 -0.0176264730 0.0062528412 0.0320148237
[31] -0.0031121066 0.0035332834 0.0128013960 -0.0055212187 0.0020812138
[36] 0.0066591697 0.0181449074 -0.0042594795
Parameter:
[1] 0.8236528 1.2691149 0.7396755 1.6589830 0.8114497 0.5427762 0.8939910
[8] 0.9169818 0.8283005 0.9417513 1.1445886 1.0087711 0.7081846 0.6836571
[15] 0.2783829 0.7925118 0.9482289 0.4682568 0.8827037 0.9774035 0.4695695
[22] 0.6678705 0.4994509 0.6039731 0.4885285 0.5504357 0.3757930 0.5838555
[29] 0.4114154 0.2299062 0.5131881 0.4504652 0.2348667 0.2574216 0.2394355
[36] 0.2030182 0.2083893 0.3776716
Function Value
[1] 0.4413355
Gradient:
[1] 0.0007395826 0.0036482169 -0.0016837696 0.0208829470 -0.0130518671
[6] -0.0086969614 -0.0028559342 -0.0029335219 -0.0043238870 -0.0016079724
[11] 0.0033395625 0.0001360938 0.0094557215 -0.0033829934 -0.0374521889
[16] -0.0053072853 0.0146599071 0.0069926926 0.0021622988 0.0002821920
[21] 0.0001346905 -0.0090667776 0.0029821337 -0.0080492484 0.0054036846
[26] -0.0064458483 0.0017916193 -0.0119174288 0.0256112962 0.1050653573
[31] 0.0250671413 -0.0056504774 0.0620314466 -0.0584121267 -0.0781332510
[36] -0.0350174503 0.1006598431 -0.0389834653
iteration = 20
Step:
[1] 0.0071305501 0.0043180112 0.0070167052 0.0332118216 0.0151696370
[6] 0.0102780638 0.0024460894 0.0040079626 0.0036355576 0.0050252107
[11] 0.0061576975 0.0035144124 -0.0012003433 0.0003954155 0.0019022978
[16] 0.0011834393 -0.0058694863 -0.0035999237 0.0019665350 0.0022577402
[21] 0.0007753356 0.0018636973 -0.0001800796 0.0018729200 -0.0015594027
[26] 0.0016293351 0.0008287907 0.0002465925 -0.0132629842 -0.0275063052
[31] -0.0018938907 0.0039170313 -0.0197714249 0.0033419895 0.0059223187
[36] -0.0120118470 -0.0132981391 0.0016872456
Parameter:
[1] 0.8307833 1.2734330 0.7466922 1.6921948 0.8266194 0.5530543 0.8964371
[8] 0.9209898 0.8319361 0.9467765 1.1507463 1.0122856 0.7069843 0.6840525
[15] 0.2802852 0.7936953 0.9423594 0.4646569 0.8846702 0.9796612 0.4703448
[22] 0.6697342 0.4992708 0.6058461 0.4869691 0.5520650 0.3766218 0.5841021
[29] 0.3981524 0.2023999 0.5112942 0.4543822 0.2150952 0.2607635 0.2453579
[36] 0.1910063 0.1950912 0.3793589
Function Value
[1] 0.4387568
Gradient:
[1] 3.124565e-03 -4.603410e-03 -4.663647e-05 -1.769044e-02 -2.091579e-02
[6] -1.358531e-02 -2.566001e-03 -1.307253e-03 -2.056961e-03 8.501825e-03
[11] 2.067038e-02 6.576959e-03 4.366910e-03 -3.690626e-03 -3.759870e-02
[16] -3.305981e-03 6.921045e-03 -1.987697e-02 1.909225e-03 1.748202e-03
[21] -1.481585e-03 -6.353442e-03 2.836725e-03 -3.961336e-03 6.231176e-04
[26] -1.328864e-03 9.075304e-03 -9.907343e-03 -2.837491e-02 -2.070669e-02
[31] 1.117085e-02 1.987550e-02 -3.808793e-02 -1.077005e-04 7.818321e-02
[36] -1.732676e-02 1.501597e-02 -5.411466e-02
iteration = 21
Step:
[1] 0.0029315570 0.0022043056 0.0035853962 0.0356781229 0.0159773268
[6] 0.0106453236 0.0007388001 0.0005718008 0.0012699072 -0.0023534610
[11] -0.0077741383 -0.0019496282 -0.0036157423 0.0019662272 0.0175616441
[16] 0.0028477396 -0.0091232073 0.0121934647 0.0046392306 0.0042334406
[21] 0.0034757491 0.0075597753 0.0014212900 0.0045193421 -0.0002804647
[26] 0.0026044164 -0.0032308335 0.0088584701 -0.0051662772 -0.0104718509
[31] 0.0032173210 -0.0090901054 -0.0067823724 -0.0026571895 -0.0121205716
[36] -0.0020380588 -0.0096289968 0.0017693308
Parameter:
[1] 0.8337149 1.2756373 0.7502776 1.7278730 0.8425967 0.5636996 0.8971759
[8] 0.9215616 0.8332060 0.9444230 1.1429721 1.0103359 0.7033686 0.6860188
[15] 0.2978468 0.7965430 0.9332362 0.4768503 0.8893094 0.9838947 0.4738206
[22] 0.6772940 0.5006921 0.6103654 0.4866886 0.5546694 0.3733910 0.5929605
[29] 0.3929861 0.1919280 0.5145115 0.4452921 0.2083129 0.2581064 0.2332373
[36] 0.1889683 0.1854622 0.3811282
Function Value
[1] 0.4380182
Gradient:
[1] -0.002677410 0.015820541 -0.004076295 -0.011800474 -0.020559813
[6] -0.013948839 0.004395442 0.007260471 0.005729650 0.002391577
[11] -0.007952115 0.004124222 0.004379611 0.006055480 0.033773926
[16] 0.005007379 -0.004424198 0.005612350 0.006556810 0.005994927
[21] 0.005377249 0.007288396 0.003996437 0.005549104 -0.000788031
[26] 0.002922331 -0.009328861 0.006479230 0.010349414 -0.013837020
[31] -0.009363344 -0.029707785 -0.031578320 0.013636818 -0.039034642
[36] 0.029812160 -0.054093423 0.048506131
iteration = 22
Step:
[1] 4.299174e-03 7.968054e-04 4.948210e-03 1.743778e-02 1.650094e-02
[6] 1.105330e-02 2.055034e-03 -2.085436e-04 5.184393e-04 6.187695e-05
[11] 2.392482e-03 6.824486e-04 -1.160896e-03 -2.523704e-03 -4.216485e-03
[16] -2.806233e-03 -7.521396e-04 -3.597325e-03 -4.350762e-03 -3.292531e-03
[21] -2.489904e-03 -2.665096e-03 -2.881826e-03 -2.311176e-03 -3.604125e-04
[26] -1.492042e-03 1.108339e-03 -1.620317e-03 3.344226e-03 1.317267e-03
[31] -4.921057e-03 6.067568e-03 3.491281e-03 -2.131400e-04 5.550719e-03
[36] -4.809220e-04 4.377981e-03 -7.836424e-04
Parameter:
[1] 0.8380140 1.2764341 0.7552258 1.7453107 0.8590976 0.5747529 0.8992310
[8] 0.9213531 0.8337244 0.9444849 1.1453646 1.0110184 0.7022077 0.6834950
[15] 0.2936303 0.7937368 0.9324841 0.4732530 0.8849587 0.9806021 0.4713307
[22] 0.6746289 0.4978103 0.6080542 0.4863282 0.5531774 0.3744993 0.5913402
[29] 0.3963303 0.1932453 0.5095904 0.4513597 0.2118041 0.2578932 0.2387880
[36] 0.1884873 0.1898402 0.3803446
Function Value
[1] 0.4368959
Gradient:
[1] 0.0019918929 0.0115233023 0.0007133103 -0.0049194451 -0.0156358162
[6] -0.0107076019 0.0012079511 -0.0024106903 0.0002703722 0.0049750852
[11] 0.0048492659 0.0074545682 0.0009402825 0.0009410641 0.0129968036
[16] 0.0006507292 -0.0061871610 0.0008631922 0.0024350193 0.0029817819
[21] -0.0024616540 0.0025944118 -0.0045602455 0.0002891483 -0.0012657466
[26] 0.0002421423 -0.0022414923 0.0044055923 -0.0047241109 -0.0197750154
[31] -0.0123805179 -0.0050778937 0.0325462111 -0.0041181778 -0.0146014294
[36] 0.0028889247 0.0047443081 0.0118546950
iteration = 23
Step:
[1] 4.612639e-03 -2.444935e-03 5.778552e-03 3.919378e-02 3.303292e-02
[6] 2.198957e-02 1.692270e-03 1.153861e-03 4.129837e-04 -4.186570e-03
[11] -2.734563e-03 -3.983928e-03 4.240284e-04 -2.025957e-03 -7.664348e-03
[16] -3.400287e-03 1.634410e-03 -9.650549e-03 -7.500758e-03 -5.861392e-03
[21] -5.175729e-04 -4.696738e-03 2.196728e-03 -9.613431e-04 -1.106670e-03
[26] -8.362433e-05 2.233371e-03 -4.175378e-03 -7.855271e-04 -6.783140e-03
[31] -1.431787e-03 7.554327e-04 -5.580758e-03 -1.652871e-03 1.012046e-04
[36] -4.804286e-03 -4.271514e-03 -1.123267e-03
Parameter:
[1] 0.8426267 1.2739891 0.7610043 1.7845045 0.8921306 0.5967425 0.9009232
[8] 0.9225069 0.8341374 0.9402983 1.1426301 1.0070344 0.7026317 0.6814691
[15] 0.2859660 0.7903365 0.9341185 0.4636025 0.8774579 0.9747408 0.4708131
[22] 0.6699321 0.5000070 0.6070929 0.4852215 0.5530937 0.3767327 0.5871649
[29] 0.3955448 0.1864622 0.5081587 0.4521151 0.2062234 0.2562403 0.2388892
[36] 0.1836830 0.1855687 0.3792213
Function Value
[1] 0.436145
Gradient:
[1] 0.0080783273 -0.0030318013 0.0068416917 -0.0050716457 -0.0100725508
[6] -0.0072073618 0.0012906227 0.0001999574 -0.0002624496 0.0018286137
[11] 0.0067363848 0.0031876524 0.0007013377 -0.0029726230 -0.0264777285
[16] -0.0043042547 -0.0052184959 -0.0118464669 -0.0044137103 -0.0021967352
[21] -0.0042349910 -0.0051059672 0.0026188722 -0.0013018315 -0.0029816114
[26] -0.0006779501 0.0057574852 -0.0049963020 -0.0090952312 -0.0104237969
[31] -0.0039830930 -0.0061021623 0.0091029904 -0.0165801843 0.0060162293
[36] 0.0123078117 0.0020106086 -0.0041815689
iteration = 24
Step:
[1] 1.985992e-03 -3.263214e-03 4.217043e-03 5.072023e-02 4.410435e-02
[6] 2.967229e-02 -4.578673e-05 -3.749631e-04 -4.134371e-04 -5.417256e-03
[11] -6.684831e-03 -6.556125e-03 -1.562061e-03 -1.279647e-03 7.442660e-03
[16] -1.072087e-03 -4.078765e-04 4.130426e-04 -3.487005e-03 -2.895538e-03
[21] -1.745918e-04 3.081900e-04 -2.190937e-04 -1.799470e-05 -1.539761e-03
[26] 2.763656e-04 -1.854631e-04 4.073755e-04 1.793572e-03 -1.054603e-02
[31] -1.908542e-03 5.154805e-03 -5.572933e-03 -4.200353e-04 3.308081e-03
[36] -7.635105e-03 -2.664479e-03 6.653214e-04
Parameter:
[1] 0.8446127 1.2707259 0.7652214 1.8352248 0.9362349 0.6264148 0.9008775
[8] 0.9221320 0.8337240 0.9348811 1.1359452 1.0004783 0.7010696 0.6801894
[15] 0.2934086 0.7892644 0.9337106 0.4640155 0.8739709 0.9718452 0.4706385
[22] 0.6702403 0.4997879 0.6070749 0.4836818 0.5533701 0.3765472 0.5875722
[29] 0.3973384 0.1759161 0.5062501 0.4572699 0.2006505 0.2558203 0.2421973
[36] 0.1760479 0.1829042 0.3798866
Function Value
[1] 0.4354876
Gradient:
[1] 0.0083245446 0.0051347897 0.0087210914 -0.0059433531 -0.0048118771
[6] -0.0036537919 -0.0003423608 -0.0024664217 -0.0018515038 0.0014120083
[11] 0.0061771441 0.0019776917 0.0014206165 -0.0022860682 -0.0012934542
[16] -0.0032316407 -0.0074663618 -0.0130843567 -0.0066547301 -0.0045953428
[21] -0.0033505430 -0.0038445123 0.0023650415 -0.0017227713 -0.0053925469
[26] -0.0002873506 0.0015896511 -0.0049827129 0.0010720562 -0.0222706369
[31] 0.0026582754 -0.0120906982 0.0011116974 -0.0074150215 0.0116848859
[36] -0.0617023730 0.0764243353 -0.0142128549
iteration = 25
Step:
[1] -1.123551e-03 -8.521227e-03 1.351053e-03 5.725745e-02 5.453291e-02
[6] 3.732958e-02 1.497043e-03 1.922521e-03 1.824599e-03 -5.953764e-03
[11] -7.772062e-03 -7.574613e-03 -5.027470e-03 -6.241691e-04 4.765880e-03
[16] 6.926696e-05 1.197919e-03 5.760689e-03 -1.739087e-03 -1.903560e-03
[21] 4.111312e-04 1.705737e-03 -1.562931e-03 9.828121e-04 -2.943070e-03
[26] 6.840138e-04 -2.208119e-04 3.266030e-03 1.565152e-03 -7.555196e-03
[31] 2.202499e-03 8.419901e-03 -3.049008e-03 4.341147e-03 4.129171e-03
[36] 1.269439e-03 -3.816627e-03 6.311279e-03
Parameter:
[1] 0.8434891 1.2622047 0.7665724 1.8924822 0.9907678 0.6637444 0.9023745
[8] 0.9240545 0.8355486 0.9289273 1.1281732 0.9929037 0.6960422 0.6795653
[15] 0.2981745 0.7893337 0.9349085 0.4697762 0.8722318 0.9699417 0.4710496
[22] 0.6719461 0.4982250 0.6080577 0.4807387 0.5540541 0.3763264 0.5908383
[29] 0.3989035 0.1683609 0.5084526 0.4656898 0.1976015 0.2601615 0.2463265
[36] 0.1773174 0.1790876 0.3861979
Function Value
[1] 0.435119
Gradient:
[1] 6.444306e-03 -3.762924e-03 9.014574e-03 2.179624e-03 4.273254e-03
[6] 1.155513e-03 1.508759e-03 -1.614996e-03 -7.132392e-04 1.191413e-03
[11] 2.970233e-03 8.750938e-04 -4.823722e-03 -2.049280e-03 3.220315e-03
[16] -1.563091e-03 -8.418862e-03 4.454794e-03 -6.368033e-03 -5.021139e-03
[21] -7.148273e-03 -2.122253e-03 -3.241734e-03 8.249295e-04 -9.800694e-03
[26] 7.912497e-04 8.937135e-04 1.558998e-03 -2.938081e-02 3.321798e-02
[31] -2.006981e-02 4.254321e-03 1.982456e-02 -1.060710e-02 3.847391e-02
[36] 6.011227e-02 -6.147771e-02 7.826628e-06
iteration = 26
Step:
[1] -0.0040354414 -0.0005189615 -0.0050047121 0.0165835251 0.0075490619
[6] 0.0055285801 -0.0024159377 -0.0008470327 -0.0010573268 -0.0018103612
[11] -0.0032361330 -0.0024200735 0.0012771140 0.0012226092 -0.0028500514
[16] 0.0013564127 0.0061442679 0.0013264352 0.0038300085 0.0027988998
[21] 0.0007599268 0.0008693324 0.0009172560 0.0002306731 0.0026805600
[26] 0.0001051569 0.0002009338 -0.0001134109 0.0012680774 -0.0073648829
[31] 0.0018470615 -0.0006460510 -0.0040581626 -0.0012136177 -0.0029601726
[36] -0.0048179662 -0.0031157825 0.0008874215
Parameter:
[1] 0.8394537 1.2616857 0.7615677 1.9090657 0.9983169 0.6692729 0.8999586
[8] 0.9232074 0.8344913 0.9271169 1.1249370 0.9904836 0.6973193 0.6807879
[15] 0.2953245 0.7906901 0.9410528 0.4711026 0.8760618 0.9727406 0.4718096
[22] 0.6728154 0.4991423 0.6082884 0.4834193 0.5541593 0.3765273 0.5907248
[29] 0.4001716 0.1609961 0.5102997 0.4650437 0.1935433 0.2589478 0.2433663
[36] 0.1724994 0.1759718 0.3870853
Function Value
[1] 0.4347439
Gradient:
[1] 6.147566e-03 3.218907e-04 7.905410e-03 -5.678617e-03 2.004438e-03
[6] 8.990497e-05 1.168093e-03 1.488498e-03 1.119744e-03 1.725908e-05
[11] -1.045728e-03 -7.253078e-04 -2.398068e-03 -4.849348e-04 -4.621512e-04
[16] -4.888570e-04 -3.607457e-03 -3.776389e-03 -2.911687e-03 -2.700887e-03
[21] -2.559638e-03 -2.916494e-04 -1.751417e-04 1.072820e-03 -1.237517e-03
[26] 9.634959e-04 -1.805489e-04 4.884839e-04 -5.514607e-03 -4.002314e-02
[31] -1.215664e-02 -8.409600e-03 1.778755e-02 -1.525603e-03 -1.286546e-02
[36] 4.286278e-03 8.918065e-03 2.135548e-02
iteration = 27
Step:
[1] -7.923508e-03 -3.868297e-03 -8.915160e-03 -1.547419e-02 -8.817636e-03
[6] -5.201326e-03 -3.001383e-03 -2.361686e-03 -2.302850e-03 -1.988068e-03
[11] -2.375711e-03 -1.839858e-03 2.078359e-03 1.241776e-03 -3.165837e-04
[16] 1.069475e-03 3.957136e-03 -1.463079e-04 1.756811e-03 1.576175e-03
[21] 1.605250e-04 2.492497e-04 7.125637e-04 -1.578050e-04 -1.153335e-04
[26] -7.805508e-05 6.873989e-04 -3.790689e-04 4.710892e-03 4.892804e-03
[31] 2.893681e-03 -1.062578e-04 2.553251e-03 1.401453e-03 1.227437e-03
[36] 4.918848e-04 1.522506e-03 -1.485955e-04
Parameter:
[1] 0.8315302 1.2578174 0.7526526 1.8935915 0.9894992 0.6640716 0.8969572
[8] 0.9208458 0.8321884 0.9251289 1.1225613 0.9886438 0.6993976 0.6820297
[15] 0.2950079 0.7917596 0.9450099 0.4709563 0.8778186 0.9743167 0.4719701
[22] 0.6730646 0.4998548 0.6081306 0.4833039 0.5540812 0.3772147 0.5903458
[29] 0.4048825 0.1658889 0.5131934 0.4649375 0.1960965 0.2603493 0.2445937
[36] 0.1729913 0.1774943 0.3869367
Function Value
[1] 0.4346761
Gradient:
[1] 0.0027662388 0.0047130113 0.0036772150 -0.0013347539 0.0026470630
[6] 0.0009434800 0.0005618261 0.0020422135 0.0012627623 -0.0019856934
[11] -0.0033688963 -0.0024725502 0.0023092319 0.0008605809 0.0047455799
[16] 0.0002689013 0.0025306797 0.0066311863 0.0006224994 -0.0007362324
[21] 0.0020036168 0.0004643255 0.0032231569 0.0009287042 -0.0004923457
[26] 0.0007551115 0.0013544472 -0.0002395488 0.0110046692 0.0493901915
[31] 0.0057257346 -0.0077191018 -0.0308987289 0.0003374083 -0.0105617985
[36] -0.0386772037 0.0102711475 0.0044960053
iteration = 28
Step:
[1] -2.241307e-03 -5.026246e-04 -2.917064e-03 1.073566e-02 3.673104e-03
[6] 3.150520e-03 -2.627541e-04 -2.172610e-04 -1.052457e-04 4.407155e-04
[11] 7.144826e-04 6.000131e-04 4.966504e-05 4.007260e-04 -4.537450e-04
[16] 5.679773e-04 1.289760e-03 -8.966118e-05 1.195528e-03 1.123133e-03
[21] -1.643652e-04 3.210902e-04 -5.634870e-04 -3.195579e-04 -4.612140e-04
[26] -2.169246e-04 -1.453382e-04 1.784946e-04 2.658817e-04 -2.703155e-03
[31] 6.408957e-04 8.011413e-04 -3.377443e-04 1.048302e-03 1.278835e-03
[36] 5.557139e-04 -4.014666e-04 3.514521e-04
Parameter:
[1] 0.8292889 1.2573148 0.7497355 1.9043272 0.9931723 0.6672221 0.8966944
[8] 0.9206285 0.8320832 0.9255696 1.1232758 0.9892438 0.6994473 0.6824304
[15] 0.2945541 0.7923275 0.9462997 0.4708667 0.8790142 0.9754399 0.4718057
[22] 0.6733857 0.4992913 0.6078110 0.4828427 0.5538643 0.3770694 0.5905243
[29] 0.4051484 0.1631857 0.5138343 0.4657386 0.1957588 0.2613976 0.2458726
[36] 0.1735470 0.1770928 0.3872882
Function Value
[1] 0.4345597
Gradient:
[1] 0.0013922730 0.0036183425 0.0019689708 -0.0032282332 0.0021446915
[6] 0.0006131735 0.0007531895 0.0013297417 0.0008467218 -0.0014511699
[11] -0.0018713017 -0.0016803376 0.0018014426 0.0005556124 0.0033042369
[16] 0.0002115179 0.0024863951 0.0008227659 0.0008795347 0.0001517755
[21] 0.0013158790 0.0005515908 0.0017879955 0.0005706084 -0.0019732624
[26] 0.0004380247 0.0012746284 0.0005794014 -0.0007079137 -0.0009146781
[31] 0.0047644839 -0.0024260345 -0.0042340318 -0.0053017786 0.0005960068
[36] -0.0028218281 0.0074629298 -0.0068671362
iteration = 29
Step:
[1] -2.565662e-03 -2.284492e-03 -3.282269e-03 1.280637e-02 5.374997e-03
[6] 4.614257e-03 -3.859303e-04 -3.909181e-04 -2.133979e-04 5.993083e-04
[11] 7.757243e-04 7.002916e-04 -1.133188e-03 1.149928e-04 -1.411461e-03
[16] 3.096054e-04 -7.043060e-05 -5.739739e-04 1.829936e-04 6.343712e-04
[21] -1.882261e-04 -7.079854e-05 -7.577960e-04 -2.641648e-04 1.249183e-03
[26] -2.308850e-04 -9.467136e-04 -2.317224e-04 2.610992e-03 -1.946170e-03
[31] 6.856615e-04 2.112123e-03 -4.155546e-05 2.002868e-03 1.590993e-03
[36] -3.535781e-04 -8.355614e-04 1.849834e-03
Parameter:
[1] 0.8267232 1.2550303 0.7464532 1.9171336 0.9985473 0.6718364 0.8963085
[8] 0.9202376 0.8318698 0.9261689 1.1240515 0.9899441 0.6983141 0.6825454
[15] 0.2931427 0.7926371 0.9462293 0.4702927 0.8791971 0.9760742 0.4716175
[22] 0.6733149 0.4985335 0.6075468 0.4840919 0.5536334 0.3761227 0.5902926
[29] 0.4077594 0.1612395 0.5145199 0.4678508 0.1957172 0.2634005 0.2474636
[36] 0.1731934 0.1762573 0.3891380
Function Value
[1] 0.4345088
Gradient:
[1] 1.282256e-03 2.951376e-03 1.167070e-03 -3.593769e-03 2.135398e-03
[6] 8.711751e-04 7.203127e-05 5.430678e-05 3.108802e-04 2.187583e-04
[11] -7.267242e-05 -2.794209e-05 -1.983231e-04 5.447731e-05 -2.046228e-03
[16] -4.440892e-06 1.539263e-03 1.562164e-04 5.971508e-04 6.760210e-04
[21] -8.277823e-05 -1.301359e-05 -1.406338e-03 -4.659952e-04 1.622837e-03
[26] -7.715784e-05 -7.653718e-04 3.487735e-04 -4.396664e-03 -1.260445e-02
[31] -4.448300e-03 4.198093e-03 1.054823e-02 8.861782e-04 -1.559489e-03
[36] 5.051067e-03 -6.747754e-03 3.150038e-03
iteration = 30
Step:
[1] -3.590777e-03 -4.098915e-03 -4.115964e-03 8.616972e-03 1.575223e-03
[6] 2.092377e-03 -1.086544e-03 -1.086201e-03 -1.003188e-03 -2.680934e-04
[11] -6.205153e-05 -5.945150e-05 -4.078647e-04 2.316525e-04 4.458170e-05
[16] 4.094844e-04 -4.011882e-04 -9.201845e-04 1.423524e-04 3.889344e-04
[21] -2.161769e-04 2.137140e-04 1.373797e-04 8.935811e-05 2.508972e-05
[26] 1.015326e-05 3.474940e-04 -8.887347e-05 2.823123e-03 -8.488732e-04
[31] 1.599710e-03 1.844153e-04 1.744014e-04 1.365212e-03 1.203701e-03
[36] -1.356842e-05 -2.852732e-04 4.927509e-04
Parameter:
[1] 0.8231324 1.2509314 0.7423373 1.9257505 1.0001226 0.6739288 0.8952220
