MTS time series simulation
2024-07-25
Simulating time series data based on an existing dataset
To use MTS package to simulate data for 1 individual based on existing data. We’ll make the dataset smaller to 50 individuals to speed things up.
# Get the first 50 unique IDs
first_50_ids <- unique(pingemadata$pid)[1:50]
# Subset the data set
subset_data <- pingemadata[pingemadata$pid %in% first_50_ids, ]
# Format data frame as list with each individual's data new list
split_subset_data <- subset_data %>% group_split(pid)Now we are going to create a function so that we can do the above for all 50 individuals in the subset data. This requires us to run the VARMA model for each individual and simulate data based on the model fit. We also create a list of the results of ‘fit’ incase we need to analyse or explore the model parameters for each individual. We then add some noise using mvrnorm function and add that to the simulated data.
# Split data by ID to get each individual's data
rawemadata <- split(subset_data, subset_data$pid)
simulate_individual <- function(rawemadata) {
# Remove ID and time columns for fitting
individual_matrix <- as.matrix(rawemadata[, -1])
# Fit VARMA model
fit <- VARMA(individual_matrix, p = 1, q = 1)
# Extract AR and MA coefficients
phi <- fit$Phi
theta <- fit$Theta
# Extract sigma matrix (covariance matrix of the residuals)
sigma <- fit$Sigma
# Simulate new data using extracted parameters
set.seed(1234)
sim_data <- VARMAsim(n = 100, arlags = c(1), malags = c(1),
phi = phi, theta = theta, sigma = sigma)
simulated_series <- sim_data$series
# Generate random noise (innovations) from a multivariate normal distribution
set.seed(1234)
random_noise <- mvrnorm(n = nrow(simulated_series), mu = rep(0, ncol(simulated_series)), Sigma = sigma)
# Add the generated noise to the simulated data
noisy_simulated_series <- simulated_series + random_noise
# Return both the fit object and the noisy simulated series
return(list(fit = fit, noisy_simulated_series = noisy_simulated_series))
}
# Loop through each individual's data and simulate new data
simulated_data_list <- lapply(rawemadata, simulate_individual)## Number of parameters: 10
## initial estimates: 5.2802 1.2883 -0.4914 0.3974 -0.3627 0