[8] 0.9191514 0.8308666 0.9259008 1.1239895 0.9898846 0.6979062 0.6827770
[15] 0.2931873 0.7930466 0.9458281 0.4693725 0.8793395 0.9764632 0.4714013
[22] 0.6735286 0.4986709 0.6076362 0.4841170 0.5536436 0.3764702 0.5902037
[29] 0.4105825 0.1603907 0.5161196 0.4680352 0.1958916 0.2647657 0.2486673
[36] 0.1731799 0.1759720 0.3896308
Function Value
[1] 0.4344697
Gradient:
[1] 2.173124e-04 2.594558e-03 -3.873524e-04 -2.665762e-03 1.825274e-03
[6] 9.790462e-04 1.381402e-04 -4.347100e-05 1.817568e-04 -2.883063e-04
[11] 4.586963e-05 -2.872511e-04 1.033023e-04 3.409646e-04 -2.566207e-03
[16] 3.528591e-04 7.604442e-04 -1.839666e-04 5.070611e-04 1.012268e-03
[21] 3.975167e-04 2.325393e-04 -8.258070e-04 -1.804743e-04 1.787907e-03
[26] -5.043077e-05 5.643592e-04 2.729692e-04 -3.501420e-03 -1.292047e-02
[31] -9.761933e-04 4.511485e-03 7.362598e-03 -1.351655e-03 1.822826e-03
[36] 1.084085e-02 -3.961933e-03 -2.806594e-03
iteration = 31
Step:
[1] -4.102826e-03 -6.498223e-03 -4.452396e-03 1.362551e-02 -1.629830e-04
[6] 1.284625e-03 -1.490465e-03 -1.671287e-03 -1.565622e-03 5.066376e-04
[11] 7.868410e-04 9.089370e-04 -8.015905e-04 1.068108e-05 9.253801e-04
[16] 1.772490e-04 -1.251282e-03 -2.878783e-03 -2.028226e-04 -1.179748e-04
[21] -3.486158e-04 -7.211202e-05 3.753518e-04 2.373072e-04 -1.035735e-04
[26] 1.590913e-04 -1.016883e-04 -9.156403e-05 3.577603e-03 -1.061040e-03
[31] 1.458538e-03 -7.945730e-04 2.384197e-05 1.329550e-03 8.358294e-04
[36] -1.071651e-03 -1.293117e-03 -2.689945e-05
Parameter:
[1] 0.8190296 1.2444332 0.7378849 1.9393761 0.9999596 0.6752134 0.8937315
[8] 0.9174801 0.8293009 0.9264074 1.1247763 0.9907936 0.6971047 0.6827877
[15] 0.2941126 0.7932239 0.9445768 0.4664937 0.8791367 0.9763452 0.4710527
[22] 0.6734565 0.4990463 0.6078735 0.4840134 0.5538027 0.3763685 0.5901121
[29] 0.4141601 0.1593296 0.5175782 0.4672406 0.1959155 0.2660952 0.2495031
[36] 0.1721082 0.1746789 0.3896039
Function Value
[1] 0.4344283
Gradient:
[1] -8.281056e-04 1.627550e-03 -1.849539e-03 -1.133937e-03 1.018012e-03
[6] 9.990444e-04 -1.751062e-04 -4.707523e-04 -2.324718e-04 -3.504894e-04
[11] -1.781764e-05 1.286082e-06 5.682281e-04 7.301111e-04 -1.939618e-03
[16] 7.255885e-04 -1.045084e-03 1.154632e-05 -3.284235e-04 6.386678e-04
[21] 9.814336e-04 6.752288e-05 1.202878e-04 1.577085e-04 1.053390e-03
[26] 3.315463e-04 5.414265e-04 2.589182e-04 -3.107772e-03 -2.653167e-03
[31] 2.432483e-03 4.940976e-03 5.538382e-03 -2.566445e-04 2.471271e-03
[36] 2.806448e-03 -5.064567e-03 -6.157386e-03
iteration = 32
Step:
[1] -4.578687e-04 -3.334472e-03 -5.509801e-05 6.558833e-03 -1.166286e-03
[6] -4.064805e-04 -1.704300e-04 -1.358148e-04 -2.553996e-04 9.762754e-04
[11] 1.229598e-03 9.483193e-04 -1.042591e-03 -6.601739e-04 1.104690e-03
[16] -4.909413e-04 -6.393223e-04 -1.263193e-03 7.156751e-05 -3.386338e-04
[21] -2.395451e-04 -8.734288e-06 6.020196e-05 -1.732465e-06 1.803419e-04
[26] -1.553655e-04 -8.899739e-05 -1.429313e-04 1.639880e-03 -4.039784e-04
[31] 4.593595e-04 -9.025859e-04 -1.597830e-04 4.120916e-04 8.953362e-05
[36] -2.344636e-04 -3.592759e-04 -2.289757e-05
Parameter:
[1] 0.8185717 1.2410987 0.7378298 1.9459349 0.9987933 0.6748069 0.8935611
[8] 0.9173443 0.8290455 0.9273837 1.1260059 0.9917419 0.6960621 0.6821275
[15] 0.2952173 0.7927329 0.9439375 0.4652305 0.8792082 0.9760066 0.4708131
[22] 0.6734478 0.4991065 0.6078718 0.4841938 0.5536473 0.3762795 0.5899692
[29] 0.4158000 0.1589256 0.5180375 0.4663380 0.1957557 0.2665073 0.2495926
[36] 0.1718738 0.1743196 0.3895810
Function Value
[1] 0.4344133
Gradient:
[1] -6.032614e-04 1.305978e-03 -1.381217e-03 -1.883403e-05 3.206253e-04
[6] 7.158647e-04 -6.370726e-05 -1.418670e-04 -2.351292e-04 -2.976890e-04
[11] 1.159453e-04 -3.813838e-05 3.240395e-04 5.288427e-04 -8.437127e-04
[16] 7.508696e-04 -1.887653e-03 1.321609e-04 -5.229239e-04 1.659615e-04
[21] 4.322445e-04 3.205258e-05 1.592255e-04 6.976464e-05 8.454997e-04
[26] -1.092992e-04 3.318590e-04 -1.848193e-04 1.423700e-03 2.693312e-03
[31] 2.060357e-03 1.327251e-03 -4.863221e-03 -7.508270e-04 -1.025739e-04
[36] 2.049973e-03 2.747711e-03 -2.631069e-03
iteration = 33
Step:
[1] 3.313904e-04 -2.058575e-03 9.347242e-04 5.932472e-03 -7.312771e-04
[6] -5.957158e-04 -5.961611e-05 -8.984529e-05 -6.130179e-05 7.736926e-04
[11] 8.218759e-04 7.007004e-04 -5.318208e-04 -5.076379e-04 1.026784e-03
[16] -5.903560e-04 7.996074e-04 -1.152024e-03 4.783003e-04 -2.089072e-04
[21] -1.122455e-04 -1.323480e-05 9.852042e-05 8.943820e-05 -1.246620e-04
[26] 1.043843e-04 -2.509263e-05 1.290323e-04 3.944069e-04 -7.790979e-04
[31] -5.268604e-04 -1.282410e-03 -2.942864e-04 -1.802142e-04 -3.441468e-04
[36] -8.916582e-04 -1.007046e-03 -7.270156e-04
Parameter:
[1] 0.8189031 1.2390401 0.7387645 1.9518674 0.9980620 0.6742112 0.8935014
[8] 0.9172544 0.8289842 0.9281574 1.1268278 0.9924426 0.6955302 0.6816199
[15] 0.2962441 0.7921426 0.9447371 0.4640785 0.8796865 0.9757977 0.4707009
[22] 0.6734346 0.4992050 0.6079612 0.4840691 0.5537517 0.3762544 0.5900982
[29] 0.4161944 0.1581465 0.5175107 0.4650556 0.1954614 0.2663271 0.2492485
[36] 0.1709821 0.1733125 0.3888540
Function Value
[1] 0.4344056
Gradient:
[1] -1.960956e-04 5.170479e-04 -5.369110e-04 3.714949e-05 -1.597513e-04
[6] 4.157066e-04 -2.416662e-04 -2.670433e-04 -3.105853e-04 -1.833911e-04
[11] -1.424203e-04 -8.078516e-05 2.327134e-04 2.635048e-04 3.556622e-05
[16] 4.391012e-04 -1.481943e-03 -2.605560e-05 -5.050396e-04 -2.932872e-04
[21] 1.316067e-04 1.521627e-05 2.462315e-04 1.643912e-04 -5.819345e-06
[26] 1.298872e-04 3.445066e-04 1.205080e-05 -3.362572e-04 3.178862e-04
[31] 1.204736e-03 -8.579377e-04 1.738780e-03 2.245848e-04 -4.683187e-05
[36] -2.848395e-03 -1.204832e-04 -2.929212e-04
iteration = 34
Step:
[1] 5.258751e-04 -2.471948e-04 8.942893e-04 -2.365234e-04 -4.113106e-04
[6] -6.711720e-04 3.202179e-04 4.096320e-04 3.806809e-04 3.459339e-04
[11] 2.960737e-04 2.320537e-04 -2.145993e-04 -2.828080e-04 3.170450e-04
[16] -4.080869e-04 9.935045e-04 -1.700699e-05 3.251204e-04 4.559608e-05
[21] 4.109075e-05 -3.481422e-05 -2.510617e-05 -7.321874e-05 -5.606358e-05
[26] -5.731616e-05 -2.313715e-04 -2.631215e-05 -1.069591e-04 7.116384e-05
[31] -3.529622e-04 7.002165e-05 -3.606748e-05 -1.398533e-04 -7.914569e-05
[36] 9.998827e-05 1.099911e-04 -3.662250e-05
Parameter:
[1] 0.8194290 1.2387929 0.7396588 1.9516308 0.9976507 0.6735400 0.8938217
[8] 0.9176641 0.8293649 0.9285034 1.1271239 0.9926746 0.6953156 0.6813371
[15] 0.2965612 0.7917345 0.9457306 0.4640615 0.8800117 0.9758433 0.4707420
[22] 0.6733998 0.4991799 0.6078880 0.4840130 0.5536944 0.3760230 0.5900719
[29] 0.4160874 0.1582177 0.5171577 0.4651256 0.1954253 0.2661872 0.2491693
[36] 0.1710821 0.1734225 0.3888173
Function Value
[1] 0.4344031
Gradient:
[1] -8.281376e-06 2.576363e-04 -5.596235e-05 9.982793e-05 -1.884395e-04
[6] 2.750440e-04 -2.734808e-04 -1.403073e-04 -2.542073e-04 2.113936e-04
[11] 7.318669e-05 1.451106e-04 1.405382e-04 6.910028e-05 2.300453e-04
[16] 1.377884e-04 -4.491909e-04 -3.291589e-05 -1.463114e-04 -2.709619e-04
[21] -1.427267e-04 -6.060574e-05 1.415081e-04 3.982947e-05 -3.502940e-04
[26] 3.687717e-05 -4.412044e-04 -4.821032e-05 4.151701e-04 7.231797e-04
[31] 5.015011e-05 -4.917595e-04 -1.214847e-03 1.091038e-04 -8.718075e-04
[36] -6.972058e-04 1.134438e-03 6.617036e-04
iteration = 35
Step:
[1] 8.642929e-05 -1.692855e-04 2.158609e-04 -5.364672e-04 1.223466e-04
[6] -2.465806e-04 2.104697e-04 1.915280e-04 2.355480e-04 -1.439025e-04
[11] -1.359894e-04 -1.624547e-04 -9.780274e-05 -7.820665e-05 3.289724e-05
[16] -1.459388e-04 4.964764e-04 2.195353e-04 1.621293e-04 1.591516e-04
[21] 3.943685e-05 4.039358e-05 -7.765123e-05 -4.154152e-05 6.621631e-05
[26] -3.902294e-05 1.464218e-04 6.735056e-06 8.602491e-05 4.190433e-05
[31] -1.503443e-04 1.040710e-04 9.697858e-05 2.885871e-05 1.251862e-04
[36] 5.421464e-05 7.908332e-05 9.216761e-06
Parameter:
[1] 0.8195154 1.2386236 0.7398746 1.9510944 0.9977731 0.6732935 0.8940321
[8] 0.9178556 0.8296005 0.9283594 1.1269879 0.9925122 0.6952178 0.6812589
[15] 0.2965940 0.7915886 0.9462271 0.4642810 0.8801738 0.9760024 0.4707814
[22] 0.6734401 0.4991022 0.6078465 0.4840793 0.5536553 0.3761694 0.5900786
[29] 0.4161735 0.1582596 0.5170074 0.4652297 0.1955223 0.2662161 0.2492945
[36] 0.1711363 0.1735016 0.3888266
Function Value
[1] 0.4344025
Gradient:
[1] 8.952128e-05 9.691042e-05 1.267608e-04 3.875566e-05 -1.031992e-04
[6] 2.336975e-04 -1.820872e-04 -1.301075e-04 -1.457039e-04 8.408918e-05
[11] 1.330564e-04 3.155876e-05 1.391598e-05 -3.191047e-05 -8.217427e-06
[16] -1.865530e-05 5.584866e-05 1.471214e-04 4.847678e-05 -1.184972e-04
[21] -2.048779e-04 2.535216e-05 -5.580247e-05 -2.334133e-06 -4.427037e-05
[26] -6.928857e-05 8.701662e-05 -5.428191e-05 -6.244960e-05 1.679723e-04
[31] -1.512603e-04 -6.233947e-04 -4.856204e-05 4.971312e-05 -4.228440e-05
[36] -9.839241e-05 3.097078e-04 7.665228e-04
iteration = 36
Step:
[1] -1.490550e-04 -2.650234e-04 -1.255140e-04 -1.649503e-04 1.287883e-04
[6] -1.687226e-04 1.190268e-04 8.794400e-05 1.125933e-04 -1.373708e-04
[11] -1.814822e-04 -1.138683e-04 -3.665469e-05 -4.767174e-07 3.059545e-05
[16] -3.637185e-05 1.653655e-04 -1.673271e-05 7.149279e-06 9.796486e-05
[21] 6.089971e-05 -1.653646e-05 9.897505e-06 -1.350715e-05 -3.801122e-05
[26] 2.676874e-05 -1.972775e-05 1.507467e-05 1.403260e-04 7.181067e-06
[31] -1.003242e-04 1.658412e-04 3.941562e-05 1.246372e-05 8.656915e-05
[36] -8.970426e-06 2.241394e-05 3.432280e-06
Parameter:
[1] 0.8193664 1.2383586 0.7397491 1.9509294 0.9979018 0.6731247 0.8941512
[8] 0.9179435 0.8297131 0.9282221 1.1268064 0.9923983 0.6951812 0.6812584
[15] 0.2966246 0.7915522 0.9463924 0.4642643 0.8801809 0.9761004 0.4708423
[22] 0.6734236 0.4991121 0.6078329 0.4840412 0.5536821 0.3761497 0.5900937
[29] 0.4163138 0.1582668 0.5169070 0.4653955 0.1955617 0.2662286 0.2493811
[36] 0.1711273 0.1735240 0.3888300
Function Value
[1] 0.4344023
Gradient:
[1] 6.205880e-05 3.000284e-05 1.067306e-04 -3.343241e-05 -5.323741e-05
[6] 2.028777e-04 -1.500950e-04 -1.312976e-04 -1.158327e-04 1.000018e-04
[11] 1.013028e-04 8.387246e-05 2.431477e-05 -1.637446e-05 -4.554579e-05
[16] -5.901413e-05 2.250857e-04 7.633716e-05 6.639667e-05 -2.736300e-05
[21] -9.179857e-05 2.123812e-05 -8.384404e-07 4.384049e-06 -6.212630e-05
[26] 8.672174e-06 -1.110223e-05 5.961454e-06 -9.003642e-05 -4.399681e-05
[31] -3.026912e-06 -3.059242e-05 4.086687e-05 -7.302958e-05 1.958789e-04
[36] 2.557385e-04 -2.533156e-04 1.103970e-04
iteration = 37
Step:
[1] -1.943738e-04 -3.663134e-04 -1.935111e-04 -2.306296e-04 -1.097226e-06
[6] -3.764369e-04 1.900110e-04 1.456415e-04 1.587968e-04 -1.718624e-04
[11] -1.917180e-04 -1.461795e-04 -8.072940e-05 -1.239211e-05 5.221009e-05
[16] -1.055525e-05 -3.164101e-05 -4.729226e-05 -3.049134e-05 9.925767e-05
[21] 7.512457e-05 -2.504078e-05 -4.986286e-06 -1.642718e-05 2.833180e-06
[26] 3.442713e-06 1.769387e-05 -9.322924e-07 1.993549e-04 4.862430e-05
[31] -1.178273e-04 1.372791e-04 7.618334e-05 3.298395e-05 9.666301e-05
[36] -1.259146e-06 4.754348e-05 -2.928976e-06
Parameter:
[1] 0.8191720 1.2379923 0.7395556 1.9506988 0.9979007 0.6727483 0.8943412
[8] 0.9180892 0.8298719 0.9280502 1.1266147 0.9922521 0.6951005 0.6812460
[15] 0.2966769 0.7915416 0.9463608 0.4642170 0.8801505 0.9761996 0.4709175
[22] 0.6733986 0.4991071 0.6078165 0.4840441 0.5536855 0.3761674 0.5900928
[29] 0.4165131 0.1583154 0.5167892 0.4655328 0.1956379 0.2662616 0.2494778
[36] 0.1711261 0.1735716 0.3888271
Function Value
[1] 0.4344021
Gradient:
[1] 2.689404e-05 -5.876076e-05 6.297540e-05 -4.189426e-05 -1.452349e-05
[6] 1.427019e-04 -6.449241e-05 -8.081358e-05 -4.786216e-05 2.885514e-05
[11] 4.423648e-05 6.420109e-05 -1.167422e-05 -1.113420e-05 -5.666578e-05
[16] -5.893597e-05 2.001315e-04 2.604850e-05 4.052936e-05 5.555734e-05
[21] 2.846434e-05 2.139799e-05 2.233591e-05 5.115908e-06 4.452261e-05
[26] 1.382006e-05 1.000444e-05 9.887202e-06 -1.444995e-04 -4.567724e-05
[31] 1.667608e-04 2.169429e-04 2.291571e-04 3.063150e-05 1.664766e-04
[36] 1.214602e-04 -2.187512e-04 -3.033200e-04
iteration = 38
Step:
[1] -7.558392e-05 -1.425540e-04 -9.764426e-05 -7.578726e-05 -6.740682e-05
[6] -3.420711e-04 1.457260e-04 1.183975e-04 1.138305e-04 -7.535135e-05
[11] -8.126283e-05 -7.676874e-05 -3.911010e-05 -9.152434e-06 3.244557e-05
[16] 1.678501e-05 -1.393417e-04 -6.193442e-05 -3.198209e-05 2.413704e-05
[21] 4.175038e-05 -2.440679e-05 -1.526624e-05 -9.537712e-06 -1.182847e-06
[26] 2.375261e-06 1.334511e-05 8.058763e-06 7.512988e-05 1.681175e-05
[31] -1.274664e-04 3.556215e-05 1.483136e-05 -2.778709e-05 1.450461e-05
[36] -2.508407e-05 2.196059e-06 -3.873809e-05
Parameter:
[1] 0.8190964 1.2378498 0.7394580 1.9506230 0.9978333 0.6724062 0.8944869
[8] 0.9182076 0.8299857 0.9279749 1.1265334 0.9921754 0.6950614 0.6812369
[15] 0.2967093 0.7915584 0.9462214 0.4641551 0.8801185 0.9762238 0.4709592
[22] 0.6733742 0.4990919 0.6078070 0.4840429 0.5536879 0.3761808 0.5901008
[29] 0.4165883 0.1583322 0.5166617 0.4655684 0.1956528 0.2662338 0.2494923
[36] 0.1711010 0.1735738 0.3887883
Function Value
[1] 0.4344021
Gradient:
[1] 1.254463e-05 -4.040196e-05 3.110756e-05 -4.923763e-05 -1.652722e-05
[6] 7.355183e-05 -9.148238e-06 -4.857625e-05 -1.431033e-05 -7.254641e-06
[11] 2.241313e-05 3.874234e-05 -2.309264e-05 -4.781953e-06 9.574563e-06
[16] -2.595257e-05 6.228618e-05 -2.762945e-05 4.611422e-06 6.341239e-05
[21] 6.079759e-05 5.993428e-06 -2.369660e-06 2.120970e-06 8.570566e-05
[26] 1.809397e-05 4.104450e-05 2.151168e-05 2.814815e-05 -6.010481e-05
[31] 1.634177e-04 2.801563e-04 -5.410783e-06 -3.907630e-05 8.255086e-05
[36] 1.509548e-04 -2.710649e-04 -3.688641e-04
iteration = 39
Step:
[1] 6.822845e-06 3.106039e-05 -1.414212e-05 2.185601e-05 -2.917649e-05
[6] -1.670769e-04 6.633797e-05 7.739846e-05 5.596609e-05 2.786853e-06
[11] -8.147212e-06 -2.078172e-05 2.342145e-06 1.986159e-06 -9.001184e-06
[16] 2.121979e-05 -7.608090e-05 -1.922935e-05 -4.808242e-06 -1.910372e-05
[21] 1.797976e-05 -5.881102e-06 3.108571e-06 -6.414919e-07 -2.258024e-06
[26] -3.594406e-06 -1.287745e-05 2.636918e-07 -2.209474e-05 9.410281e-06
[31] -6.134567e-05 -1.584342e-05 2.425754e-06 -1.839625e-05 -1.410291e-05
[36] -9.365332e-06 5.191379e-06 -2.283468e-05
Parameter:
[1] 0.8191032 1.2378808 0.7394438 1.9506449 0.9978042 0.6722391 0.8945532
[8] 0.9182850 0.8300417 0.9279777 1.1265253 0.9921546 0.6950637 0.6812388
[15] 0.2967003 0.7915796 0.9461454 0.4641358 0.8801137 0.9762047 0.4709772
[22] 0.6733683 0.4990950 0.6078063 0.4840406 0.5536843 0.3761679 0.5901011
[29] 0.4165662 0.1583416 0.5166004 0.4655525 0.1956552 0.2662154 0.2494782
[36] 0.1710916 0.1735790 0.3887655
Function Value
[1] 0.434402
Gradient:
[1] 7.084111e-06 -4.779405e-05 1.416822e-05 -1.797807e-05 -1.605827e-05
[6] 3.869260e-05 8.657963e-06 5.329071e-06 4.181544e-06 -1.009681e-05
[11] -1.648119e-05 8.164136e-06 -3.370459e-05 -8.938628e-06 6.998846e-07
[16] -5.279333e-06 -1.601208e-05 -3.035794e-05 -2.739142e-06 3.422329e-05
[21] 6.377476e-05 6.821210e-06 1.820055e-05 1.733724e-06 7.084111e-05
[26] 6.725287e-06 -3.299405e-05 6.203038e-06 -3.971934e-05 -8.203571e-05
[31] 1.097398e-04 1.064500e-04 1.294644e-04 7.289103e-05 -7.764811e-05
[36] -5.754686e-05 5.848833e-05 -2.113474e-04
iteration = 40
Step:
[1] 2.127376e-05 7.663880e-05 7.140795e-06 1.058051e-04 3.630663e-05
[6] -4.644012e-05 2.072591e-05 2.387940e-05 1.904666e-05 1.327697e-05
[11] 1.694491e-05 -1.727294e-06 2.321013e-05 6.365194e-06 -1.242975e-05
[16] 1.198268e-05 -1.553123e-05 -6.789864e-06 4.482341e-07 -2.607315e-05
[21] -5.584360e-06 -4.850297e-06 -1.068356e-05 -8.761060e-07 -8.233047e-06
[26] -4.782327e-06 1.117287e-05 1.468846e-06 -3.652075e-05 -1.673510e-05
[31] -3.486644e-05 -1.673166e-05 -2.234283e-05 -2.491605e-05 -1.877614e-05
[36] -1.642599e-05 -1.626782e-05 -1.566167e-05
Parameter:
[1] 0.8191245 1.2379575 0.7394510 1.9507507 0.9978405 0.6721927 0.8945740
[8] 0.9183089 0.8300607 0.9279909 1.1265422 0.9921529 0.6950869 0.6812452
[15] 0.2966879 0.7915916 0.9461298 0.4641291 0.8801141 0.9761786 0.4709716
[22] 0.6733634 0.4990843 0.6078055 0.4840324 0.5536795 0.3761791 0.5901026
[29] 0.4165296 0.1583249 0.5165655 0.4655358 0.1956328 0.2661905 0.2494594
[36] 0.1710752 0.1735627 0.3887498
Function Value
[1] 0.434402
Gradient:
[1] 3.826273e-06 -4.982006e-06 3.382183e-06 -1.291962e-05 -1.823963e-05
[6] 1.834266e-05 8.476775e-06 5.389467e-06 5.066170e-06 -6.391332e-06
[11] 7.846268e-06 -5.659473e-06 -1.319478e-05 -5.886847e-06 2.649614e-05
[16] 3.254286e-06 -3.464606e-05 -2.166445e-05 -2.479794e-06 4.014566e-06
[21] 2.345502e-05 -3.218759e-06 -1.408651e-05 -1.840306e-06 4.190071e-05
[26] -4.426681e-06 1.322320e-05 2.135181e-06 3.057465e-05 -4.769163e-05
[31] 2.383516e-05 5.910294e-05 -1.974243e-05 1.057288e-05 -6.532019e-05
[36] 1.966072e-05 -2.298961e-05 -8.380852e-05
iteration = 41
Step:
[1] 7.238481e-06 3.988897e-05 2.937180e-06 8.881149e-05 5.532473e-05
[6] 6.690087e-06 -1.133120e-06 4.046202e-06 1.472445e-06 8.635007e-06
[11] 1.790370e-06 2.198822e-06 1.438357e-05 7.429172e-06 -1.496593e-05
[16] 5.180355e-06 2.018375e-05 6.331739e-06 4.188802e-06 -1.046967e-05
[21] -3.792049e-06 3.022968e-06 3.930628e-06 1.357929e-06 -6.718888e-06
[26] 1.519648e-06 -2.865842e-06 1.376197e-06 -1.629591e-05 -1.103175e-05
[31] -2.300627e-06 -3.580610e-06 -8.272686e-06 -2.391533e-06 -9.443627e-07
[36] -5.123355e-06 -4.304288e-06 1.538556e-06
Parameter:
[1] 0.8191317 1.2379973 0.7394539 1.9508395 0.9978958 0.6721994 0.8945728
[8] 0.9183129 0.8300622 0.9279996 1.1265440 0.9921551 0.6951013 0.6812526
[15] 0.2966729 0.7915968 0.9461500 0.4641354 0.8801183 0.9761681 0.4709678
[22] 0.6733665 0.4990882 0.6078068 0.4840257 0.5536811 0.3761762 0.5901039
[29] 0.4165134 0.1583139 0.5165632 0.4655322 0.1956246 0.2661881 0.2494584
[36] 0.1710701 0.1735584 0.3887514
Function Value
[1] 0.434402
Gradient:
[1] 2.277289e-06 -1.325814e-06 -5.009326e-07 -1.642651e-06 -1.247003e-05
[6] 1.332978e-05 4.540368e-06 1.088196e-05 4.916956e-06 1.772804e-06
[11] -7.789490e-07 -6.892265e-06 -5.044853e-06 -2.600586e-06 4.710898e-06
[16] 2.810197e-06 -1.726264e-05 -3.549161e-06 3.051781e-06 -7.890577e-06
[21] 9.201528e-06 5.400125e-07 -4.170886e-06 -6.927792e-07 1.610445e-05
[26] -9.912071e-07 -6.767920e-06 1.744382e-06 4.853007e-06 -1.978862e-05
[31] -4.089173e-06 -1.303846e-06 1.723066e-06 3.872458e-06 -2.799538e-05
[36] 9.947598e-07 1.361755e-05 -1.466560e-05
iteration = 42
Step:
[1] -4.792987e-06 7.519530e-06 -4.123300e-06 5.007931e-05 4.120663e-05
[6] 4.591631e-06 -3.538245e-06 -5.520446e-06 -2.737250e-06 -2.281168e-06
[11] -3.109722e-06 5.119904e-07 6.228938e-06 3.811295e-06 -4.542155e-06
[16] 4.492285e-07 1.897947e-05 1.206863e-06 -9.832568e-07 1.043092e-06
[21] -3.424127e-06 1.211612e-07 1.801796e-06 3.858596e-07 -5.607388e-06
[26] -5.655744e-08 2.635902e-06 -1.195258e-06 -5.788872e-08 -6.500891e-06
[31] 5.677492e-06 5.250995e-06 -3.142621e-06 3.336652e-06 4.080989e-06
[36] -2.138609e-06 -2.076212e-06 5.538626e-06
Parameter:
[1] 0.8191269 1.2380049 0.7394498 1.9508896 0.9979370 0.6722040 0.8945693
[8] 0.9183074 0.8300594 0.9279973 1.1265409 0.9921556 0.6951075 0.6812565
[15] 0.2966684 0.7915972 0.9461690 0.4641366 0.8801173 0.9761692 0.4709644
[22] 0.6733666 0.4990900 0.6078072 0.4840201 0.5536810 0.3761788 0.5901028
[29] 0.4165133 0.1583074 0.5165689 0.4655375 0.1956214 0.2661914 0.2494625
[36] 0.1710679 0.1735563 0.3887569
Function Value
[1] 0.434402
Gradient:
[1] -1.197265e-06 1.127796e-06 -3.321787e-06 1.187340e-06 -7.045031e-06
[6] 1.087486e-05 3.769429e-06 7.528200e-06 5.091039e-06 1.879386e-06
[11] 1.848038e-06 -3.254286e-06 1.548983e-06 1.598721e-07 -1.278977e-07
[16] 5.471179e-07 3.481659e-07 3.236522e-06 2.945200e-06 -7.585044e-06
[21] 1.435296e-06 9.237056e-08 -1.286082e-06 -4.511946e-07 2.664535e-07
[26] -1.659117e-06 4.796163e-07 -2.806644e-07 -1.115552e-06 2.422951e-06
[31] -9.354295e-06 -3.925749e-06 4.725109e-07 1.428191e-06 -4.835243e-06
[36] -1.172396e-07 3.666401e-06 -1.811884e-07
iteration = 43
Step:
[1] -3.682144e-06 -3.460764e-06 -2.142703e-06 1.061705e-05 1.518893e-05
[6] -8.993584e-06 -3.573180e-06 -6.274705e-06 -4.090105e-06 -3.355249e-06
[11] -4.390662e-06 -5.384338e-08 1.845322e-07 1.128702e-06 -5.694056e-07
[16] -1.028786e-07 5.046792e-06 -3.750218e-07 -1.993229e-06 4.674201e-06
[21] -1.893552e-06 1.427617e-07 1.490267e-06 5.249937e-07 -1.717844e-06
[26] 1.394112e-06 5.849922e-07 -1.119459e-07 3.245296e-06 -1.119520e-06
[31] 5.289021e-06 3.640130e-06 1.465042e-07 2.567725e-06 3.213265e-06
[36] 2.084293e-07 2.284269e-07 4.097673e-06
Parameter:
[1] 0.8191233 1.2380014 0.7394476 1.9509002 0.9979522 0.6721950 0.8945657
[8] 0.9183011 0.8300554 0.9279939 1.1265365 0.9921555 0.6951077 0.6812576
[15] 0.2966678 0.7915971 0.9461740 0.4641362 0.8801153 0.9761738 0.4709625
[22] 0.6733667 0.4990915 0.6078077 0.4840184 0.5536824 0.3761794 0.5901026
[29] 0.4165165 0.1583063 0.5165742 0.4655411 0.1956216 0.2661940 0.2494657
[36] 0.1710681 0.1735565 0.3887610
Function Value
[1] 0.434402
Gradient:
[1] -2.142286e-06 4.304576e-07 -3.169021e-06 1.516946e-06 -4.170886e-06
[6] 8.199663e-06 3.709033e-06 3.865352e-06 4.149570e-06 1.090683e-06
[11] -7.411102e-07 2.486900e-08 2.582823e-06 1.747935e-06 -2.859935e-06
[16] 2.060574e-07 5.190515e-06 4.593659e-06 1.421085e-06 -3.542056e-06
[21] -7.958079e-07 1.882938e-07 9.308110e-07 1.350031e-07 -3.659295e-06
[26] 1.136868e-06 1.989520e-07 1.669775e-07 -4.476419e-07 1.104183e-05
[31] -8.569145e-06 -7.005951e-06 -4.543921e-06 -6.881606e-06 1.152856e-05
[36] 9.414691e-07 -2.170708e-06 6.100009e-06
iteration = 44
Step:
[1] -1.566398e-06 -3.456871e-06 2.744917e-07 -3.732022e-06 7.933713e-06
[6] -1.920643e-05 -5.543743e-06 -7.666083e-06 -6.278767e-06 -3.074008e-06
[11] -2.477518e-06 7.041784e-08 -9.699219e-07 -2.331052e-07 1.023491e-06
[16] -4.793396e-07 1.672739e-08 -1.828523e-06 -2.672344e-06 5.656679e-06
[21] -2.340685e-06 -2.015256e-07 1.092432e-06 5.278756e-07 -1.525938e-06
[26] 1.497444e-07 6.936277e-07 -5.711251e-07 2.228667e-06 9.904173e-07
[31] 7.632983e-06 2.935248e-06 1.090348e-06 3.020762e-06 1.792877e-06
[36] 1.556480e-06 1.082705e-06 4.463735e-06
Parameter:
[1] 0.8191217 1.2379979 0.7394479 1.9508964 0.9979601 0.6721758 0.8945602
[8] 0.9182934 0.8300491 0.9279909 1.1265340 0.9921556 0.6951067 0.6812574
[15] 0.2966688 0.7915967 0.9461740 0.4641344 0.8801127 0.9761795 0.4709601
[22] 0.6733665 0.4990926 0.6078083 0.4840168 0.5536825 0.3761801 0.5901021
[29] 0.4165188 0.1583072 0.5165818 0.4655440 0.1956227 0.2661970 0.2494675
[36] 0.1710697 0.1735576 0.3887655
Function Value
[1] 0.434402
Gradient:
[1] -2.625455e-06 -1.033101e-07 -2.067679e-06 7.393533e-07 -1.438849e-06
[6] 4.295231e-06 3.378631e-06 7.034373e-07 2.646772e-06 -8.739676e-07
[11] -9.461002e-07 2.341238e-06 2.192024e-06 1.826095e-06 -1.808331e-06
[16] 6.750156e-08 5.375256e-06 2.433609e-06 -8.917311e-07 1.161737e-06
[21] -2.842171e-06 -5.684342e-07 2.160050e-06 1.847411e-07 -7.400303e-06
[26] 8.313350e-07 1.989520e-06 -5.684342e-07 -2.451372e-07 9.261925e-06
[31] -6.100009e-06 -6.384226e-06 -3.183231e-06 -4.021672e-06 1.044143e-05
[36] -3.414158e-06 -4.689582e-07 1.042721e-05
iteration = 45
Step:
[1] 2.047473e-06 -1.919215e-07 2.541311e-06 -1.153757e-05 -1.570551e-06
[6] -1.557974e-05 -5.100983e-06 -4.718085e-06 -4.999733e-06 -1.317495e-07
[11] 9.474451e-08 -3.021984e-07 -1.034762e-06 -8.904351e-07 9.297055e-07
[16] -3.667656e-07 -3.616112e-06 -1.030947e-06 -7.476273e-07 2.071323e-06
[21] -1.333741e-06 3.401213e-07 -8.111094e-08 4.369343e-07 6.194171e-07
[26] 1.555822e-07 -4.857711e-07 1.547817e-07 -6.539235e-07 1.724015e-06
[31] 4.530180e-06 -1.708187e-08 7.450466e-07 7.191504e-07 -4.740831e-07
[36] 1.515549e-06 8.664714e-07 1.781017e-06
Parameter:
[1] 0.8191237 1.2379978 0.7394505 1.9508849 0.9979586 0.6721602 0.8945551
[8] 0.9182887 0.8300441 0.9279907 1.1265341 0.9921553 0.6951057 0.6812565
[15] 0.2966697 0.7915963 0.9461704 0.4641334 0.8801119 0.9761816 0.4709588
[22] 0.6733669 0.4990925 0.6078087 0.4840174 0.5536827 0.3761796 0.5901022
[29] 0.4165181 0.1583090 0.5165864 0.4655440 0.1956234 0.2661977 0.2494670
[36] 0.1710712 0.1735585 0.3887672
Function Value
[1] 0.434402
Gradient:
[1] -1.733724e-06 -5.222900e-07 -6.501466e-07 -1.365809e-07 -3.907985e-07
[6] 1.524114e-06 1.879386e-06 -9.059420e-07 8.064660e-07 -1.008971e-06
[11] -1.479070e-06 2.010836e-06 1.001865e-06 1.094236e-06 -8.064660e-07
[16] 2.096101e-07 2.106759e-06 2.557954e-07 -1.353584e-06 2.621903e-06
[21] -3.179679e-06 -7.425172e-07 1.186606e-06 1.847411e-07 -5.755396e-06
[26] 1.104894e-06 5.258016e-07 -4.760636e-07 4.192202e-07 3.304024e-06
[31] -5.279333e-06 -7.691625e-06 -2.362555e-06 -4.405365e-06 7.368328e-06
[36] -2.575717e-06 8.917311e-07 1.324807e-05
iteration = 46
Step:
[1] 2.574458e-06 1.692021e-06 2.094599e-06 -6.329007e-06 -2.259945e-06
[6] -6.597494e-06 -2.761926e-06 -1.104084e-06 -2.105507e-06 1.121037e-06
[11] 1.537651e-06 -3.562350e-07 -3.440562e-07 -8.113065e-07 4.031425e-07
[16] -2.912993e-07 -2.420088e-06 -3.430489e-07 4.411000e-07 -7.525741e-07
[21] -3.382319e-07 4.601947e-07 -4.781188e-07 6.497313e-08 7.532794e-07
[26] -6.008906e-07 -4.157780e-07 2.202896e-07 -1.481228e-06 8.610455e-07
[31] 1.804509e-06 -8.070818e-07 1.479095e-07 1.087160e-08 -1.104194e-06
[36] 7.338906e-07 2.377060e-07 7.653362e-08
Parameter:
[1] 0.8191263 1.2379994 0.7394525 1.9508786 0.9979563 0.6721536 0.8945523
[8] 0.9182876 0.8300420 0.9279918 1.1265356 0.9921549 0.6951054 0.6812556
[15] 0.2966701 0.7915960 0.9461680 0.4641330 0.8801123 0.9761808 0.4709585
[22] 0.6733673 0.4990921 0.6078088 0.4840182 0.5536821 0.3761792 0.5901024
[29] 0.4165166 0.1583098 0.5165882 0.4655432 0.1956236 0.2661977 0.2494659
[36] 0.1710719 0.1735587 0.3887673
Function Value
[1] 0.434402
Gradient:
[1] -7.851497e-07 -3.587152e-07 -1.065814e-08 -5.718204e-07 -1.598721e-07
[6] 3.659295e-07 6.394885e-07 -4.547474e-07 -3.197442e-08 -6.501466e-07
[11] -4.478201e-07 6.643575e-07 2.060574e-07 8.881784e-08 1.172396e-07
[16] 6.039613e-08 -1.740830e-07 -8.917311e-07 -7.496226e-07 1.605827e-06
[21] -2.550848e-06 -5.506706e-07 2.877698e-07 -4.263256e-08 -3.932854e-06
[26] -9.237056e-08 2.060574e-07 -3.161915e-07 6.394885e-08 -1.836753e-06
[31] -3.627321e-06 -5.183409e-06 4.192202e-07 -4.938272e-07 7.212009e-07
[36] -2.369660e-06 2.355449e-06 9.645618e-06
iteration = 47
Step:
[1] -2.831318e-06 -5.052940e-06 -3.014650e-06 -1.059774e-04 -3.778390e-05
[6] -3.013387e-05 -3.647302e-06 -2.534391e-06 -2.607754e-06 -1.598580e-06
[11] -1.776620e-06 -1.853362e-06 -9.011706e-07 -1.891887e-07 -4.719144e-08
[16] -3.380640e-07 -4.785029e-06 8.567382e-06 -1.427185e-06 2.649818e-06
[21] 1.740776e-06 7.601643e-07 -9.208099e-08 -1.274066e-07 2.914619e-06
[26] 3.083642e-07 1.856616e-07 -7.747531e-07 1.160355e-05 1.982220e-05
[31] 1.215288e-05 1.032141e-05 1.602983e-05 1.064372e-05 9.627978e-06
[36] 1.610383e-05 1.594195e-05 9.716194e-06
Parameter:
[1] 0.8191235 1.2379944 0.7394495 1.9507726 0.9979185 0.6721235 0.8945487
[8] 0.9182851 0.8300394 0.9279902 1.1265339 0.9921531 0.6951045 0.6812555
[15] 0.2966701 0.7915957 0.9461632 0.4641416 0.8801109 0.9761835 0.4709602
[22] 0.6733681 0.4990920 0.6078086 0.4840211 0.5536824 0.3761794 0.5901017
[29] 0.4165282 0.1583297 0.5166003 0.4655535 0.1956396 0.2662084 0.2494756
[36] 0.1710880 0.1735747 0.3887770
Function Value
[1] 0.434402
Gradient:
[1] 3.334932e-07 1.436273e-06 1.521627e-07 3.485453e-06 2.119283e-06
[6] 5.368683e-07 1.238298e-07 6.840750e-08 -1.126566e-07 -1.213252e-07
[11] 1.539952e-06 6.014034e-07 -1.488480e-06 -1.292992e-06 -6.970780e-07
[16] -1.065477e-06 -4.064837e-07 5.582734e-06 -2.048317e-07 4.738041e-06
[21] 3.803873e-06 -3.604228e-07 -2.619771e-07 -1.001990e-06 5.176961e-06
[26] 2.018830e-07 6.735945e-08 -2.382894e-06 1.081606e-06 2.401132e-05
[31] 4.351666e-06 5.851639e-06 -3.525589e-06 7.426770e-07 -5.531398e-06
[36] 3.519141e-07 -2.053682e-06 -1.810186e-05
iteration = 48
Step:
[1] -2.118595e-06 -3.592084e-06 -1.855933e-06 -1.523729e-05 -7.199977e-06
[6] -5.577775e-06 -8.779495e-07 -1.082753e-06 -7.988149e-07 -9.821659e-07
[11] -1.833556e-06 -1.173786e-06 2.887816e-07 7.564088e-07 5.103014e-07
[16] 5.277807e-07 1.384689e-07 -7.545013e-08 -9.728782e-08 -1.768062e-06
[21] -3.468388e-07 1.302562e-07 4.650969e-07 5.774091e-07 -1.514119e-07
[26] 6.715157e-08 9.373391e-08 7.528135e-07 2.262343e-06 1.707758e-06
[31] 2.345920e-06 2.339573e-06 1.670455e-06 1.737014e-06 1.945235e-06
[36] 1.644669e-06 1.720923e-06 2.265488e-06
Parameter:
[1] 0.8191214 1.2379908 0.7394477 1.9507574 0.9979113 0.6721179 0.8945478
[8] 0.9182840 0.8300386 0.9279893 1.1265320 0.9921519 0.6951047 0.6812562
[15] 0.2966706 0.7915962 0.9461634 0.4641415 0.8801108 0.9761817 0.4709599
[22] 0.6733682 0.4990924 0.6078092 0.4840210 0.5536825 0.3761795 0.5901024
[29] 0.4165305 0.1583314 0.5166027 0.4655559 0.1956413 0.2662101 0.2494775
[36] 0.1710897 0.1735764 0.3887793
Function Value
[1] 0.434402
Gradient:
[1] 2.031442e-07 5.772772e-07 -1.746159e-08 1.062623e-06 1.529870e-06
[6] -1.022116e-07 3.397815e-07 3.182343e-07 3.419132e-07 3.671730e-07
[11] 1.149624e-06 1.240164e-06 -2.474465e-07 1.668354e-07 1.788081e-07
[16] -2.063061e-07 2.190781e-07 2.140457e-06 -3.856471e-07 2.893206e-06
[21] 3.542411e-06 -1.550760e-07 8.473222e-07 1.935518e-07 5.518661e-06
[26] 3.854872e-07 -3.537082e-07 -8.348522e-07 8.046186e-07 8.366161e-06
[31] 5.455014e-06 5.953602e-06 -3.593907e-06 4.571277e-07 -1.126743e-07
[36] 2.647589e-06 -8.724221e-07 -1.519634e-05
iteration = 49
Step:
[1] -1.615526e-06 -2.529724e-06 -1.230725e-06 -1.057239e-05 -6.767033e-06
[6] -3.476119e-06 -4.169357e-07 -8.254346e-07 -6.060549e-07 -1.040817e-06
[11] -1.901935e-06 -1.627039e-06 9.367186e-08 3.824945e-07 2.622792e-07
[16] 4.267138e-07 5.590737e-08 -2.532350e-07 1.605021e-07 -2.743590e-06
[21] -4.832965e-07 1.863969e-07 1.093543e-07 3.123962e-07 -1.271376e-06
[26] 1.540610e-07 5.314538e-07 8.133939e-07 1.445520e-06 1.278075e-06
[31] 9.691341e-07 1.570171e-06 1.187167e-06 8.117267e-07 1.041994e-06
[36] 9.064908e-07 1.063366e-06 1.535179e-06
Parameter:
[1] 0.8191198 1.2379883 0.7394464 1.9507468 0.9979045 0.6721144 0.8945474
[8] 0.9182832 0.8300380 0.9279882 1.1265301 0.9921503 0.6951048 0.6812566
[15] 0.2966709 0.7915966 0.9461634 0.4641413 0.8801110 0.9761789 0.4709594
[22] 0.6733684 0.4990925 0.6078095 0.4840197 0.5536826 0.3761800 0.5901032
[29] 0.4165319 0.1583326 0.5166036 0.4655575 0.1956424 0.2662109 0.2494786
[36] 0.1710906 0.1735775 0.3887808
Function Value
[1] 0.434402
Gradient:
[1] -3.728573e-08 -1.302722e-07 -4.344969e-08 -3.265151e-07 8.250467e-07
[6] -4.106404e-07 4.846790e-07 -6.117773e-08 3.505818e-07 6.474288e-07
[11] 8.361347e-07 1.203748e-06 4.278533e-07 8.869172e-07 3.439737e-07
[16] 4.854606e-07 6.145129e-07 1.050005e-07 -4.210321e-07 8.387957e-08
[21] 2.258673e-06 1.368861e-07 6.114576e-07 5.960921e-07 2.527010e-06
[26] 7.081091e-07 5.334755e-07 4.895462e-07 5.621104e-07 -6.264322e-07
[31] 2.921041e-06 3.321343e-06 -5.094591e-07 2.442313e-07 6.932588e-07
[36] 1.365841e-06 -1.212541e-06 -6.523866e-06
iteration = 50
Step:
[1] -1.742659e-07 -1.779785e-07 -8.132006e-08 -2.217431e-06 -2.128865e-06
[6] 1.356454e-07 -2.047126e-07 -7.461373e-08 -2.132816e-07 -5.996206e-07
[11] -8.841211e-07 -9.775672e-07 -1.629381e-07 -1.900974e-07 2.725808e-08
[16] -6.108531e-08 -3.039901e-07 -1.358154e-08 2.701984e-07 -7.803253e-07
[21] -5.220923e-07 6.789385e-08 -5.380042e-09 -4.492903e-08 -6.204105e-07
[26] -1.167926e-07 1.005925e-07 1.463100e-07 -4.630734e-08 2.769049e-07
[31] -1.169249e-08 4.218309e-07 1.473494e-07 -9.119917e-08 8.421040e-08
[36] 1.103733e-07 2.303373e-07 3.684573e-07
Parameter:
[1] 0.8191196 1.2379881 0.7394464 1.9507446 0.9979024 0.6721146 0.8945472
[8] 0.9182831 0.8300377 0.9279876 1.1265293 0.9921493 0.6951047 0.6812564
[15] 0.2966709 0.7915966 0.9461631 0.4641412 0.8801113 0.9761782 0.4709589
[22] 0.6733685 0.4990925 0.6078095 0.4840191 0.5536825 0.3761801 0.5901034
[29] 0.4165319 0.1583329 0.5166036 0.4655579 0.1956426 0.2662108 0.2494786
[36] 0.1710907 0.1735777 0.3887812
Function Value
[1] 0.434402
Gradient:
[1] -2.177281e-07 -2.562254e-07 -1.053913e-07 -4.731137e-07 5.296386e-07
[6] -2.533440e-07 3.663914e-07 6.803447e-09 1.973888e-07 5.090151e-07
[11] 4.685581e-07 7.709922e-07 2.015277e-07 5.313616e-07 2.175682e-07
[16] 4.222045e-07 3.868372e-07 -1.157652e-07 -1.993428e-07 -6.631318e-07
[21] 6.739675e-07 1.488942e-07 4.152945e-07 3.178613e-07 9.579360e-07
[26] 2.750511e-07 2.802381e-07 4.587442e-07 1.698375e-07 -1.506795e-06
[31] 1.035509e-06 7.242029e-07 1.354117e-07 -1.895017e-07 6.223821e-07
[36] 2.208012e-07 -6.265921e-07 -1.703562e-06
iteration = 51
Step:
[1] 2.058384e-07 2.693253e-07 1.662787e-07 -4.137795e-07 -1.124731e-06
[6] 6.265770e-07 -2.564626e-07 -2.549231e-08 -1.559782e-07 -5.781499e-07
[11] -6.792431e-07 -8.488666e-07 -1.343126e-07 -2.680030e-07 -3.223647e-08
[16] -2.183234e-07 -3.601499e-07 -1.556621e-08 2.435717e-07 7.341504e-08
[21] -2.712009e-07 1.548222e-08 -1.208807e-07 -7.272277e-08 -5.209405e-07
[26] -6.324879e-08 4.745079e-08 -3.757526e-08 -2.512313e-07 9.251128e-08
[31] -1.335355e-07 3.071463e-07 -1.720765e-08 -1.645736e-07 -4.871062e-08
[36] 4.090384e-09 1.017760e-07 1.682881e-07
Parameter:
[1] 0.8191198 1.2379884 0.7394465 1.9507442 0.9979013 0.6721152 0.8945469
[8] 0.9182831 0.8300376 0.9279870 1.1265286 0.9921485 0.6951045 0.6812561
[15] 0.2966709 0.7915963 0.9461628 0.4641412 0.8801115 0.9761782 0.4709586
[22] 0.6733685 0.4990924 0.6078094 0.4840186 0.5536825 0.3761802 0.5901033
[29] 0.4165316 0.1583330 0.5166035 0.4655582 0.1956426 0.2662107 0.2494786
[36] 0.1710907 0.1735778 0.3887814
Function Value
[1] 0.434402
Gradient:
[1] -2.545342e-07 -2.475444e-07 -1.423928e-07 -3.445000e-07 3.362466e-07
[6] -3.531397e-08 9.084289e-08 -4.414247e-08 1.902478e-08 2.938449e-07
[11] 2.587281e-07 2.924416e-07 -7.068124e-08 5.385914e-08 -3.623768e-09
[16] 1.227463e-07 4.138911e-08 -3.502976e-08 1.234568e-08 -5.458034e-07
[21] -1.772804e-07 5.226042e-08 -2.357226e-08 2.993161e-08 -3.611333e-07
[26] -5.311307e-09 2.380318e-08 1.059242e-07 -5.167422e-08 -9.478285e-07
[31] -4.670042e-07 -9.126921e-07 3.564260e-07 -1.319300e-07 -6.146195e-08
[36] -4.513367e-07 2.831158e-07 1.040874e-06
iteration = 52
Parameter:
[1] 0.8191200 1.2379886 0.7394467 1.9507446 0.9979010 0.6721154 0.8945468
[8] 0.9182831 0.8300375 0.9279867 1.1265282 0.9921481 0.6951046 0.6812560
[15] 0.2966709 0.7915962 0.9461626 0.4641411 0.8801116 0.9761786 0.4709585
[22] 0.6733685 0.4990924 0.6078094 0.4840184 0.5536824 0.3761802 0.5901033
[29] 0.4165315 0.1583330 0.5166035 0.4655584 0.1956425 0.2662106 0.2494786
[36] 0.1710907 0.1735778 0.3887815
Function Value
[1] 0.434402
Gradient:
[1] -1.941380e-07 -1.934640e-07 -1.448086e-07 -2.266586e-07 2.532730e-07
[6] 4.572343e-08 -3.932854e-08 1.461942e-08 -3.545608e-08 1.612932e-07
[11] 1.584884e-07 1.091571e-07 -9.663381e-08 -1.142908e-07 -3.961276e-08
[16] -4.757084e-08 -1.088374e-07 1.218581e-08 5.861978e-08 -1.739231e-07
[21] -4.764367e-07 -1.877609e-08 -8.268941e-08 -8.256507e-08 -5.334577e-07
[26] -1.166534e-07 -1.181633e-07 -5.471179e-08 -9.526602e-08 -4.096457e-07
[31] -7.377210e-07 -1.117755e-06 3.048939e-07 -1.385736e-07 -1.938893e-07
[36] -4.005152e-07 3.779199e-07 1.362945e-06
Successive iterates within tolerance.
Current iterate is probably solution.We can safely ignore the warning messages again in this case, as explained above.
Check the code first to see if the minimization terminated normally (see the help page for the meaning of different code):
f_ml_min$code[1] 2Compare with lavaan Output
mod_cfa <-
"
f1 =~ x1 + x2 + x3 + x4
f2 =~ x5 + x6 + x7 + x8
f3 =~ x9 + x10 + x11 + x12
f4 =~ x13 + x14 + x15 + x16
"
fit_cfa <- cfa(model = mod_cfa,
data = dat)
summary(fit_cfa)lavaan 0.6-19 ended normally after 47 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 38
Number of observations 400
Model Test User Model:
Test statistic 173.761
Degrees of freedom 98
P-value (Chi-square) 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
f1 =~
x1 1.000
x2 0.819 0.095 8.651 0.000
x3 1.238 0.113 10.939 0.000
x4 0.739 0.095 7.776 0.000
f2 =~
x5 1.000
x6 1.951 0.314 6.211 0.000
x7 0.998 0.199 5.004 0.000
x8 0.672 0.174 3.867 0.000
f3 =~
x9 1.000
x10 0.895 0.083 10.764 0.000
x11 0.918 0.078 11.761 0.000
x12 0.830 0.078 10.621 0.000
f4 =~
x13 1.000
x14 0.928 0.082 11.373 0.000
x15 1.127 0.085 13.255 0.000
x16 0.992 0.086 11.577 0.000
Covariances:
Estimate Std.Err z-value P(>|z|)
f1 ~~
f2 0.196 0.037 5.235 0.000
f3 0.266 0.040 6.659 0.000
f4 0.249 0.038 6.635 0.000
f2 ~~
f3 0.171 0.034 5.047 0.000
f4 0.174 0.034 5.178 0.000
f3 ~~
f4 0.389 0.046 8.534 0.000
Variances:
Estimate Std.Err z-value P(>|z|)
.x1 0.695 0.058 12.011 0.000
.x2 0.681 0.054 12.722 0.000
.x3 0.297 0.044 6.712 0.000
.x4 0.792 0.060 13.162 0.000
.x5 0.946 0.071 13.326 0.000
.x6 0.464 0.071 6.549 0.000
.x7 0.880 0.066 13.267 0.000
.x8 0.976 0.071 13.789 0.000
.x9 0.471 0.045 10.501 0.000
.x10 0.673 0.055 12.135 0.000
.x11 0.499 0.044 11.261 0.000
.x12 0.608 0.050 12.229 0.000
.x13 0.484 0.042 11.480 0.000
.x14 0.554 0.046 12.153 0.000
.x15 0.376 0.039 9.767 0.000
.x16 0.590 0.049 12.005 0.000
f1 0.417 0.069 6.078 0.000
f2 0.158 0.047 3.384 0.001
f3 0.517 0.068 7.560 0.000
f4 0.466 0.063 7.414 0.000Compare the parameter estimates from the two methods:
round(f_ml_min$estimate, 3) [1] 0.819 1.238 0.739 1.951 0.998 0.672 0.895 0.918 0.830 0.928 1.127 0.992
[13] 0.695 0.681 0.297 0.792 0.946 0.464 0.880 0.976 0.471 0.673 0.499 0.608
[25] 0.484 0.554 0.376 0.590 0.417 0.158 0.517 0.466 0.196 0.266 0.249 0.171
[37] 0.174 0.389coef(fit_cfa) f1=~x2 f1=~x3 f1=~x4 f2=~x6 f2=~x7 f2=~x8 f3=~x10 f3=~x11
0.819 1.238 0.739 1.951 0.998 0.672 0.895 0.918
f3=~x12 f4=~x14 f4=~x15 f4=~x16 x1~~x1 x2~~x2 x3~~x3 x4~~x4
0.830 0.928 1.127 0.992 0.695 0.681 0.297 0.792
x5~~x5 x6~~x6 x7~~x7 x8~~x8 x9~~x9 x10~~x10 x11~~x11 x12~~x12
0.946 0.464 0.880 0.976 0.471 0.673 0.499 0.608
x13~~x13 x14~~x14 x15~~x15 x16~~x16 f1~~f1 f2~~f2 f3~~f3 f4~~f4
0.484 0.554 0.376 0.590 0.417 0.158 0.517 0.466
f1~~f2 f1~~f3 f1~~f4 f2~~f3 f2~~f4 f3~~f4
0.196 0.266 0.249 0.171 0.174 0.389 Compute the differences:
f_ml_min$estimate - coef(fit_cfa) f1=~x2 f1=~x3 f1=~x4 f2=~x6 f2=~x7 f2=~x8 f3=~x10 f3=~x11
0 0 0 0 0 0 0 0
f3=~x12 f4=~x14 f4=~x15 f4=~x16 x1~~x1 x2~~x2 x3~~x3 x4~~x4
0 0 0 0 0 0 0 0
x5~~x5 x6~~x6 x7~~x7 x8~~x8 x9~~x9 x10~~x10 x11~~x11 x12~~x12
0 0 0 0 0 0 0 0
x13~~x13 x14~~x14 x15~~x15 x16~~x16 f1~~f1 f2~~f2 f3~~f3 f4~~f4
0 0 0 0 0 0 0 0
f1~~f2 f1~~f3 f1~~f4 f2~~f3 f2~~f4 f3~~f4
0 0 0 0 0 0 Compare the values of the discrepancy function:
lavInspect(fit_cfa, "optim")$fx[1] 0.217201f_ml_min$minimum / 2[1] 0.217201A Structural Equation Model
mod_sem <-
"
f1 =~ x1 + x2 + x3 + x4
f2 =~ x5 + x6 + x7 + x8
f3 =~ x9 + x10 + x11 + x12
f4 =~ x13 + x14 + x15 + x16
f3 ~ f1 + f2
f4 ~ f3
"Write a Function to Create the Model Matrices
# Parameters in thetas in this order (as in lavaan)
# (lambda1 .... lambda12, b31, b32, b43, ev1 .... ev16, v1, v2, d3, d4, v21)
# b?? is the regression coefficient of a path
# ev?? is the error variance of an item
# v? is the variance of a factor
# d? is the error variance of a factor
# v?? is the covariance between two factors
# - 1:12: lambda1 .... lambda12,
# - 13:15: b31, b32, b43,
# - 16:31: ev1 .... ev16,
# - 32:35: v1, v2, d3, d4,
# - 36: v21
matrices_sem <- function(thetas) {
vnames <- paste0("x", 1:16)
fnames <- c("f1", "f2", "f3", "f4")
# Create the 16x4 lambda matrix
lambda <- matrix(c( 1, 0, 0, 0,
thetas[1], 0, 0, 0,
thetas[2], 0, 0, 0,
thetas[3], 0, 0, 0,
0, 1, 0, 0,
0, thetas[4], 0, 0,
0, thetas[5], 0, 0,
0, thetas[6], 0, 0,
0, 0, 1, 0,
0, 0, thetas[7], 0,
0, 0, thetas[8], 0,
0, 0, thetas[9], 0,
0, 0, 0, 1,
0, 0, 0, thetas[10],
0, 0, 0, thetas[11],
0, 0, 0, thetas[12]),
byrow = TRUE,
nrow = 16,
ncol = 4)
rownames(lambda) <- vnames
colnames(lambda) <- fnames
# Create the 4x4 beta matrix
beta <- matrix(c( 0, 0, 0, 0,
0, 0, 0, 0,
thetas[13], thetas[14], 0, 0,
0, 0, thetas[15], 0),
byrow = TRUE,
nrow = 4,
ncol = 4)
rownames(beta) <- fnames
colnames(beta) <- fnames
# Create the 16x16 theta matrix
theta <- diag(thetas[16:31])
rownames(theta) <- vnames
colnames(theta) <- vnames
# Create the 4x4 psi matrix
psi <- diag(thetas[32:35])
psi[2, 1] <- psi[1, 2] <- thetas[36]
rownames(psi) <- fnames
colnames(psi) <- fnames
# Return the matrices as a list
out <- list(lambda = lambda,
beta = beta,
theta = theta,
psi = psi)
return(out)
}Test the function by using arbitrary numbers:
matrices_sem(thetas = 1:36)$lambda
f1 f2 f3 f4
x1 1 0 0 0
x2 1 0 0 0
x3 2 0 0 0
x4 3 0 0 0
x5 0 1 0 0
x6 0 4 0 0
x7 0 5 0 0
x8 0 6 0 0
x9 0 0 1 0
x10 0 0 7 0
x11 0 0 8 0
x12 0 0 9 0
x13 0 0 0 1
x14 0 0 0 10
x15 0 0 0 11
x16 0 0 0 12
$beta
f1 f2 f3 f4
f1 0 0 0 0
f2 0 0 0 0
f3 13 14 0 0
f4 0 0 15 0
$theta
x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16
x1 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
x2 0 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0
x3 0 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0
x4 0 0 0 19 0 0 0 0 0 0 0 0 0 0 0 0
x5 0 0 0 0 20 0 0 0 0 0 0 0 0 0 0 0
x6 0 0 0 0 0 21 0 0 0 0 0 0 0 0 0 0
x7 0 0 0 0 0 0 22 0 0 0 0 0 0 0 0 0
x8 0 0 0 0 0 0 0 23 0 0 0 0 0 0 0 0
x9 0 0 0 0 0 0 0 0 24 0 0 0 0 0 0 0
x10 0 0 0 0 0 0 0 0 0 25 0 0 0 0 0 0
x11 0 0 0 0 0 0 0 0 0 0 26 0 0 0 0 0
x12 0 0 0 0 0 0 0 0 0 0 0 27 0 0 0 0
x13 0 0 0 0 0 0 0 0 0 0 0 0 28 0 0 0
x14 0 0 0 0 0 0 0 0 0 0 0 0 0 29 0 0
x15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 30 0
x16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 31
$psi
f1 f2 f3 f4
f1 32 36 0 0
f2 36 33 0 0
f3 0 0 34 0
f4 0 0 0 35Write a Function to Compute the Implied Covariance Matrices
implied_cov_sem <- function(thetas) {
# Create the matrices
m <- matrices_sem(thetas)
lambda <- m$lambda
beta <- m$beta
theta <- m$theta
psi <- m$psi
# Compute the implied covariance matrix
sigma_implied <- lambda %*% solve(diag(4) - beta) %*%
psi %*% t(solve(diag(4) - beta)) %*%
t(lambda) + theta
sigma_implied
}Write the ML Discrepancy Function
Again, no need. The discrepancy can be used again. We only need to tell it how to compute the implied covariance matrix by setting implied.
Find the Solution
We can use the item level covariance matrix created above for the CFA model:
round(my_data_items_cov, 3) x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12
x1 1.112 0.445 0.491 0.418 0.023 0.420 0.091 0.009 0.195 0.223 0.155 0.134
x2 0.445 0.961 0.396 0.340 0.041 0.339 0.039 -0.002 0.143 0.166 0.173 0.121
x3 0.491 0.396 0.935 0.344 0.237 0.531 0.227 0.161 0.377 0.325 0.361 0.295
x4 0.418 0.340 0.344 1.019 0.044 0.264 -0.005 0.093 0.193 0.170 0.143 0.143
x5 0.023 0.041 0.237 0.044 1.104 0.290 0.297 0.193 0.162 0.184 0.183 0.150
x6 0.420 0.339 0.531 0.264 0.290 1.067 0.287 0.174 0.314 0.223 0.296 0.310
x7 0.091 0.039 0.227 -0.005 0.297 0.287 1.038 0.176 0.140 0.196 0.207 0.176
x8 0.009 -0.002 0.161 0.093 0.193 0.174 0.176 1.048 0.134 0.181 0.146 0.214
x9 0.195 0.143 0.377 0.193 0.162 0.314 0.140 0.134 0.988 0.441 0.497 0.425
x10 0.223 0.166 0.325 0.170 0.184 0.223 0.196 0.181 0.441 1.087 0.410 0.390
x11 0.155 0.173 0.361 0.143 0.183 0.296 0.207 0.146 0.497 0.410 0.935 0.396
x12 0.134 0.121 0.295 0.143 0.150 0.310 0.176 0.214 0.425 0.390 0.396 0.964
x13 0.208 0.175 0.346 0.200 0.275 0.294 0.174 0.172 0.383 0.398 0.369 0.319
x14 0.203 0.137 0.308 0.140 0.229 0.322 0.228 0.073 0.325 0.309 0.321 0.301
x15 0.236 0.204 0.360 0.183 0.202 0.337 0.256 0.168 0.482 0.453 0.374 0.363
x16 0.256 0.126 0.353 0.139 0.183 0.314 0.256 0.166 0.349 0.340 0.309 0.304
x13 x14 x15 x16
x1 0.208 0.203 0.236 0.256
x2 0.175 0.137 0.204 0.126
x3 0.346 0.308 0.360 0.353
x4 0.200 0.140 0.183 0.139
x5 0.275 0.229 0.202 0.183
x6 0.294 0.322 0.337 0.314
x7 0.174 0.228 0.256 0.256
x8 0.172 0.073 0.168 0.166
x9 0.383 0.325 0.482 0.349
x10 0.398 0.309 0.453 0.340
x11 0.369 0.321 0.374 0.309
x12 0.319 0.301 0.363 0.304
x13 0.950 0.451 0.505 0.462
x14 0.451 0.955 0.480 0.432
x15 0.505 0.480 0.967 0.536
x16 0.462 0.432 0.536 1.048Set the starting values:
- Positive numbers for variances or error variances.
# Parameters in thetas in this order (as in lavaan)
# - 1:12: lambda1 .... lambda12,
# - 13:15: b31, b32, b43,
# - 16:31: ev1 .... ev16,
# - 32:35: v1, v2, d3, d4,
# - 36: v21
start <- rep(.6, 36)
start[1:12] <- .80
start[16:31] <- .50
start[32:35] <- 1
start [1] 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.6 0.6 0.6 0.5 0.5 0.5 0.5
[20] 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 0.6Put the starting values into the matrices:
matrices_sem(thetas = start)$lambda
f1 f2 f3 f4
x1 1.0 0.0 0.0 0.0
x2 0.8 0.0 0.0 0.0
x3 0.8 0.0 0.0 0.0
x4 0.8 0.0 0.0 0.0
x5 0.0 1.0 0.0 0.0
x6 0.0 0.8 0.0 0.0
x7 0.0 0.8 0.0 0.0
x8 0.0 0.8 0.0 0.0
x9 0.0 0.0 1.0 0.0
x10 0.0 0.0 0.8 0.0
x11 0.0 0.0 0.8 0.0
x12 0.0 0.0 0.8 0.0
x13 0.0 0.0 0.0 1.0
x14 0.0 0.0 0.0 0.8
x15 0.0 0.0 0.0 0.8
x16 0.0 0.0 0.0 0.8
$beta
f1 f2 f3 f4
f1 0.0 0.0 0.0 0
f2 0.0 0.0 0.0 0
f3 0.6 0.6 0.0 0
f4 0.0 0.0 0.6 0
$theta
x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16
x1 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x2 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x3 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x4 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x5 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x6 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x7 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0
x10 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0
x11 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0
x12 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0
x13 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0
x14 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0
x15 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0
x16 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5
$psi
f1 f2 f3 f4
f1 1.0 0.6 0 0
f2 0.6 1.0 0 0
f3 0.0 0.0 1 0
f4 0.0 0.0 0 1We use nlm() again. The call is nearly the same. We use the item level covariance this time, and use implied_cov_sem() to compute the implied covariance matrix.
f_ml_min <- nlm(f = f_ml,
p = start,
data_cov = my_data_items_cov,
implied = implied_cov_sem,
print.level = 2)iteration = 0
Step:
[1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Parameter:
[1] 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.6 0.6 0.6 0.5 0.5 0.5 0.5
[20] 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 0.6
Function Value
[1] 2.185797
Gradient:
[1] 0.07170679 -0.07912282 0.09101749 -0.05131903 0.08907650 0.29651604
[7] 0.13209417 0.21259447 0.30476247 0.22887000 0.01687442 0.06809838
[13] 0.38813082 0.30578360 -0.02664099 -0.20518877 -0.32920460 0.01483169
[19] -0.59456861 -0.81583696 -0.79122645 -0.90033001 -1.27192723 0.03359370
[25] -0.47254402 0.00684150 -0.25668534 0.09197354 -0.07471056 0.21487352
[31] -0.19258366 0.21731919 0.36083593 0.36243739 0.48513248 0.02778078
iteration = 1
Step:
[1] -0.07170679 0.07912282 -0.09101749 0.05131903 -0.08907650 -0.29651604
[7] -0.13209417 -0.21259447 -0.30476247 -0.22887000 -0.01687442 -0.06809838
[13] -0.38813082 -0.30578360 0.02664099 0.20518877 0.32920460 -0.01483169
[19] 0.59456861 0.81583696 0.79122645 0.90033001 1.27192723 -0.03359370
[25] 0.47254402 -0.00684150 0.25668534 -0.09197354 0.07471056 -0.21487352
[31] 0.19258366 -0.21731919 -0.36083593 -0.36243739 -0.48513248 -0.02778078
Parameter:
[1] 0.7282932 0.8791228 0.7089825 0.8513190 0.7109235 0.5034840 0.6679058
[8] 0.5874055 0.4952375 0.5711300 0.7831256 0.7319016 0.2118692 0.2942164
[15] 0.6266410 0.7051888 0.8292046 0.4851683 1.0945686 1.3158370 1.2912264
[22] 1.4003300 1.7719272 0.4664063 0.9725440 0.4931585 0.7566853 0.4080265
[29] 0.5747106 0.2851265 0.6925837 0.7826808 0.6391641 0.6375626 0.5148675
[36] 0.5722192
Function Value
[1] 1.701483
Gradient:
[1] 0.0665906725 -0.0772163276 0.1017474425 0.0004215863 0.1247777561
[6] 0.0818862240 0.0043334261 -0.4236611169 -0.2458907460 -0.2864450082
[11] -0.4969814853 0.0138367398 -0.2768040090 -0.2510263570 -0.2008304705
[16] 0.1364858946 0.2276742954 0.2608040823 0.2565509384 0.1913207233
[21] 0.3474669549 0.2478669147 0.2469692908 0.2303726774 0.2545073947
[26] -0.1731594566 0.1428490677 -0.1856606389 -0.0637451514 -0.8981019981
[31] 0.1502703526 0.1305765309 0.2683399210 0.1047250144 0.3120960343
[36] -0.0091478682
iteration = 2
Step:
[1] -0.048464147 0.055730088 -0.071898065 0.005702814 -0.085555365
[6] -0.083779379 -0.017945233 0.230704384 0.112846378 0.146101715
[11] 0.297620223 -0.016245381 0.121803677 0.115823581 0.124152405
[16] -0.058455650 -0.099028395 -0.158933534 -0.085632566 -0.020627884
[21] -0.117609073 -0.044906084 -0.001231214 -0.142767406 -0.098564938
[26] 0.103585863 -0.056313800 0.101239690 0.047097543 0.516431382
[31] -0.068228039 -0.103936839 -0.203639150 -0.105198466 -0.244443139
[36] 0.002289606
Parameter:
[1] 0.6798291 0.9348529 0.6370844 0.8570218 0.6253681 0.4197046 0.6499606
[8] 0.8181099 0.6080839 0.7172317 1.0807458 0.7156562 0.3336729 0.4100400
[15] 0.7507934 0.6467331 0.7301762 0.3262348 1.0089360 1.2952091 1.1736174
[22] 1.3554239 1.7706960 0.3236389 0.8739791 0.5967444 0.7003715 0.5092661
[29] 0.6218081 0.8015579 0.6243556 0.6787440 0.4355249 0.5323641 0.2704244
[36] 0.5745088
Function Value
[1] 1.449853
Gradient:
[1] 0.003220514 -0.313758271 0.035147863 -0.081325215 0.123500453
[6] 0.064465798 -0.089759421 0.122932690 -0.114827856 -0.131629097
[11] 0.274682980 -0.230414191 0.052608474 0.064407345 0.146005487
[16] -0.098307424 0.055042648 -0.175118110 0.193177724 0.079894712
[21] 0.336391004 0.195498967 0.236316033 -0.327978807 0.175565550
[26] 0.198868566 0.090807706 0.208593111 0.107600435 0.487775157
[31] -0.017343872 -0.496717806 -0.286216647 0.241401057 0.299799634
[36] 1.118726740
iteration = 3
Step:
[1] -0.012797633 0.074410266 -0.025229849 0.015934726 -0.046231899
[6] -0.028888545 0.015533659 0.048970637 0.062890691 0.073772451
[11] 0.034058662 0.041376947 0.035504959 0.029325425 0.007277524
[16] -0.003493858 -0.048030665 -0.012091987 -0.077704978 -0.042895844
[21] -0.119715542 -0.074401062 -0.079380372 0.022484033 -0.074851504
[26] -0.007972560 -0.040588070 -0.008274870 -0.008983068 0.061857900
[31] -0.021563195 0.071050371 0.005423215 -0.067381449 -0.115799634
[36] -0.213668854
Parameter:
[1] 0.6670314 1.0092632 0.6118546 0.8729566 0.5791362 0.3908160 0.6654943
[8] 0.8670805 0.6709746 0.7910042 1.1148045 0.7570332 0.3691778 0.4393654
[15] 0.7580709 0.6432393 0.6821455 0.3141428 0.9312311 1.2523132 1.0539018
[22] 1.2810229 1.6913156 0.3461229 0.7991276 0.5887718 0.6597835 0.5009913
[29] 0.6128250 0.8634158 0.6027924 0.7497943 0.4409481 0.4649827 0.1546247
[36] 0.3608400
Function Value
[1] 1.2685
Gradient:
[1] -0.0182374542 0.0730685081 0.0119734906 -0.0506178139 -0.0087350500
[6] -0.0007115162 -0.1236033249 0.1660697606 -0.0613440676 -0.0929077260
[11] 0.1870811694 -0.2371021601 0.0382837264 -0.0022535396 0.0817270767
[16] -0.0121440316 0.0212669491 -0.0266993858 0.1623722881 0.2116460721
[21] 0.3046946164 0.2338750992 0.2465039299 -0.3928235408 0.1110296175
[26] 0.1913565377 0.0479129909 0.1343827876 0.0868633130 0.4970480632
[31] -0.0982750592 0.3040509107 0.2675720481 0.2819969680 -0.0594503398
[36] -0.3167596780
iteration = 4
Step:
[1] -0.002813620 0.060593711 -0.046640233 0.061962721 -0.065715138
[6] -0.025076664 0.133961762 -0.019881887 0.184735845 0.222583192
[11] -0.074867760 0.260575757 0.068806881 0.083070501 -0.048524905
[16] -0.017328095 -0.130071506 -0.005712399 -0.313150225 -0.311011432
[21] -0.513757958 -0.389140272 -0.437919738 0.342913402 -0.257769814
[26] -0.158326985 -0.130252015 -0.106406187 -0.087575132 -0.245170149
[31] 0.021593976 -0.109448919 -0.181075523 -0.307029917 -0.113302279
[36] -0.098752259
Parameter:
[1] 0.66421781 1.06985689 0.56521436 0.93491930 0.51342110 0.36573937
[7] 0.79945602 0.84719866 0.85571044 1.01358735 1.03993671 1.01760895
[13] 0.43798470 0.52243591 0.70954601 0.62591117 0.55207403 0.30843038
[19] 0.61808084 0.94130180 0.54014387 0.89188259 1.25339590 0.68903633
[25] 0.54135776 0.43044482 0.52953145 0.39458509 0.52524991 0.61824561
[31] 0.62438640 0.64034543 0.25987261 0.15795278 0.04132247 0.26208771
Function Value
[1] 1.083706
Gradient:
[1] -0.084331653 0.181588087 -0.148195312 -0.329380651 -0.133784443
[6] -0.054697001 -0.160223500 -0.100157862 0.074346936 -0.083459810
[11] -0.179628853 -0.102700149 0.072529204 -0.166067117 -0.685247336
[16] -0.114941280 -0.380814434 -0.080821884 -0.418873555 0.052334819
[21] -0.348484392 -0.008390721 0.172073752 0.266291085 -0.485039685
[26] -0.500652817 -0.304314529 -0.636958582 -0.170757630 0.320050763
[31] -0.046795428 0.284648110 -0.686938431 -1.389838971 -2.559883669
[36] -0.132765056
iteration = 5
Step:
[1] 0.007712389 -0.001423237 0.004899262 0.026460630 0.001174501
[6] 0.007645280 0.034641076 -0.009483340 0.026672847 0.038013631
[11] -0.022824357 0.053195405 0.006675321 0.020078919 0.017376629
[16] 0.003630390 -0.002799810 0.013738930 -0.038016321 -0.067892503
[21] -0.077941362 -0.078794477 -0.104805165 0.056369056 -0.022436564
[26] -0.009268862 -0.008275418 0.007871000 -0.011046276 -0.088196914
[31] 0.007200791 -0.020614620 0.022692380 0.027429135 0.129093955
[36] -0.016462479
Parameter:
[1] 0.6719302 1.0684337 0.5701136 0.9613799 0.5145956 0.3733847 0.8340971
[8] 0.8377153 0.8823833 1.0516010 1.0171123 1.0708044 0.4446600 0.5425148
[15] 0.7269226 0.6295416 0.5492742 0.3221693 0.5800645 0.8734093 0.4622025
[22] 0.8130881 1.1485907 0.7454054 0.5189212 0.4211760 0.5212560 0.4024561
[29] 0.5142036 0.5300487 0.6315872 0.6197308 0.2825650 0.1853819 0.1704164
[36] 0.2456252
Function Value
[1] 0.9661629
Gradient:
[1] -0.109696778 0.149659615 -0.192456227 -0.392674853 -0.154417698
[6] -0.057980532 -0.145339765 -0.174097458 0.075934249 0.123731361
[11] -0.093079923 0.090614869 0.269076438 0.044380329 -0.069094796
[16] -0.074688533 -0.365063212 -0.047366420 -0.558331681 -0.006009977
[21] -0.616881053 -0.112911255 0.129415311 0.330966934 -0.528879696
[26] -0.487315489 -0.263869850 -0.280275639 -0.037588890 0.279417694
[31] 0.094312060 0.288131297 -0.499659571 -0.718924962 0.157155977
[36] -0.252871672
iteration = 6
Step:
[1] 0.0371190204 -0.0514715408 0.0627126818 0.1041126122 0.0553181516
[6] 0.0295261501 0.0426299745 0.0129974697 -0.0355807201 -0.0552312152
[11] -0.0198426401 -0.0220931731 -0.0898221604 -0.0289943208 -0.0058226872
[16] 0.0265577522 0.1103002294 0.0345874614 0.1594398180 -0.0003958867
[21] 0.1794226469 0.0323403443 -0.0405972517 -0.0651893462 0.1536067483
[26] 0.1135524678 0.0771087780 0.0566061738 0.0012161789 -0.1513110302
[31] -0.0161723156 -0.0684750578 0.1568198652 0.2000588880 -0.0273244399
[36] 0.0812655309
Parameter:
[1] 0.7090492 1.0169621 0.6328263 1.0654925 0.5699137 0.4029108 0.8767271
[8] 0.8507128 0.8468026 0.9963698 0.9972697 1.0487112 0.3548379 0.5135205
[15] 0.7211000 0.6560993 0.6595745 0.3567568 0.7395043 0.8730134 0.6416252
[22] 0.8454285 1.1079935 0.6802160 0.6725279 0.5347284 0.5983648 0.4590623
[29] 0.5154198 0.3787377 0.6154149 0.5512557 0.4393849 0.3854408 0.1430920
[36] 0.3268908
Function Value
[1] 0.6493205
Gradient:
[1] -0.053255530 -0.072068539 -0.066661276 -0.029323007 -0.081500499
[6] -0.023855087 0.062466359 0.033564802 0.124844941 0.085040178
[11] -0.263792405 0.088012555 0.112516513 0.081671583 -0.103898298
[16] 0.017112868 -0.012882740 0.036120344 -0.060458397 0.007083354
[21] 0.148118282 -0.027658981 0.112059671 0.310660095 0.014997457
[26] 0.055347936 -0.004178094 -0.064214575 -0.075993736 -0.175184354
[31] 0.060162900 0.037930306 0.220327223 0.317531775 -0.122119967
[36] -0.122877744
iteration = 7
Step:
[1] 0.047063077 0.061187792 0.067116138 0.051340195 0.069241080
[6] 0.015700053 -0.046323557 -0.035751920 -0.123286068 -0.103280142
[11] 0.162219247 -0.086734981 -0.132057644 -0.093864466 0.064181833
[16] 0.013886065 0.064229552 0.004014211 0.132714436 0.054893496
[21] 0.012079186 0.091232412 -0.016745737 -0.258162152 0.067895804
[26] -0.002721569 0.042710789 0.054012603 0.058107864 0.059606520
[31] -0.043916304 0.017343379 -0.059958830 -0.152321227 0.053234988
[36] 0.008002211
Parameter:
[1] 0.7561123 1.0781499 0.6999424 1.1168327 0.6391548 0.4186109 0.8304035
[8] 0.8149609 0.7235165 0.8930896 1.1594890 0.9619762 0.2227802 0.4196560
[15] 0.7852818 0.6699854 0.7238040 0.3607710 0.8722188 0.9279069 0.6537043
[22] 0.9366609 1.0912478 0.4220539 0.7404237 0.5320069 0.6410756 0.5130749
[29] 0.5735277 0.4383442 0.5714986 0.5685991 0.3794260 0.2331196 0.1963270
[36] 0.3348930
Function Value
[1] 0.6459101
Gradient:
[1] 0.032547231 0.063858537 0.040516753 -0.034162772 -0.018109514
[6] -0.019264405 -0.092777704 -0.197757462 -0.163687830 -0.028699674
[11] 0.129772990 -0.041075147 -0.378993004 -0.353402790 -0.033357978
[16] 0.019251839 0.096135267 0.163060420 0.117765698 0.031330721
[21] 0.180737040 0.070783660 0.098845518 -0.215871548 0.066151429
[26] -0.012026568 0.001003926 0.108592637 0.047675535 0.256883364
[31] -0.033774921 0.191328802 0.042490832 -0.601101938 0.353075599
[36] -0.166446583
iteration = 8
Step:
[1] 0.007052650 0.023808487 0.005436343 0.042516111 0.019703991
[6] 0.012247441 0.037853265 0.056762924 0.046034763 0.014515084
[11] 0.004332987 0.026639827 0.101750604 0.107564043 0.038897383
[16] -0.003207546 -0.034779112 -0.049011585 -0.052054844 -0.050272967
[21] -0.159234738 -0.068157409 -0.135941168 0.027591930 -0.047609892
[26] -0.019953089 -0.008855259 -0.026649295 -0.007341365 -0.104404994
[31] -0.006118198 -0.042206302 -0.031315167 0.128484697 -0.069634599
[36] -0.013084416
Parameter:
[1] 0.7631649 1.1019584 0.7053788 1.1593488 0.6588588 0.4308583 0.8682568
[8] 0.8717238 0.7695513 0.9076047 1.1638219 0.9886160 0.3245308 0.5272201
[15] 0.8241792 0.6667778 0.6890249 0.3117594 0.8201639 0.8776339 0.4944696
[22] 0.8685035 0.9553066 0.4496458 0.6928139 0.5120538 0.6322203 0.4864256
[29] 0.5661863 0.3339392 0.5653804 0.5263928 0.3481109 0.3616043 0.1266924
[36] 0.3218086
Function Value
[1] 0.5401939
Gradient:
[1] 0.012044797 -0.042948798 0.026409332 -0.161260420 -0.026625827
[6] -0.027398503 0.018694340 0.009269790 -0.021180618 0.012766094
[11] 0.078201630 0.021431728 0.079020985 0.058380834 0.238216074
[16] -0.014853928 0.027277462 -0.018967892 0.050736556 -0.037645940
[21] -0.094997521 -0.008749584 -0.019797216 -0.109064139 0.022047033
[26] -0.029352989 0.013539978 -0.015148075 -0.002351676 -0.136670032
[31] -0.085216087 0.055904948 -0.090898737 0.314178266 -0.132116746
[36] 0.122180193
iteration = 9
Step:
[1] -0.0072649856 0.0024128248 -0.0127063676 0.0476576853 0.0046735992
[6] 0.0078629255 0.0067515094 0.0169107091 0.0264057975 0.0088905315
[11] -0.0331666777 0.0044041196 0.0106122089 0.0151203432 -0.0615594074
[16] 0.0011669903 -0.0164135103 -0.0071450666 -0.0290912296 -0.0016480158
[21] 0.0103817298 -0.0141136740 -0.0100152447 0.0561515989 -0.0134959038
[26] 0.0142970227 -0.0058902744 -0.0001625374 -0.0051059844 0.0199481593
[31] 0.0261108664 -0.0358444711 0.0262194169 -0.0330094776 0.0179676087
[36] -0.0174328023
Parameter:
[1] 0.7559000 1.1043712 0.6926724 1.2070065 0.6635324 0.4387212 0.8750083
[8] 0.8886345 0.7959571 0.9164952 1.1306553 0.9930201 0.3351430 0.5423404
[15] 0.7626198 0.6679448 0.6726114 0.3046143 0.7910727 0.8759859 0.5048513
[22] 0.8543898 0.9452913 0.5057974 0.6793180 0.5263508 0.6263301 0.4862630
[29] 0.5610803 0.3538874 0.5914912 0.4905484 0.3743303 0.3285948 0.1446600
[36] 0.3043758
Function Value
[1] 0.5133186
Gradient:
[1] -0.0159833213 -0.0939924690 -0.0037100492 -0.0608985489 -0.0236173285
[6] -0.0242751312 0.0247987302 0.0421777067 0.0115353274 -0.0026916034
[11] -0.0163275569 0.0108031308 0.0744655715 0.0609192377 0.0051420272
[16] -0.0141602641 -0.0060687135 -0.0757366116 0.0104896962 -0.0296503018
[21] -0.0107178906 -0.0167918621 -0.0261686317 0.0664394584 0.0070576576
[26] 0.0386316614 0.0226664909 0.0032323406 0.0023724063 -0.0689410449
[31] -0.0057164087 -0.0005617942 0.1718356266 0.1929300311 -0.0227852510
[36] -0.0700183804
iteration = 10
Step:
[1] 0.0050839636 0.0714334286 -0.0047966225 0.0797559840 0.0177153652
[6] 0.0195929440 -0.0026391338 0.0044634268 0.0196209704 0.0095786485
[11] -0.0207082257 -0.0024682299 -0.0144030509 -0.0002393794 -0.0130463524
[16] 0.0180075960 0.0025687335 0.0450957223 -0.0107373476 0.0333871768
[21] 0.0256632281 0.0137500014 0.0202427665 -0.0116137442 0.0044699413
[26] 0.0004472779 -0.0076581571 -0.0002222382 -0.0062075897 0.0203863575
[31] 0.0176743947 -0.0101826774 -0.0704567139 -0.0355225556 0.0192894851
[36] 0.0072045968
Parameter:
[1] 0.7609839 1.1758046 0.6878758 1.2867625 0.6812478 0.4583142 0.8723692
[8] 0.8930979 0.8155780 0.9260739 1.1099470 0.9905519 0.3207400 0.5421010
[15] 0.7495734 0.6859524 0.6751801 0.3497101 0.7803354 0.9093731 0.5305146
[22] 0.8681398 0.9655341 0.4941837 0.6837879 0.5267981 0.6186719 0.4860408
[29] 0.5548727 0.3742737 0.6091656 0.4803657 0.3038736 0.2930722 0.1639495
[36] 0.3115804
Function Value
[1] 0.5053238
Gradient:
[1] -0.028845971 0.055720257 -0.025880915 -0.084718331 -0.025431852
[6] -0.021163245 -0.006958135 0.004829353 0.005148145 0.002799382
[11] -0.038551331 0.009581065 -0.003452250 -0.025997341 -0.076337400
[16] -0.005113403 -0.015562293 0.172848086 -0.015940778 -0.024859538
[21] 0.022155508 -0.024921675 -0.012156935 0.038011223 0.009462561
[26] 0.044860730 0.012536681 0.018020614 0.002628109 0.005243553
[31] 0.040169606 -0.071209133 -0.263203624 0.026412259 0.086645215
[36] 0.448313010
iteration = 11
Step:
[1] 0.023000768 0.015902726 0.012603424 0.103530734 0.038896818
[6] 0.030414892 0.003687282 -0.002415680 0.007794707 0.007417760
[11] 0.026202573 -0.003401880 -0.010812791 0.018211475 0.054072395
[16] 0.010900249 0.013474514 -0.050683596 0.001828664 0.026409937
[21] -0.006422933 0.017524293 0.013936831 -0.043632085 0.002164404
[26] -0.027740969 -0.010873343 -0.001965069 -0.003136726 0.013446089
[31] -0.004276884 -0.044274364 -0.023225367 -0.051066279 -0.002395276
[36] -0.064032232
Parameter:
[1] 0.7839847 1.1917074 0.7004792 1.3902932 0.7201446 0.4887291 0.8760564
[8] 0.8906823 0.8233727 0.9334917 1.1361496 0.9871500 0.3099272 0.5603125
[15] 0.8036458 0.6968527 0.6886546 0.2990265 0.7821640 0.9357830 0.5240916
[22] 0.8856641 0.9794709 0.4505516 0.6859523 0.4990571 0.6077986 0.4840757
[29] 0.5517360 0.3877198 0.6048888 0.4360913 0.2806482 0.2420060 0.1615542
[36] 0.2475481
Function Value
[1] 0.4929997
Gradient:
[1] -0.008719596 -0.013015894 -0.020112079 -0.015187249 -0.023903851
[6] -0.019244929 -0.039709828 -0.073385138 -0.031874482 0.014606204
[11] 0.036317145 0.006565561 -0.058448375 -0.065709720 0.021281512
[16] 0.010153471 0.013138898 0.008823637 -0.012660060 0.021204329
[21] 0.062792779 0.013210663 0.009163262 -0.137289586 -0.004868642
[26] -0.063311873 -0.024445445 0.011943893 -0.002198764 0.077464453
[31] 0.029421493 0.054650101 0.150400581 -0.208496438 0.149054319
[36] -0.265486168
iteration = 12
Step:
[1] 0.0121124600 0.0108882510 0.0172063903 0.0281620426 0.0164211696
[6] 0.0125546300 0.0134708061 0.0189882509 0.0028379833 -0.0079842479
[11] 0.0026634051 -0.0045781376 0.0006483338 0.0109859203 -0.0051266862
[16] -0.0021219236 -0.0035301839 -0.0244090295 0.0055938614 -0.0111581997
[21] -0.0463318643 -0.0080040370 -0.0165857818 0.0504580784 -0.0068161292
[26] 0.0179752333 0.0070350040 0.0038906399 0.0083988626 -0.0152357264
[31] -0.0198594848 0.0067675544 -0.0123090417 0.0302458983 -0.0110941426
[36] 0.0054338316
Parameter:
[1] 0.7960972 1.2025956 0.7176856 1.4184553 0.7365658 0.5012837 0.8895272
[8] 0.9096705 0.8262107 0.9255074 1.1388130 0.9825719 0.3105755 0.5712984
[15] 0.7985191 0.6947307 0.6851244 0.2746174 0.7877579 0.9246248 0.4777598
[22] 0.8776600 0.9628852 0.5010097 0.6791362 0.5170323 0.6148336 0.4879664
[29] 0.5601349 0.3724841 0.5850293 0.4428589 0.2683392 0.2722519 0.1504600
[36] 0.2529820
Function Value
[1] 0.4793253
Gradient:
[1] 0.009586671 -0.030327966 0.004759848 -0.055459836 -0.018728763
[6] -0.014525725 -0.016638459 -0.011450833 -0.012930986 0.005428166
[11] 0.020444223 -0.009809998 -0.021794552 -0.024792584 0.006899924
[16] -0.003064699 0.002519357 -0.091079311 -0.008188870 0.001477712
[21] -0.024060686 -0.001081808 -0.010394718 0.031185049 -0.004016655
[26] 0.005796252 -0.002475357 0.015121341 0.009320772 0.019788377
[31] -0.019377840 0.038865917 0.014280509 0.003653259 0.057413718
[36] -0.095141324
iteration = 13
Step:
[1] 0.0034541920 0.0339142658 0.0065622737 0.0812762139 0.0295966156
[6] 0.0236572768 0.0187931851 0.0163207157 0.0136363028 -0.0034150764
[11] -0.0060238734 0.0066628300 0.0181564554 0.0310985716 0.0066638367
[16] 0.0042471547 -0.0053480657 0.0367583927 0.0002531248 -0.0029671252
[21] -0.0207675174 -0.0046243143 -0.0069491869 -0.0053258870 -0.0087525265
[26] -0.0058859763 0.0002268070 -0.0064604419 -0.0008923154 -0.0147171792
[31] 0.0057702361 -0.0215176694 0.0055115301 -0.0053091710 -0.0072087486
[36] 0.0092800549
Parameter:
[1] 0.7995513 1.2365099 0.7242479 1.4997315 0.7661624 0.5249410 0.9083204
[8] 0.9259912 0.8398470 0.9220923 1.1327891 0.9892347 0.3287320 0.6023970
[15] 0.8051830 0.6989779 0.6797764 0.3113758 0.7880110 0.9216577 0.4569923
[22] 0.8730357 0.9559360 0.4956838 0.6703836 0.5111464 0.6150604 0.4815059
[29] 0.5592426 0.3577669 0.5907995 0.4213412 0.2738507 0.2669427 0.1432513
[36] 0.2622620
Function Value
[1] 0.4764828
Gradient:
[1] -0.0241878411 0.0005565002 -0.0179116100 -0.0181525737 -0.0050582827
[6] -0.0043952042 0.0038684682 0.0134361109 0.0059004606 0.0013689068
[11] -0.0096440541 0.0027528451 0.0376897660 0.0257098236 0.0039846455
[16] 0.0008224781 -0.0096205852 0.0617312494 -0.0080903604 -0.0109372671
[21] -0.0350727554 -0.0097151798 -0.0189195930 0.0065055126 -0.0178677482
[26] -0.0118239178 -0.0015887025 -0.0114160628 0.0008758292 -0.0560180133
[31] -0.0086767535 -0.0793403743 0.0589580402 0.0092741210 -0.0302193577
[36] 0.1756385473
iteration = 14
Step:
[1] 0.0152103620 0.0267464248 0.0115123779 0.0865640275 0.0318568660
[6] 0.0248617323 0.0129597566 0.0110537321 0.0131578913 -0.0022774438
[11] -0.0029613921 0.0016846092 0.0010232082 0.0206786778 0.0058537662
[16] 0.0041885184 0.0014439412 -0.0079374069 0.0036459423 0.0138849267
[21] 0.0103768484 0.0100550694 0.0201348255 -0.0030432455 0.0061654760
[26] 0.0022543110 0.0011038844 -0.0012303768 -0.0027109600 0.0195146870
[31] 0.0142294556 -0.0079954524 -0.0622762088 -0.0030172066 0.0002720054
[36] -0.0338966984
Parameter:
[1] 0.8147617 1.2632563 0.7357603 1.5862955 0.7980193 0.5498027 0.9212802
[8] 0.9370450 0.8530049 0.9198149 1.1298278 0.9909193 0.3297552 0.6230757
[15] 0.8110367 0.7031664 0.6812203 0.3034384 0.7916569 0.9355426 0.4673691
[22] 0.8830908 0.9760708 0.4926405 0.6765491 0.5134007 0.6161643 0.4802755
[29] 0.5565316 0.3772816 0.6050290 0.4133457 0.2115745 0.2639255 0.1435233
[36] 0.2283653
Function Value
[1] 0.4712777
Gradient:
[1] -0.0076948758 0.0441056688 -0.0062302163 -0.0641951571 -0.0191194047
[6] -0.0116273497 0.0065665446 0.0114588445 0.0090252996 -0.0084187235
[11] -0.0007935645 0.0060025229 0.0089642356 -0.0054876850 -0.0062068040
[16] 0.0036543213 -0.0062883814 0.0664602169 -0.0031753302 -0.0025939322
[21] -0.0464108112 -0.0053297029 -0.0003525606 -0.0056533658 -0.0042872728
[26] -0.0009535341 0.0031134348 -0.0074692075 -0.0034226098 0.0218590444
[31] 0.0240740334 0.0214807265 -0.2481522081 0.0079998799 -0.0166959921
[36] 0.1313253328
iteration = 15
Step:
[1] 0.0150977638 0.0076343946 0.0111825619 0.0490610537 0.0228034520
[6] 0.0169341042 -0.0027511753 -0.0062736506 -0.0019547581 0.0040476231
[11] 0.0034734383 -0.0038695707 -0.0103217734 0.0024065616 0.0097801111
[16] -0.0026709342 0.0002234791 -0.0248854656 -0.0027542383 0.0033090817
[21] 0.0100148585 0.0026427010 0.0057598992 0.0042640313 0.0010622268
[26] -0.0016774216 -0.0040457181 0.0005783117 0.0010003744 -0.0001974349
[31] -0.0125386816 -0.0095260354 0.0067188267 -0.0038014143 0.0006716260
[36] -0.0063415851
Parameter:
[1] 0.8298595 1.2708907 0.7469428 1.6353566 0.8208227 0.5667368 0.9185290
[8] 0.9307713 0.8510502 0.9238625 1.1333012 0.9870498 0.3194334 0.6254823
[15] 0.8208168 0.7004955 0.6814438 0.2785530 0.7889027 0.9388517 0.4773840
[22] 0.8857335 0.9818307 0.4969046 0.6776113 0.5117232 0.6121185 0.4808539
[29] 0.5575320 0.3770841 0.5924903 0.4038197 0.2182933 0.2601241 0.1441949
[36] 0.2220237
Function Value
[1] 0.4674551
Gradient:
[1] 0.0050893938 0.0016383584 0.0017909692 -0.0125730560 -0.0115303855
[6] -0.0062832051 -0.0022737972 -0.0072438304 -0.0014615011 0.0011804921
[11] 0.0128318786 -0.0006920438 -0.0150719224 -0.0180749531 0.0139494531
[16] -0.0062830132 -0.0069950481 -0.0376839289 -0.0088945598 0.0054727920
[21] 0.0221541399 0.0045766768 0.0081146787 0.0031168703 -0.0045557158
[26] -0.0115071117 -0.0069857435 -0.0059310956 0.0012163923 0.0252285091
[31] -0.0031788829 0.0203316866 0.0556025483 -0.0075086177 0.0050459192
[36] -0.0807964291
iteration = 16
Step:
[1] 1.087869e-02 1.177282e-02 1.068483e-02 7.081064e-02 3.078262e-02
[6] 2.194925e-02 6.381053e-03 6.524988e-03 4.312492e-03 5.632258e-04
[11] -3.174589e-03 -5.682515e-04 3.073657e-03 2.037285e-02 -1.589908e-03
[16] 5.670841e-03 5.403456e-03 8.161789e-04 5.031248e-03 -1.127325e-03
[21] -1.830520e-02 -3.262505e-03 -1.011734e-02 -3.011479e-03 1.235096e-03
[26] 5.442300e-03 1.873036e-03 5.137074e-03 8.718874e-05 -1.357552e-02
[31] -3.688969e-03 -1.204744e-02 -1.698468e-02 -8.348649e-03 5.492606e-07
[36] -9.114737e-03
Parameter:
[1] 0.8407382 1.2826635 0.7576277 1.7061672 0.8516053 0.5886860 0.9249101
[8] 0.9372963 0.8553626 0.9244257 1.1301266 0.9864815 0.3225071 0.6458551
[15] 0.8192269 0.7061663 0.6868473 0.2793691 0.7939340 0.9377244 0.4590788
[22] 0.8824710 0.9717134 0.4938931 0.6788464 0.5171655 0.6139916 0.4859909
[29] 0.5576192 0.3635086 0.5888013 0.3917723 0.2013086 0.2517754 0.1441955
[36] 0.2129090
Function Value
[1] 0.4658235
Gradient:
[1] 0.0084232390 -0.0060346470 0.0053586753 -0.0173221544 -0.0085377145
[6] -0.0045181601 -0.0001186642 -0.0018418547 -0.0014973196 0.0012358541
[11] -0.0126235656 -0.0045965365 -0.0157491193 -0.0179486968 -0.0131015057
[16] -0.0016805863 0.0016955468 -0.0365689381 -0.0025803999 -0.0013496937
[21] -0.0136885951 -0.0020823414 -0.0032113370 -0.0096066337 -0.0028081857
[26] 0.0031841978 -0.0033046668 0.0046698538 -0.0004523883 -0.0322204912
[31] -0.0123242287 -0.0247856384 -0.0394861210 -0.0590863145 -0.0209003552
[36] 0.0225441958
iteration = 17
Step:
[1] 1.190607e-02 1.962068e-02 1.332835e-02 1.190712e-01 5.651518e-02
[6] 3.900852e-02 7.522835e-03 6.358755e-03 4.335885e-03 -5.425566e-03
[11] 4.683331e-03 -6.553502e-04 1.289826e-02 3.968855e-02 1.035006e-03
[16] 6.606240e-03 3.779343e-03 2.287294e-02 8.360705e-03 1.897412e-03
[21] -1.553619e-02 1.585626e-03 -1.552017e-03 6.484041e-03 1.280215e-03
[26] -9.948209e-04 3.403941e-03 -2.512523e-03 -9.749701e-05 1.210121e-02
[31] 5.016655e-03 -5.250360e-03 -2.003713e-02 1.015984e-02 -4.895357e-03
[36] -1.226547e-02
Parameter:
[1] 0.8526442 1.3022842 0.7709560 1.8252384 0.9081205 0.6276946 0.9324329
[8] 0.9436550 0.8596985 0.9190002 1.1348099 0.9858262 0.3354053 0.6855437
[15] 0.8202619 0.7127726 0.6906266 0.3022421 0.8022947 0.9396218 0.4435426
[22] 0.8840566 0.9701613 0.5003771 0.6801267 0.5161707 0.6173955 0.4834784
[29] 0.5575217 0.3756098 0.5938180 0.3865219 0.1812715 0.2619353 0.1393001
[36] 0.2006435
Function Value
[1] 0.4647371
Gradient:
[1] 0.0032741880 0.0319229396 0.0037579788 -0.0169923233 -0.0041686405
[6] -0.0015668249 0.0142427794 0.0151421382 0.0105584803 -0.0099084296
[11] 0.0055394580 -0.0059505290 0.0094272110 0.0045228639 -0.0016941790
[16] 0.0131318671 0.0150166919 0.0648713687 0.0138004950 -0.0045512003
[21] -0.0271342913 -0.0010943708 -0.0054745328 0.0097873496 0.0026359963
[26] 0.0039860240 0.0064189507 -0.0009673542 -0.0030468783 0.0179360846
[31] -0.0030659955 0.0296107387 -0.0228509158 0.0166531464 -0.0473004889
[36] -0.0130845095
iteration = 18
Step:
[1] -0.0003190154 -0.0002901824 0.0001327677 0.0330944194 0.0136185359
[6] 0.0091272205 -0.0068395374 -0.0051888681 -0.0037181494 0.0017215085
[11] -0.0034084348 0.0016003149 -0.0006258905 0.0060083489 -0.0004766189
[16] -0.0036006158 -0.0076332251 -0.0148838892 -0.0038684614 0.0075877484
[21] 0.0126013866 0.0046280273 0.0076147053 -0.0053796170 -0.0002638931
[26] -0.0032261774 -0.0024603100 -0.0050214471 0.0002150435 -0.0023161565
[31] 0.0036031075 -0.0008051534 -0.0071078409 0.0024425187 0.0032038571
[36] 0.0012990645
Parameter:
[1] 0.8523252 1.3019940 0.7710888 1.8583328 0.9217390 0.6368218 0.9255934
[8] 0.9384662 0.8559804 0.9207217 1.1314015 0.9874265 0.3347794 0.6915520
[15] 0.8197853 0.7091719 0.6829934 0.2873582 0.7984262 0.9472096 0.4561439
[22] 0.8886847 0.9777760 0.4949975 0.6798628 0.5129445 0.6149352 0.4784570
[29] 0.5577367 0.3732937 0.5974211 0.3857168 0.1741637 0.2643778 0.1425040
[36] 0.2019426
Function Value
[1] 0.4637526
Gradient:
[1] 0.0061461520 0.0089838118 0.0077211979 -0.0112251572 -0.0030730831
[6] -0.0011516441 0.0087572118 0.0081879818 0.0079076976 -0.0030774814
[11] 0.0040489390 0.0018117063 0.0057846634 -0.0023957334 0.0082583895
[16] 0.0003347864 -0.0050765010 -0.0016264785 0.0041294612 -0.0006473257
[21] -0.0069783468 0.0011689245 0.0012515962 -0.0015863861 0.0011719550
[26] -0.0045398849 0.0005687362 -0.0152702633 -0.0009078427 0.0074127797
[31] 0.0063986398 -0.0529344355 -0.1366345970 0.0161038223 -0.0235980195
[36] 0.1949483632
iteration = 19
Step:
[1] -0.0064542311 -0.0133863943 -0.0066817944 0.0055921175 0.0077264601
[6] 0.0039086723 -0.0123425613 -0.0085663485 -0.0085016483 0.0057159105
[11] -0.0044381274 0.0017169555 -0.0034333797 0.0030189192 -0.0067321718
[16] -0.0089870429 -0.0057927190 -0.0060739383 -0.0081772299 -0.0029637938
[21] 0.0090631194 -0.0041733209 0.0001165527 -0.0043740597 0.0002996121
[26] 0.0046056626 -0.0023345626 0.0061985196 -0.0002615859 -0.0116095120
[31] -0.0015047220 0.0042290667 0.0004745296 -0.0026247927 0.0040313879
[36] -0.0084415967
Parameter:
[1] 0.8458710 1.2886076 0.7644070 1.8639249 0.9294655 0.6407305 0.9132508
[8] 0.9298998 0.8474787 0.9264376 1.1269634 0.9891434 0.3313461 0.6945709
[15] 0.8130531 0.7001849 0.6772007 0.2812842 0.7902490 0.9442458 0.4652071
[22] 0.8845113 0.9778926 0.4906235 0.6801624 0.5175502 0.6126006 0.4846555
[29] 0.5574751 0.3616842 0.5959164 0.3899458 0.1746382 0.2617530 0.1465354
[36] 0.1935010
Function Value
[1] 0.4637351
Gradient:
[1] 0.0063338241 0.0053504775 0.0063304597 0.0029089396 -0.0041539110
[6] -0.0020173765 -0.0026695446 0.0006058336 -0.0015825208 0.0073038002
[11] -0.0159787089 0.0050688627 -0.0116393934 -0.0128712756 -0.0019136763
[16] -0.0077609563 -0.0122169048 -0.0288367268 -0.0047840025 0.0017367512
[21] 0.0301238501 0.0024975719 0.0037576946 -0.0100825268 -0.0011454055
[26] 0.0068485306 -0.0054616756 0.0012648727 0.0006460539 -0.0403705869
[31] 0.0050228941 0.0328474563 0.1106555096 -0.0221361098 -0.0011041088
[36] -0.1683079951
iteration = 20
Step:
[1] 5.825382e-04 -3.525786e-04 2.817743e-04 2.928849e-02 1.286762e-02
[6] 8.636039e-03 1.059454e-03 -1.603563e-03 -3.643244e-04 -3.667569e-03
[11] 3.157553e-03 -3.041700e-03 3.218513e-03 1.115678e-02 -1.811946e-03
[16] 5.617796e-03 7.583313e-03 6.269627e-03 3.792124e-03 2.735834e-03
[21] -1.119278e-02 1.044754e-03 -1.786850e-03 3.314424e-03 9.741435e-04
[26] -2.977076e-03 2.325560e-03 6.488505e-04 -5.450394e-04 9.362056e-03
[31] -4.332447e-03 -9.811320e-06 -4.112833e-03 2.253696e-03 -1.103024e-03
[36] 1.679702e-03
Parameter:
[1] 0.8464535 1.2882550 0.7646888 1.8932134 0.9423331 0.6493665 0.9143103
[8] 0.9282963 0.8471144 0.9227700 1.1301209 0.9861017 0.3345646 0.7057277
[15] 0.8112412 0.7058027 0.6847840 0.2875539 0.7940411 0.9469816 0.4540143
[22] 0.8855561 0.9761057 0.4939379 0.6811365 0.5145731 0.6149262 0.4853043
[29] 0.5569301 0.3710462 0.5915839 0.3899360 0.1705254 0.2640067 0.1454323
[36] 0.1951807
Function Value
[1] 0.4624658
Gradient:
[1] 0.0060274381 0.0054931040 0.0053603983 -0.0022879280 -0.0017387904
[6] -0.0005844143 0.0019146178 0.0002015277 0.0015881625 -0.0003374190
[11] -0.0011055019 -0.0025044358 -0.0015764066 -0.0054447824 -0.0013143442
[16] 0.0009482086 0.0017262529 -0.0046886548 0.0002556781 0.0009381047
[21] 0.0062966095 0.0010759358 0.0008084058 0.0002644285 0.0011665833
[26] -0.0012143389 0.0001374119 0.0056012617 -0.0012092620 0.0011023573
[31] -0.0052265996 -0.0009451782 0.0231076775 -0.0120534160 -0.0046212172
[36] -0.0255453649
iteration = 21
Step:
[1] -0.0031498984 -0.0045963377 -0.0024386150 0.0441785138 0.0206411588
[6] 0.0134125321 -0.0036847506 -0.0024371400 -0.0036771508 -0.0005779876
[11] 0.0006011947 0.0009225740 0.0008955921 0.0152381601 -0.0032001878
[16] -0.0003997782 -0.0005156318 0.0031677318 0.0007963247 0.0009166070
[21] -0.0054571502 -0.0002875816 -0.0012264353 -0.0014229308 -0.0005628938
[26] 0.0010576235 -0.0001527682 -0.0042233007 0.0009695610 -0.0006886701
[31] 0.0030936619 0.0035239016 -0.0082987840 0.0047471283 0.0002603165
[36] -0.0024492868
Parameter:
[1] 0.8433036 1.2836587 0.7622501 1.9373920 0.9629743 0.6627790 0.9106255
[8] 0.9258591 0.8434373 0.9221920 1.1307221 0.9870243 0.3354602 0.7209659
[15] 0.8080410 0.7054029 0.6842683 0.2907216 0.7948374 0.9478982 0.4485571
[22] 0.8852685 0.9748793 0.4925149 0.6805736 0.5156308 0.6147734 0.4810810
[29] 0.5578996 0.3703576 0.5946776 0.3934599 0.1622266 0.2687538 0.1456927
[36] 0.1927314
Function Value
[1] 0.4621288
Gradient:
[1] 4.906589e-03 1.021401e-02 5.134961e-03 -7.239384e-03 -9.899530e-04
[6] -2.594938e-04 1.846541e-03 2.961215e-03 1.372790e-03 -3.418528e-04
[11] 5.062683e-05 4.128253e-04 1.215710e-03 -3.354906e-03 8.589218e-04
[16] 2.032518e-03 1.357392e-03 5.443017e-03 1.715318e-03 -1.234856e-03
[21] -5.426841e-03 -1.001951e-03 -1.244519e-03 -3.442047e-04 3.249205e-04
[26] 2.754458e-03 -2.565237e-04 -7.571810e-03 6.857768e-04 -1.579490e-03
[31] 1.528544e-03 -5.350778e-03 -5.060993e-02 1.927646e-03 -3.521603e-03
[36] 3.360356e-02
iteration = 22
Step:
[1] -9.593541e-03 -1.590923e-02 -8.881403e-03 4.004505e-02 2.005048e-02
[6] 1.212172e-02 -8.848163e-03 -8.342836e-03 -7.647687e-03 -9.625687e-04
[11] -7.160060e-04 -1.115516e-05 -1.020582e-04 1.679095e-02 -7.224899e-03
[16] -2.565642e-03 -1.125816e-03 1.820964e-03 -9.444454e-04 2.183365e-03
[21] -4.960041e-03 2.499088e-04 7.399841e-04 -2.692328e-03 2.981555e-04
[26] -1.328686e-03 8.622692e-04 2.868268e-03 -3.360975e-04 9.863614e-04
[31] 1.056187e-03 9.134592e-03 -2.252701e-03 5.617026e-03 5.970171e-04
[36] 1.437093e-03
Parameter:
[1] 0.8337101 1.2677495 0.7533687 1.9774370 0.9830248 0.6749008 0.9017773
[8] 0.9175163 0.8357896 0.9212295 1.1300061 0.9870132 0.3353581 0.7377568
[15] 0.8008161 0.7028373 0.6831425 0.2925426 0.7938930 0.9500816 0.4435971
[22] 0.8855184 0.9756193 0.4898226 0.6808718 0.5143021 0.6156357 0.4839493
[29] 0.5575635 0.3713439 0.5957338 0.4025945 0.1599739 0.2743708 0.1462897
[36] 0.1941685
Function Value
[1] 0.4618409
Gradient:
[1] 1.835829e-03 4.132040e-03 2.631079e-03 -6.088225e-04 2.259661e-03
[6] 1.541082e-03 8.741594e-04 1.072426e-03 8.724541e-04 -1.764910e-03
[11] -4.730554e-04 8.902141e-04 7.267655e-03 1.595065e-03 5.480025e-04
[16] 1.683670e-03 -3.426592e-05 2.259291e-03 7.590231e-04 -5.950156e-04
[21] -5.027385e-03 -8.001741e-04 -7.331096e-04 -2.145661e-03 -1.521059e-04
[26] -9.628209e-04 1.368917e-03 1.684647e-03 -1.733866e-04 3.508841e-03
[31] 4.214591e-03 -1.651901e-02 -1.066742e-02 7.972560e-03 -1.042551e-03
[36] 6.178922e-02
iteration = 23
Step:
[1] -0.0086273271 -0.0148700961 -0.0088061224 0.0439100124 0.0194115625
[6] 0.0121372063 -0.0065612912 -0.0063615941 -0.0050637467 0.0014182471
[11] 0.0010539108 -0.0006796506 -0.0027750433 0.0172628692 -0.0037611213
[16] -0.0031047936 -0.0006511411 0.0019005013 -0.0017585277 0.0022895555
[21] -0.0009169787 0.0003759793 0.0013283464 0.0010479017 0.0006277529
[26] -0.0012027704 -0.0002075821 0.0008010023 -0.0003618854 -0.0001420625
[31] -0.0040360705 0.0030633897 -0.0096387825 0.0022065661 0.0011988956
[36] -0.0063986126
Parameter:
[1] 0.8250828 1.2528794 0.7445626 2.0213470 1.0024363 0.6870380 0.8952160
[8] 0.9111547 0.8307258 0.9226477 1.1310600 0.9863335 0.3325831 0.7550197
[15] 0.7970550 0.6997325 0.6824914 0.2944431 0.7921344 0.9523711 0.4426801
[22] 0.8858944 0.9769476 0.4908705 0.6814995 0.5130993 0.6154281 0.4847503
[29] 0.5572017 0.3712019 0.5916977 0.4056579 0.1503351 0.2765774 0.1474886
[36] 0.1877699
Function Value
[1] 0.4617251
Gradient:
[1] -0.0008845120 -0.0003347585 -0.0006376553 -0.0049166705 0.0011157470
[6] 0.0006642082 -0.0034970959 -0.0055062017 -0.0026517384 0.0002008775
[11] 0.0018420675 -0.0016552519 0.0015049935 -0.0021549873 0.0005035119
[16] 0.0010734098 0.0001591047 0.0011801831 -0.0009561241 -0.0002714842
[21] -0.0062642513 -0.0010156711 0.0002456737 0.0041640611 0.0000365965
[26] -0.0053660685 0.0005487735 0.0038759786 -0.0003295888 0.0046194515
[31] -0.0044538453 -0.0131299096 -0.0461829508 0.0037473491 0.0084233633
[36] 0.0177883521
iteration = 24
Step:
[1] -4.885761e-04 -2.365020e-03 -8.468853e-04 -9.752266e-03 -5.562397e-03
[6] -3.808688e-03 1.898205e-03 2.580177e-03 1.373878e-03 4.894905e-04
[11] 4.324068e-04 8.687006e-04 -2.022709e-03 -1.570547e-03 9.401783e-04
[16] -1.176093e-03 1.196459e-04 -5.307102e-04 -9.381877e-05 -1.077984e-03
[21] 1.448337e-03 -2.579899e-04 -3.851519e-04 -7.646463e-04 -9.874366e-05
[26] 2.843902e-03 -4.118639e-04 -2.922619e-03 4.352144e-04 -1.212352e-03
[31] 1.304783e-03 5.236674e-03 3.683178e-03 -2.087595e-03 2.542938e-04
[36] 2.826556e-03
Parameter:
[1] 0.8245942 1.2505144 0.7437157 2.0115948 0.9968739 0.6832293 0.8971143
[8] 0.9137349 0.8320997 0.9231372 1.1314924 0.9872022 0.3305603 0.7534491
[15] 0.7979952 0.6985564 0.6826110 0.2939124 0.7920406 0.9512931 0.4441285
[22] 0.8856364 0.9765625 0.4901059 0.6814008 0.5159432 0.6150163 0.4818277
[29] 0.5576369 0.3699895 0.5930025 0.4108946 0.1540183 0.2744898 0.1477429
[36] 0.1905964
Function Value
[1] 0.461632
Gradient:
[1] 9.093881e-04 2.545867e-03 2.360636e-04 -3.235705e-05 1.249362e-03
[6] 7.046808e-04 -2.995975e-03 -2.087408e-03 -2.832980e-03 1.082206e-03
[11] 1.548667e-03 1.947953e-05 3.763329e-03 -3.821938e-04 -2.467004e-05
[16] 3.483898e-04 1.202608e-03 2.150600e-04 -5.354970e-04 -1.775362e-04
[21] 1.000668e-03 -4.091838e-04 2.341167e-04 5.427374e-04 -5.575984e-05
[26] 3.026052e-03 -3.308287e-04 -5.456442e-03 7.868408e-04 -5.729675e-04
[31] -1.410086e-03 6.022379e-03 1.834136e-02 -4.114575e-04 1.140696e-02
[36] -1.773182e-02
iteration = 25
Step:
[1] 1.391171e-05 -1.706676e-04 2.072776e-04 4.630960e-04 -1.770650e-03
[6] -9.584864e-04 3.231833e-03 2.590215e-03 2.825577e-03 -6.790937e-05
[11] -7.825467e-04 9.119994e-04 -2.961023e-03 4.203233e-04 1.967011e-03
[16] -2.090203e-04 -9.304139e-04 -8.213827e-05 -2.440203e-05 1.974693e-05
[21] -1.391488e-04 2.504474e-04 -2.177721e-04 -2.697099e-04 -5.454196e-04
[26] -1.103886e-03 -7.885161e-05 3.310640e-03 4.499957e-05 -1.137412e-04
[31] 2.120388e-03 5.311179e-04 -1.372731e-04 -3.875476e-04 -1.425740e-03
[36] 3.447768e-04
Parameter:
[1] 0.8246081 1.2503437 0.7439230 2.0120578 0.9951033 0.6822708 0.9003461
[8] 0.9163251 0.8349253 0.9230693 1.1307099 0.9881142 0.3275993 0.7538695
[15] 0.7999622 0.6983474 0.6816806 0.2938302 0.7920162 0.9513129 0.4439893
[22] 0.8858868 0.9763447 0.4898362 0.6808554 0.5148393 0.6149374 0.4851383
[29] 0.5576819 0.3698758 0.5951229 0.4114257 0.1538810 0.2741023 0.1463171
[36] 0.1909412
Function Value
[1] 0.4615905
Gradient:
[1] 9.757954e-04 3.270161e-03 6.902781e-04 -3.389460e-04 8.386003e-04
[6] 5.093490e-04 -1.158622e-03 -8.447465e-04 -9.181100e-04 4.825651e-05
[11] -2.465273e-03 1.150241e-03 2.488974e-03 -8.799752e-04 -5.091501e-04
[16] 1.488694e-04 -4.243468e-04 -5.156267e-04 -5.396892e-04 -3.865068e-04
[21] 2.474216e-04 -4.956107e-04 -1.369784e-04 -1.831292e-03 -5.662777e-04
[26] -1.618474e-04 -2.530491e-04 4.273911e-03 4.894218e-04 -1.872678e-03
[31] 3.105946e-03 4.941519e-03 7.055764e-03 2.631236e-03 1.307825e-04
[36] -7.158931e-03
iteration = 26
Step:
[1] -2.088289e-03 -3.990933e-03 -1.785835e-03 6.244684e-03 5.705686e-04
[6] 4.177172e-04 1.964472e-03 1.636550e-03 1.777386e-03 2.183380e-04
[11] 9.040542e-04 7.679319e-05 -3.823775e-03 3.553154e-03 1.215111e-03
[16] -5.463998e-04 -3.723794e-04 9.454532e-04 1.684776e-04 8.173509e-04
[21] -6.394597e-04 6.376741e-04 1.999146e-04 7.528125e-04 1.346470e-04
[26] -8.707736e-05 1.978904e-04 -8.636442e-04 -3.519661e-04 2.766964e-04
[31] -7.344269e-04 6.978120e-04 -9.259570e-04 -7.940747e-04 -2.547619e-04
[36] -1.847992e-04
Parameter:
[1] 0.8225198 1.2463528 0.7421372 2.0183025 0.9956738 0.6826885 0.9023106
[8] 0.9179616 0.8367027 0.9232876 1.1316139 0.9881910 0.3237755 0.7574226
[15] 0.8011773 0.6978010 0.6813082 0.2947757 0.7921847 0.9521302 0.4433498
[22] 0.8865245 0.9765446 0.4905890 0.6809900 0.5147522 0.6151353 0.4842747
[29] 0.5573299 0.3701525 0.5943884 0.4121235 0.1529550 0.2733082 0.1460624
[36] 0.1907564
Function Value
[1] 0.461554
Gradient:
[1] -1.686580e-04 6.847300e-04 2.174261e-06 -6.844902e-05 6.319318e-04
[6] 3.849578e-04 -5.790319e-04 -6.206768e-04 -3.583729e-04 -2.438085e-04
[11] -9.177731e-04 5.475087e-04 9.610481e-04 -1.368441e-03 -3.613359e-04
[16] 2.845155e-04 -8.174190e-04 -4.388383e-04 -1.166178e-04 -2.671996e-05
[21] -5.936904e-04 -2.070877e-04 -1.270948e-04 -8.449490e-04 -1.008758e-04
[26] -4.369447e-04 4.039507e-04 1.426180e-03 -4.572414e-04 -6.875744e-04
[31] 1.329997e-03 -2.181096e-03 -2.237819e-04 2.446239e-03 -9.235883e-04
[36] 2.392184e-03
iteration = 27
Step:
[1] -2.510119e-03 -6.031006e-03 -2.465328e-03 9.465213e-03 1.089181e-03
[6] 7.483883e-04 2.620828e-03 2.331402e-03 2.283706e-03 6.806599e-04
[11] 8.962639e-04 5.410125e-05 -4.861537e-03 6.860176e-03 1.708138e-03
[16] -1.386752e-03 1.525583e-04 9.618377e-04 -4.681896e-05 7.865539e-04
[21] 2.066227e-04 7.639300e-04 4.605109e-04 1.241332e-03 7.492952e-05
[26] 1.341512e-05 -4.204107e-04 -3.369127e-04 3.242852e-04 8.693303e-05
[31] -1.028382e-03 3.712559e-03 -1.424170e-03 -2.116939e-03 -1.999311e-04
[36] 1.863516e-04
Parameter:
[1] 0.8200097 1.2403218 0.7396718 2.0277677 0.9967630 0.6834369 0.9049314
[8] 0.9202930 0.8389864 0.9239683 1.1325102 0.9882451 0.3189140 0.7642828
[15] 0.8028854 0.6964142 0.6814608 0.2957375 0.7921379 0.9529168 0.4435565
[22] 0.8872885 0.9770051 0.4918303 0.6810649 0.5147657 0.6147149 0.4839378
[29] 0.5576542 0.3702394 0.5933600 0.4158361 0.1515309 0.2711912 0.1458624
[36] 0.1909428
Function Value
[1] 0.4615367
Gradient:
[1] 1.684910e-04 1.916335e-04 1.127276e-05 7.966314e-05 -8.146728e-05
[6] -8.961720e-05 -1.189342e-04 -3.966996e-04 -2.812222e-04 2.671854e-04
[11] 1.380480e-04 -3.779519e-04 5.204477e-04 -1.441325e-03 -5.726299e-04
[16] -2.574758e-04 2.138059e-04 -1.309068e-04 2.717044e-04 1.830252e-04
[21] -5.259402e-04 1.687255e-04 1.464890e-04 7.707328e-04 1.874270e-04
[26] -6.035243e-04 -3.582130e-04 1.158860e-04 5.218439e-04 -1.383214e-04
[31] -1.014559e-03 -3.026202e-05 -8.630920e-03 -2.252477e-03 -8.125234e-04
[36] 6.904084e-03
iteration = 28
Step:
[1] -4.407722e-04 -9.176381e-04 -3.221423e-04 -1.977223e-03 -1.165949e-03
[6] -7.785845e-04 5.444335e-04 5.491149e-04 5.471523e-04 -1.689687e-04
[11] 2.009082e-05 2.171136e-04 -1.606241e-03 7.175124e-04 3.125654e-04
[16] -6.020327e-05 -1.576742e-04 2.820458e-04 -2.329972e-04 -2.629033e-04
[21] -3.089342e-05 -1.538684e-04 -2.131541e-04 -3.001620e-04 -2.079181e-04
[26] 2.364656e-04 1.085113e-04 -2.851771e-04 -2.825112e-04 1.751819e-04
[31] 4.922208e-04 -2.453281e-04 4.524757e-04 1.342745e-04 -1.340608e-04
[36] -4.269355e-05
Parameter:
[1] 0.8195689 1.2394041 0.7393497 2.0257905 0.9955971 0.6826583 0.9054758
[8] 0.9208422 0.8395335 0.9237993 1.1325303 0.9884622 0.3173078 0.7650003
[15] 0.8031980 0.6963540 0.6813031 0.2960196 0.7919049 0.9526539 0.4435256
[22] 0.8871346 0.9767920 0.4915301 0.6808570 0.5150021 0.6148234 0.4836526
[29] 0.5573717 0.3704146 0.5938523 0.4155907 0.1519833 0.2713255 0.1457284
[36] 0.1909001
Function Value
[1] 0.4615333
Gradient:
[1] -3.809895e-04 -8.260791e-04 -3.707541e-04 7.390409e-04 -8.174439e-05
[6] -8.284573e-05 2.146301e-04 2.820890e-04 2.007532e-04 -1.593357e-04
[11] 2.753413e-04 7.565504e-05 -1.012666e-04 -1.352820e-03 -3.314859e-04
[16] 1.093987e-04 1.692833e-04 -3.976197e-05 1.105036e-04 1.315392e-04
[21] 2.834888e-04 1.390781e-04 -1.290346e-05 -2.937561e-04 -7.521450e-05
[26] 1.975593e-04 2.778933e-05 -7.396643e-04 -2.826646e-04 4.126690e-04
[31] 5.835332e-05 -3.590443e-04 3.478199e-03 -2.596074e-04 -1.711516e-03
[36] -3.478597e-03
iteration = 29
Step:
[1] 2.899527e-04 5.549009e-04 3.415829e-04 -1.077619e-03 -1.299025e-04
[6] -6.593748e-05 -2.213982e-04 -2.202689e-04 -1.876886e-04 -9.718512e-05
[11] -1.739463e-04 -1.451842e-04 -8.253432e-05 6.287653e-04 -7.690945e-05
[16] 2.925388e-05 -1.309098e-04 -6.196701e-05 -2.354820e-05 -1.065685e-04
[21] 2.313320e-04 -6.323144e-05 -1.121282e-05 5.884180e-06 5.221993e-05
[26] -6.461159e-05 5.240091e-05 1.069742e-04 -2.586072e-05 -9.812776e-05
[31] -2.136571e-05 -7.683650e-06 1.167839e-04 3.987253e-05 1.059118e-04
[36] 1.208291e-04
Parameter:
[1] 0.8198589 1.2399590 0.7396913 2.0247129 0.9954672 0.6825924 0.9052544
[8] 0.9206219 0.8393458 0.9237021 1.1323563 0.9883170 0.3172252 0.7656291
[15] 0.8031211 0.6963833 0.6811722 0.2959576 0.7918813 0.9525473 0.4437569
[22] 0.8870714 0.9767808 0.4915360 0.6809092 0.5149375 0.6148758 0.4837596
[29] 0.5573458 0.3703164 0.5938309 0.4155830 0.1521001 0.2713654 0.1458343
[36] 0.1910209
Function Value
[1] 0.4615309
Gradient:
[1] -2.661906e-04 -2.873581e-04 -1.910330e-04 6.207901e-04 -6.862422e-05
[6] -7.927170e-05 1.833094e-04 1.658940e-04 1.833236e-04 -1.035865e-04
[11] 1.674458e-04 7.224088e-05 1.804352e-04 -1.182322e-03 -2.348095e-04
[16] 2.832934e-05 -1.030394e-04 1.574350e-04 7.270273e-05 5.464429e-05
[21] 2.310436e-04 9.100987e-05 -3.897327e-06 -1.387193e-04 -8.324008e-06
[26] 2.054534e-05 1.367191e-04 -3.450218e-04 -3.295426e-04 4.498801e-05
[31] 2.592415e-05 2.961613e-04 2.441265e-03 -1.923475e-04 -1.099362e-03
[36] -2.105519e-03
iteration = 30
Step:
[1] 7.394667e-04 9.610198e-04 8.202070e-04 -3.356673e-03 -3.667912e-04
[6] -1.290251e-04 -6.271391e-04 -5.104602e-04 -5.414105e-04 -3.638958e-04
[11] -7.871111e-04 -5.729448e-04 -2.079935e-03 4.971998e-03 -3.794950e-05
[16] 5.451791e-06 -9.967177e-05 -1.339692e-04 -1.735493e-04 -1.888437e-04
[21] 8.615360e-04 -1.184075e-04 4.214175e-05 -4.980854e-05 7.281031e-05
[26] -2.005243e-05 -1.247669e-04 2.078023e-04 3.011021e-04 -4.754218e-05
[31] 4.938932e-05 -4.820185e-05 2.239786e-04 -1.499818e-05 3.232822e-04
[36] 2.743906e-04
Parameter:
[1] 0.8205983 1.2409200 0.7405115 2.0213562 0.9951004 0.6824633 0.9046273
[8] 0.9201114 0.8388044 0.9233382 1.1315692 0.9877441 0.3151453 0.7706011
[15] 0.8030831 0.6963887 0.6810725 0.2958236 0.7917078 0.9523585 0.4446184
[22] 0.8869529 0.9768229 0.4914862 0.6809821 0.5149175 0.6147510 0.4839674
[29] 0.5576469 0.3702689 0.5938803 0.4155348 0.1523241 0.2713504 0.1461576
[36] 0.1912953
Function Value
[1] 0.4615243
Gradient:
[1] 1.517293e-04 5.032381e-04 2.583249e-04 1.546081e-04 -7.007017e-05
[6] -1.026912e-04 5.397283e-05 6.587797e-05 -3.787193e-05 2.285567e-04
[11] -2.079945e-04 5.148948e-05 7.499352e-04 -5.296670e-04 1.656488e-04
[16] -1.589200e-04 -2.611777e-04 2.478622e-04 -1.367653e-04 -6.741274e-05
[21] -2.859082e-04 1.144329e-05 1.101732e-04 2.664180e-05 1.721290e-05
[26] 1.313438e-05 -1.232401e-04 6.652101e-04 5.514345e-04 -2.015383e-04
[31] 1.879457e-04 1.255739e-03 -9.302461e-04 2.135181e-05 9.112817e-04
[36] 1.320988e-03
iteration = 31
Step:
[1] 1.884579e-04 6.115165e-06 2.183788e-04 -2.290585e-03 -2.938095e-04
[6] -3.108388e-05 -1.850612e-04 -1.944181e-04 -3.062229e-05 -4.529563e-04
[11] -4.593584e-04 -4.331353e-04 -3.328416e-03 6.101402e-03 1.879839e-04
[16] -9.342212e-05 -1.084315e-04 4.150072e-05 -1.196089e-04 -1.305973e-04
[21] 9.244166e-04 -1.316339e-04 -1.194198e-04 6.721304e-05 2.431545e-05
[26] -1.324038e-04 9.760876e-05 -6.018646e-05 -3.731509e-04 -6.318195e-05
[31] -3.958437e-05 4.175347e-05 7.661209e-05 -1.908992e-04 2.277594e-04
[36] 1.337982e-04
Parameter:
[1] 0.8207868 1.2409262 0.7407299 2.0190656 0.9948066 0.6824323 0.9044422
[8] 0.9199170 0.8387738 0.9228853 1.1311099 0.9873109 0.3118169 0.7767025
[15] 0.8032711 0.6962953 0.6809641 0.2958651 0.7915882 0.9522279 0.4455429
[22] 0.8868213 0.9767035 0.4915534 0.6810064 0.5147851 0.6148486 0.4839072
[29] 0.5572738 0.3702057 0.5938407 0.4155766 0.1524007 0.2711595 0.1463853
[36] 0.1914291
Function Value
[1] 0.4615204
Gradient:
[1] 2.572804e-04 6.481268e-04 3.832881e-04 -2.119594e-05 -1.400799e-04
[6] -1.624514e-04 2.320988e-05 -1.289031e-04 6.719247e-05 -4.011014e-06
[11] -1.441960e-04 4.324363e-05 5.914949e-04 -1.212754e-04 4.275300e-04
[16] -2.012008e-04 -3.326868e-04 3.389751e-04 -2.226734e-04 -1.516902e-04
[21] -3.806129e-04 -9.563905e-05 5.683987e-05 2.420073e-04 1.808331e-06
[26] -3.564828e-04 1.873062e-04 7.197194e-04 -3.862510e-04 -5.375753e-04
[31] 1.003464e-04 1.460034e-03 -1.501991e-03 2.940048e-04 2.076273e-03
[36] 1.555318e-03
iteration = 32
Step:
[1] -1.029674e-04 -1.919536e-04 -1.738451e-04 -9.105141e-04 1.396086e-04
[6] 2.645280e-04 -7.834744e-05 -1.852192e-05 -5.056159e-05 -9.057256e-05
[11] -2.794403e-04 -2.288481e-04 -2.640909e-03 4.848612e-03 1.655253e-04
[16] 2.991446e-05 2.760163e-05 3.253349e-05 1.994513e-05 1.110866e-04
[21] 6.297255e-04 3.281341e-05 -2.659853e-06 -3.392936e-05 2.648654e-05
[26] 1.421668e-04 -1.101262e-04 -1.249438e-04 4.237777e-04 1.700937e-04
[31] -4.916450e-06 -2.255495e-04 -7.499525e-05 -1.840099e-04 -3.902512e-05
[36] -7.070102e-05
Parameter:
[1] 0.8206838 1.2407342 0.7405560 2.0181551 0.9949462 0.6826968 0.9043639
[8] 0.9198985 0.8387232 0.9227947 1.1308304 0.9870821 0.3091760 0.7815511
[15] 0.8034366 0.6963252 0.6809917 0.2958977 0.7916081 0.9523390 0.4461726
[22] 0.8868541 0.9767008 0.4915195 0.6810329 0.5149272 0.6147385 0.4837822
[29] 0.5576975 0.3703758 0.5938358 0.4153510 0.1523257 0.2709755 0.1463463
[36] 0.1913584
Function Value
[1] 0.4615185
Gradient:
[1] 9.708145e-05 1.866304e-04 1.891571e-04 -6.674117e-05 -1.534630e-04
[6] -1.744702e-04 1.840306e-06 -6.409095e-06 -2.092548e-05 1.859384e-04
[11] -2.663364e-04 -1.067200e-04 2.910951e-04 1.230873e-04 4.961223e-04
[16] -6.378897e-05 -2.430234e-04 2.457021e-04 -1.867946e-04 -2.663469e-05
[21] -4.159553e-04 -2.154010e-05 1.060023e-04 5.860201e-05 -8.064660e-07
[26] 1.223910e-05 -2.813039e-05 4.807568e-04 7.225616e-04 -1.520561e-05
[31] 5.166356e-05 4.359819e-04 -8.482282e-04 4.289511e-04 1.825160e-03
[36] 7.440910e-04
iteration = 33
Step:
[1] -1.319904e-04 -1.331543e-04 -2.461272e-04 6.784299e-04 4.567580e-04
[6] 4.170148e-04 6.329399e-05 5.611362e-05 7.058375e-05 -1.327668e-06
[11] 2.211743e-04 1.603111e-04 -7.180657e-04 1.330265e-03 -1.818882e-05
[16] 2.377177e-05 1.776385e-04 -7.012265e-05 8.648212e-05 5.935114e-05
[21] 1.782418e-04 -1.029388e-05 -9.942425e-05 1.781805e-05 -1.760783e-05
[26] 3.692848e-05 -1.604135e-05 -9.441209e-05 -3.313731e-04 2.849066e-05
[31] 3.275821e-05 -6.611756e-05 -1.533715e-04 -1.124766e-04 -1.072348e-04
[36] -1.137328e-04
Parameter:
[1] 0.8205518 1.2406010 0.7403099 2.0188336 0.9954029 0.6831138 0.9044272
[8] 0.9199546 0.8387938 0.9227934 1.1310516 0.9872424 0.3084579 0.7828813
[15] 0.8034185 0.6963490 0.6811693 0.2958275 0.7916946 0.9523983 0.4463508
[22] 0.8868438 0.9766014 0.4915373 0.6810153 0.5149641 0.6147225 0.4836878
[29] 0.5573662 0.3704043 0.5938685 0.4152849 0.1521723 0.2708630 0.1462391
[36] 0.1912447
Function Value
[1] 0.4615179
Gradient:
[1] 6.769341e-05 -9.919010e-05 4.093437e-05 -3.054987e-06 -1.501590e-04
[6] -1.611795e-04 -1.135092e-05 -2.167155e-07 -2.558664e-05 -1.442331e-04
[11] -9.552940e-05 -6.076561e-05 1.022471e-05 5.470113e-05 3.249383e-04
[16] -2.150813e-05 5.576339e-05 -2.394884e-05 -1.068443e-04 1.000444e-05
[21] -2.875744e-04 -2.062706e-05 2.197709e-05 5.826450e-07 -4.522605e-05
[26] 6.859580e-05 -6.335199e-05 8.819256e-05 -1.810676e-04 7.613465e-05
[31] 1.027445e-04 2.550848e-06 -4.553300e-04 2.231140e-04 1.070934e-03
[36] 2.767564e-05
iteration = 34
Step:
[1] -8.658355e-05 9.218412e-05 -1.209802e-04 4.164366e-04 3.691433e-04
[6] 3.406695e-04 3.392886e-05 -1.964993e-06 4.881617e-05 2.032690e-04
[11] 2.537676e-04 1.940598e-04 -1.237922e-05 1.212243e-04 -1.237287e-04
[16] 6.287790e-05 3.363007e-05 -4.046225e-05 9.971063e-05 1.099875e-05
[21] 1.095631e-04 -1.268585e-05 -5.983658e-05 1.835429e-05 1.528434e-05
[26] -4.511845e-05 7.729600e-05 -2.680436e-05 6.262975e-05 -2.157100e-05
[31] -3.721541e-05 -7.886755e-05 -5.827163e-05 -3.023431e-05 -1.280176e-04
[36] -6.227695e-05
Parameter:
[1] 0.8204652 1.2406932 0.7401889 2.0192500 0.9957721 0.6834545 0.9044611
[8] 0.9199526 0.8388426 0.9229966 1.1313054 0.9874365 0.3084455 0.7830026
[15] 0.8032947 0.6964119 0.6812030 0.2957871 0.7917943 0.9524093 0.4464604
[22] 0.8868311 0.9765416 0.4915557 0.6810305 0.5149190 0.6147998 0.4836610
[29] 0.5574288 0.3703827 0.5938313 0.4152061 0.1521141 0.2708328 0.1461110
[36] 0.1911824
Function Value
[1] 0.4615176
Gradient:
[1] -3.030465e-05 -1.235997e-04 -6.103207e-05 9.441412e-05 -1.143405e-04
[6] -1.222737e-04 8.348877e-06 -4.775913e-05 5.067946e-05 -1.046523e-04
[11] -1.065558e-04 -9.644197e-05 -9.706014e-05 -1.465494e-05 1.356888e-04
[16] 3.662848e-05 6.110312e-05 -1.630696e-06 -6.039613e-06 2.103917e-05
[21] -4.029488e-05 -5.304202e-06 -2.109246e-05 1.137224e-05 -1.689315e-05
[26] -1.031815e-04 9.803003e-05 -1.426628e-04 -4.132517e-05 4.725109e-07
[31] -9.130474e-07 -1.405489e-04 3.825207e-04 1.392522e-04 3.026521e-04
[36] -5.374297e-04
iteration = 35
Step:
[1] 1.257063e-05 2.451553e-04 2.987749e-06 2.547690e-04 4.544404e-04
[6] 4.222353e-04 -4.521116e-05 -1.697200e-05 -7.601039e-05 2.213847e-04
[11] 3.024472e-04 2.559495e-04 1.595583e-04 7.986099e-05 -1.836473e-04
[16] 6.841748e-05 1.545493e-05 -7.977673e-05 7.048191e-05 1.473772e-05
[21] 1.062654e-04 -1.634283e-06 -1.241420e-05 -1.274874e-05 1.717349e-05
[26] 9.119769e-05 -5.050529e-05 7.160377e-05 -2.308865e-06 -4.220699e-06
[31] -1.024428e-05 -8.225467e-05 -5.548275e-05 -2.907448e-05 -1.180226e-04
[36] -4.500202e-05
Parameter:
[1] 0.8204778 1.2409384 0.7401919 2.0195048 0.9962265 0.6838767 0.9044159
[8] 0.9199357 0.8387666 0.9232180 1.1316078 0.9876924 0.3086051 0.7830824
[15] 0.8031111 0.6964803 0.6812184 0.2957073 0.7918648 0.9524241 0.4465667
[22] 0.8868295 0.9765292 0.4915429 0.6810477 0.5150102 0.6147493 0.4837326
[29] 0.5574265 0.3703785 0.5938211 0.4151238 0.1520586 0.2708037 0.1459930
[36] 0.1911374
Function Value
[1] 0.4615174
Gradient:
[1] -6.305001e-05 -4.173000e-05 -8.441958e-05 9.230877e-05 -5.641354e-05
[6] -6.446399e-05 -1.055511e-05 2.814105e-05 -3.092993e-05 -9.753975e-05
[11] -5.571719e-05 -7.300827e-05 -3.828049e-05 -2.041389e-05 6.483702e-06
[16] 5.056222e-05 1.462652e-05 -3.981526e-05 4.823875e-05 3.369038e-05
[21] 5.682210e-05 2.681233e-05 -1.193712e-05 -3.687717e-05 7.673862e-07
[26] 1.244835e-04 -4.622080e-05 -8.138556e-05 -5.756817e-05 6.347989e-05
[31] -1.606537e-05 -1.545288e-04 3.475442e-04 -1.913492e-05 -2.128964e-04
[36] -3.317133e-04
iteration = 36
Step:
[1] 6.032324e-05 8.385407e-05 7.589694e-05 -2.101970e-04 1.437048e-04
[6] 1.667830e-04 -2.845169e-05 -4.400560e-05 -1.356974e-05 1.336606e-04
[11] 1.356022e-04 1.323709e-04 -2.527306e-05 1.427352e-04 -1.270574e-04
[16] -3.525758e-06 2.044913e-05 -1.901025e-05 -7.281479e-06 -3.973116e-05
[21] 7.847080e-05 -3.736089e-05 -2.336592e-05 5.574602e-06 1.013287e-05
[26] -5.791578e-05 2.764788e-05 2.984279e-05 2.676731e-05 -3.593401e-05
[31] 3.296270e-06 7.981923e-06 1.448365e-05 2.264073e-06 -2.055565e-05
[36] 1.776803e-05
Parameter:
[1] 0.8205381 1.2410222 0.7402678 2.0192946 0.9963702 0.6840435 0.9043874
[8] 0.9198917 0.8387531 0.9233517 1.1317434 0.9878248 0.3085798 0.7832252
[15] 0.8029840 0.6964768 0.6812389 0.2956883 0.7918575 0.9523843 0.4466451
[22] 0.8867921 0.9765058 0.4915485 0.6810578 0.5149523 0.6147769 0.4837625
[29] 0.5574533 0.3703426 0.5938244 0.4151318 0.1520731 0.2708060 0.1459725
[36] 0.1911552
Function Value
[1] 0.4615174
Gradient:
[1] -1.344347e-05 2.841834e-05 -3.323208e-05 6.325512e-05 -2.443912e-05
[6] -3.144507e-05 -7.034373e-07 -2.261302e-05 1.481482e-06 -2.631850e-05
[11] -5.604954e-05 -3.011280e-05 -5.446310e-06 -6.401990e-06 -3.884537e-05
[16] 1.955058e-05 4.826006e-05 -3.989342e-05 3.953105e-05 3.549161e-06
[21] 6.818013e-05 7.013057e-06 -1.996625e-05 4.966694e-06 1.743317e-05
[26] -4.074607e-05 1.928768e-05 -6.273737e-05 2.368239e-05 -2.971490e-05
[31] 8.217427e-06 -1.244160e-05 2.327276e-04 -2.780709e-05 -2.020961e-04
[36] -1.459455e-04
iteration = 37
Step:
[1] 1.305382e-05 -3.433195e-05 4.111206e-05 -2.597650e-04 -4.960021e-06
[6] 3.136305e-05 -4.387602e-06 6.773762e-06 -8.113641e-07 5.000533e-05
[11] 5.938917e-05 5.156199e-05 -7.655118e-05 9.682753e-05 -3.670830e-05
[16] -1.810758e-05 -4.173174e-05 2.543222e-05 -2.994590e-05 -1.295670e-05
[21] 3.496107e-05 -9.530372e-06 1.140186e-05 -2.229449e-06 -8.759535e-06
[26] 1.133335e-05 -6.858820e-06 3.231107e-05 -1.157291e-05 -1.066970e-05
[31] -1.706243e-05 2.732574e-05 2.362712e-05 -4.793852e-06 5.444463e-06
[36] 2.454124e-05
Parameter:
[1] 0.8205512 1.2409879 0.7403089 2.0190348 0.9963653 0.6840749 0.9043830
[8] 0.9198984 0.8387523 0.9234017 1.1318028 0.9878763 0.3085033 0.7833220
[15] 0.8029473 0.6964586 0.6811971 0.2957137 0.7918276 0.9523714 0.4466801
[22] 0.8867826 0.9765172 0.4915463 0.6810491 0.5149636 0.6147701 0.4837948
[29] 0.5574417 0.3703319 0.5938073 0.4151591 0.1520967 0.2708012 0.1459779
[36] 0.1911797
Function Value
[1] 0.4615173
Gradient:
[1] -5.947243e-06 4.947796e-05 -1.165290e-06 2.833676e-05 -1.117684e-05
[6] -1.603340e-05 -5.559997e-06 -2.756906e-06 -1.485034e-06 4.618528e-07
[11] -1.689402e-05 -1.003286e-05 1.580247e-05 1.062972e-05 -1.540457e-05
[16] 9.219292e-06 -1.126210e-05 4.035883e-06 1.430678e-05 -1.886491e-06
[21] 3.889866e-05 5.101697e-06 -1.460165e-06 3.304024e-06 2.337686e-06
[26] 3.694822e-07 9.549694e-06 1.227107e-05 4.806822e-06 -2.830092e-05
[31] -1.535483e-05 3.084821e-05 7.730350e-05 -3.232969e-06 -5.302780e-05
[36] -7.815970e-08
iteration = 38
Step:
[1] -1.466794e-06 -6.068012e-05 3.929093e-06 -1.453976e-04 -3.170783e-05
[6] -7.094035e-06 1.154376e-05 8.412202e-06 7.826414e-06 1.287737e-05
[11] 1.576615e-05 1.915285e-05 -3.444857e-05 -1.158977e-05 -3.732864e-06
[16] -1.822101e-05 -2.194031e-06 1.551037e-05 -1.770750e-05 -4.130408e-06
[21] -4.193722e-06 -5.959812e-06 1.442982e-06 1.408837e-06 6.169865e-07
[26] -3.296365e-06 -8.264141e-06 1.442517e-06 -2.611337e-06 2.169906e-06
[31] 6.659287e-06 1.863238e-05 1.500806e-05 -3.349694e-06 4.591087e-06
[36] 1.224908e-05
Parameter:
[1] 0.8205497 1.2409272 0.7403128 2.0188894 0.9963336 0.6840678 0.9043946
[8] 0.9199068 0.8387601 0.9234146 1.1318186 0.9878955 0.3084688 0.7833104
[15] 0.8029436 0.6964404 0.6811950 0.2957292 0.7918099 0.9523672 0.4466759
[22] 0.8867767 0.9765186 0.4915477 0.6810497 0.5149603 0.6147618 0.4837962
[29] 0.5574391 0.3703341 0.5938140 0.4151777 0.1521117 0.2707978 0.1459825
[36] 0.1911919
Function Value
[1] 0.4615173
Gradient:
[1] 6.529888e-06 1.733517e-05 9.425349e-06 8.330593e-06 -6.473044e-06
[6] -9.482193e-06 7.105427e-08 -3.396394e-06 -4.025225e-06 7.407408e-06
[11] 1.635389e-06 7.833734e-06 1.147882e-05 1.083933e-05 -7.425172e-07
[16] -1.588063e-06 -5.826450e-07 -3.147704e-06 -3.446132e-07 -1.463718e-06
[21] 1.740830e-06 1.090683e-06 2.103206e-06 4.511946e-06 5.744738e-06
[26] -5.080381e-06 -5.105250e-06 1.378808e-05 2.987832e-06 -7.645440e-06
[31] 6.082246e-06 1.461586e-05 4.249046e-06 2.053469e-06 2.331646e-05
[36] 2.054890e-05
iteration = 39
Step:
[1] -1.209704e-05 -3.599733e-05 -1.243049e-05 -6.384901e-05 -1.886667e-05
[6] -5.463394e-06 6.838973e-06 8.199442e-06 8.851570e-06 2.380335e-07
[11] 2.356273e-06 2.269548e-07 -8.123484e-06 -3.737175e-05 4.800199e-06
[16] -6.081494e-06 -3.066186e-06 8.617050e-06 -5.002454e-06 -4.752413e-07
[21] -6.591348e-07 -1.359839e-06 6.735955e-08 -1.281069e-06 -5.983060e-06
[26] 2.099469e-06 2.743896e-06 -2.523929e-06 -1.291849e-06 1.817374e-06
[31] -3.526539e-06 1.087329e-05 7.374724e-06 -1.182675e-06 -6.758986e-07
[36] 5.849923e-06
Parameter:
[1] 0.8205376 1.2408912 0.7403004 2.0188256 0.9963147 0.6840623 0.9044014
[8] 0.9199150 0.8387689 0.9234148 1.1318209 0.9878957 0.3084607 0.7832730
[15] 0.8029484 0.6964343 0.6811919 0.2957378 0.7918049 0.9523668 0.4466752
[22] 0.8867753 0.9765187 0.4915464 0.6810437 0.5149624 0.6147645 0.4837937
[29] 0.5574378 0.3703359 0.5938105 0.4151886 0.1521191 0.2707966 0.1459818
[36] 0.1911978
Function Value
[1] 0.4615173
Gradient:
[1] 4.583001e-06 1.196748e-06 5.730527e-06 3.449193e-06 -4.796163e-06
[6] -6.426859e-06 -1.495692e-06 1.165290e-06 1.172396e-06 5.886847e-06
[11] 6.406569e-06 5.517364e-06 1.584510e-06 4.213518e-06 -1.335820e-06
[16] -1.037392e-06 -1.026734e-06 8.775203e-07 -4.064304e-06 5.968559e-07
[21] -2.216893e-06 9.379164e-07 3.023359e-06 -3.581135e-06 -3.577583e-06
[26] 1.673328e-06 2.163603e-06 5.776712e-06 -7.034373e-07 -7.105427e-08
[31] -2.195577e-06 1.421085e-07 -1.232792e-06 7.094769e-06 1.922018e-05
[36] 4.085621e-06
iteration = 40
Step:
[1] -8.408480e-06 -1.153472e-05 -9.465225e-06 -3.094277e-05 -5.373911e-06
[6] 1.638162e-06 3.832465e-06 1.812902e-06 1.341555e-06 -3.715673e-06
[11] -3.104479e-06 -3.338927e-06 2.142687e-06 -2.459210e-05 6.520438e-06
[16] -8.241349e-07 7.494898e-08 1.299549e-06 2.055524e-06 -1.146624e-06
[21] 6.547305e-07 -1.545185e-06 -2.713882e-06 2.804540e-06 1.954137e-06
[26] -1.856586e-07 -1.745532e-06 -2.609388e-06 2.610070e-07 1.191042e-06
[31] 1.851865e-06 4.013246e-06 3.833502e-06 -2.229399e-06 -1.546529e-06
[36] 2.612173e-06
Parameter:
[1] 0.8205292 1.2408797 0.7402909 2.0187946 0.9963093 0.6840639 0.9044053
[8] 0.9199169 0.8387703 0.9234111 1.1318178 0.9878924 0.3084628 0.7832484
[15] 0.8029549 0.6964335 0.6811920 0.2957391 0.7918069 0.9523656 0.4466759
[22] 0.8867738 0.9765160 0.4915492 0.6810457 0.5149623 0.6147628 0.4837911
[29] 0.5574380 0.3703371 0.5938123 0.4151926 0.1521229 0.2707944 0.1459803
[36] 0.1912004
Function Value
[1] 0.4615173
Gradient:
[1] 1.374900e-06 -4.085587e-06 1.715961e-06 2.150499e-06 -3.375078e-06
[6] -4.266809e-06 -4.902745e-07 -8.562040e-07 -1.453060e-06 3.019807e-06
[11] 5.656378e-06 4.337863e-06 -2.096101e-06 5.790923e-07 -7.212009e-07
[16] -1.136868e-07 -1.126210e-06 1.776357e-06 -1.350031e-06 1.126210e-06
[21] -2.298606e-06 6.252776e-07 1.087130e-06 9.166001e-07 3.765876e-07
[26] -6.572520e-07 -2.614797e-06 -7.069900e-07 -1.115552e-06 1.623590e-06
[31] 6.288303e-07 -5.247358e-06 7.446488e-06 2.486900e-06 4.888534e-06
[36] -9.030998e-06
iteration = 41
Step:
[1] -4.470553e-06 -1.291806e-06 -5.622677e-06 -1.552752e-05 3.710047e-06
[6] 7.394137e-06 7.177526e-07 6.489473e-07 1.005105e-06 -5.727716e-06
[11] -6.435736e-06 -6.478358e-06 3.424513e-06 -1.046808e-05 4.351634e-06
[16] 4.677933e-07 1.863346e-06 -2.073116e-06 1.877437e-06 -9.905281e-07
[21] 2.800664e-06 -1.007088e-06 -1.647866e-06 -7.538384e-07 -2.639127e-07
[26] 8.377115e-07 2.233524e-06 -1.872656e-06 7.278887e-07 1.208137e-06
[31] 2.110375e-07 2.589138e-06 1.135522e-06 -1.235421e-06 -3.644323e-07
[36] 1.335347e-06
Parameter:
[1] 0.8205247 1.2408784 0.7402853 2.0187791 0.9963130 0.6840713 0.9044060
[8] 0.9199175 0.8387713 0.9234054 1.1318114 0.9878859 0.3084663 0.7832380
[15] 0.8029593 0.6964340 0.6811938 0.2957371 0.7918088 0.9523646 0.4466787
[22] 0.8867727 0.9765143 0.4915485 0.6810454 0.5149631 0.6147650 0.4837892
[29] 0.5574388 0.3703383 0.5938125 0.4151952 0.1521241 0.2707932 0.1459799
[36] 0.1912017
Function Value
[1] 0.4615173
Gradient:
[1] 6.146195e-07 -3.275345e-06 -3.694822e-07 -4.047615e-08 -1.957545e-06
[6] -2.337686e-06 -7.815970e-07 -4.405365e-07 2.842171e-08 -2.344791e-07
[11] 1.855127e-06 5.115908e-07 -2.138734e-06 -9.556800e-07 -4.259704e-06
[16] -3.126388e-07 5.009326e-07 -1.062261e-06 3.907985e-08 9.663381e-07
[21] -2.032152e-06 6.785683e-07 2.025047e-07 -2.646772e-06 -5.329071e-08
[26] 1.048051e-06 1.765699e-06 -3.694822e-06 -4.085621e-07 2.586376e-06
[31] -4.227729e-07 -2.650324e-06 -3.197442e-06 -1.087130e-06 -8.910206e-06
[36] -5.382361e-06
iteration = 42
Step:
[1] -1.233237e-06 2.960946e-06 -8.994970e-07 -3.500689e-06 5.702015e-06
[6] 6.919623e-06 2.140612e-07 2.557013e-07 -1.861410e-07 -3.172214e-06
[11] -4.570141e-06 -3.976887e-06 -2.333266e-08 1.465113e-06 3.858378e-06
[16] 1.082904e-06 6.541771e-07 -7.761991e-07 1.000529e-06 -1.102142e-06
[21] 2.992900e-06 -1.158435e-06 -1.192494e-06 1.570654e-06 -8.303064e-08
[26] -3.196708e-07 -1.084279e-06 1.628584e-08 1.268876e-07 -3.989030e-07
[31] 2.159552e-07 3.248987e-07 1.687393e-07 -8.975178e-07 5.667488e-07
[36] 4.484801e-07
Parameter:
[1] 0.8205235 1.2408814 0.7402844 2.0187756 0.9963187 0.6840782 0.9044062
[8] 0.9199178 0.8387711 0.9234022 1.1318068 0.9878819 0.3084662 0.7832394
[15] 0.8029631 0.6964351 0.6811945 0.2957363 0.7918098 0.9523635 0.4466817
[22] 0.8867716 0.9765132 0.4915500 0.6810453 0.5149628 0.6147639 0.4837892
[29] 0.5574389 0.3703379 0.5938127 0.4151955 0.1521242 0.2707923 0.1459805
[36] 0.1912022
Function Value
[1] 0.4615173
Gradient:
[1] -4.263256e-07 -7.730253e-08 -9.556800e-07 -7.567294e-08 -9.485746e-07
[6] -1.111999e-06 -1.268319e-06 -9.308110e-07 -1.197265e-06 -4.014566e-07
[11] -3.233145e-07 -3.623768e-07 -1.438849e-06 -9.947598e-07 -1.925571e-06
[16] 3.019807e-07 5.080381e-07 1.307399e-06 7.922552e-07 1.598721e-07
[21] 2.948752e-07 1.421085e-07 -4.440892e-07 9.627854e-07 -1.953993e-07
[26] -2.593481e-07 -9.201528e-07 -1.758593e-06 -2.877698e-07 -7.851497e-07
[31] -4.405365e-07 -7.105427e-08 -2.525979e-06 -1.069367e-06 -9.141132e-06
[36] 1.030287e-07
iteration = 43
Parameter:
[1] 0.8205236 1.2408818 0.7402846 2.0187766 0.9963197 0.6840792 0.9044064
[8] 0.9199179 0.8387712 0.9234020 1.1318065 0.9878817 0.3084662 0.7832402
[15] 0.8029633 0.6964351 0.6811944 0.2957362 0.7918098 0.9523635 0.4466818
[22] 0.8867715 0.9765132 0.4915500 0.6810454 0.5149628 0.6147640 0.4837892
[29] 0.5574389 0.3703379 0.5938128 0.4151955 0.1521240 0.2707922 0.1459806
[36] 0.1912021
Function Value
[1] 0.4615173
Gradient:
[1] -4.121148e-07 9.448084e-08 -8.419931e-07 -1.460663e-07 -8.597567e-07
[6] -1.008971e-06 -1.119105e-06 -8.810730e-07 -1.083578e-06 -4.298784e-07
[11] -3.672602e-07 -3.907985e-07 -1.200817e-06 -8.526513e-07 -1.847411e-06
[16] 2.486900e-07 3.659295e-07 1.083578e-06 7.744916e-07 1.172396e-07
[21] 1.776357e-07 1.350031e-07 -4.192202e-07 8.100187e-07 -4.263256e-08
[26] -2.309264e-07 -7.318590e-07 -1.559641e-06 -2.522427e-07 -6.998846e-07
[31] -3.694822e-07 2.167155e-07 -2.788880e-06 -1.111999e-06 -8.395062e-06
[36] 3.588241e-07
Successive iterates within tolerance.
Current iterate is probably solution.We can safely ignore the warning messages again in this case, as explained above.
Check the code first to see if the minimization terminated normally (see the help page for the meaning of different code):
f_ml_min$code[1] 2Compare with lavaan Output
mod_sem <-
"
f1 =~ x1 + x2 + x3 + x4
f2 =~ x5 + x6 + x7 + x8
f3 =~ x9 + x10 + x11 + x12
f4 =~ x13 + x14 + x15 + x16
f3 ~ f1 + f2
f4 ~ f3
"
fit_sem <- sem(model = mod_sem,
data = dat)
summary(fit_sem)lavaan 0.6-19 ended normally after 49 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 36
Number of observations 400
Model Test User Model:
Test statistic 184.607
Degrees of freedom 100
P-value (Chi-square) 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
f1 =~
x1 1.000
x2 0.821 0.095 8.647 0.000
x3 1.241 0.114 10.933 0.000
x4 0.740 0.095 7.770 0.000
f2 =~
x5 1.000
x6 2.019 0.333 6.063 0.000
x7 0.996 0.204 4.884 0.000
x8 0.684 0.179 3.831 0.000
f3 =~
x9 1.000
x10 0.904 0.084 10.703 0.000
x11 0.920 0.079 11.618 0.000
x12 0.839 0.079 10.556 0.000
f4 =~
x13 1.000
x14 0.923 0.082 11.306 0.000
x15 1.132 0.085 13.261 0.000
x16 0.988 0.086 11.516 0.000
Regressions:
Estimate Std.Err z-value P(>|z|)
f3 ~
f1 0.308 0.143 2.151 0.031
f2 0.783 0.271 2.890 0.004
f4 ~
f3 0.803 0.076 10.600 0.000
Covariances:
Estimate Std.Err z-value P(>|z|)
f1 ~~
f2 0.191 0.037 5.142 0.000
Variances:
Estimate Std.Err z-value P(>|z|)
.x1 0.696 0.058 12.028 0.000
.x2 0.681 0.054 12.725 0.000
.x3 0.296 0.044 6.698 0.000
.x4 0.792 0.060 13.166 0.000
.x5 0.952 0.071 13.357 0.000
.x6 0.447 0.073 6.112 0.000
.x7 0.887 0.067 13.304 0.000
.x8 0.977 0.071 13.789 0.000
.x9 0.492 0.044 11.085 0.000
.x10 0.681 0.055 12.354 0.000
.x11 0.515 0.044 11.682 0.000
.x12 0.615 0.049 12.440 0.000
.x13 0.484 0.042 11.443 0.000
.x14 0.557 0.046 12.161 0.000
.x15 0.370 0.039 9.603 0.000
.x16 0.594 0.049 12.010 0.000
f1 0.415 0.068 6.069 0.000
f2 0.152 0.046 3.310 0.001
.f3 0.271 0.043 6.312 0.000
.f4 0.146 0.029 4.954 0.000Compare the parameter estimates from the two methods:
round(f_ml_min$estimate, 3) [1] 0.821 1.241 0.740 2.019 0.996 0.684 0.904 0.920 0.839 0.923 1.132 0.988
[13] 0.308 0.783 0.803 0.696 0.681 0.296 0.792 0.952 0.447 0.887 0.977 0.492
[25] 0.681 0.515 0.615 0.484 0.557 0.370 0.594 0.415 0.152 0.271 0.146 0.191coef(fit_sem) f1=~x2 f1=~x3 f1=~x4 f2=~x6 f2=~x7 f2=~x8 f3=~x10 f3=~x11
0.821 1.241 0.740 2.019 0.996 0.684 0.904 0.920
f3=~x12 f4=~x14 f4=~x15 f4=~x16 f3~f1 f3~f2 f4~f3 x1~~x1
0.839 0.923 1.132 0.988 0.308 0.783 0.803 0.696
x2~~x2 x3~~x3 x4~~x4 x5~~x5 x6~~x6 x7~~x7 x8~~x8 x9~~x9
0.681 0.296 0.792 0.952 0.447 0.887 0.977 0.492
x10~~x10 x11~~x11 x12~~x12 x13~~x13 x14~~x14 x15~~x15 x16~~x16 f1~~f1
0.681 0.515 0.615 0.484 0.557 0.370 0.594 0.415
f2~~f2 f3~~f3 f4~~f4 f1~~f2
0.152 0.271 0.146 0.191 Compute the differences:
f_ml_min$estimate - coef(fit_sem) f1=~x2 f1=~x3 f1=~x4 f2=~x6 f2=~x7 f2=~x8 f3=~x10 f3=~x11
0 0 0 0 0 0 0 0
f3=~x12 f4=~x14 f4=~x15 f4=~x16 f3~f1 f3~f2 f4~f3 x1~~x1
0 0 0 0 0 0 0 0
x2~~x2 x3~~x3 x4~~x4 x5~~x5 x6~~x6 x7~~x7 x8~~x8 x9~~x9
0 0 0 0 0 0 0 0
x10~~x10 x11~~x11 x12~~x12 x13~~x13 x14~~x14 x15~~x15 x16~~x16 f1~~f1
0 0 0 0 0 0 0 0
f2~~f2 f3~~f3 f4~~f4 f1~~f2
0 0 0 0 Compare the values of the discrepancy function:
lavInspect(fit_sem, "optim")$fx[1] 0.2307587f_ml_min$minimum / 2[1] 0.2307587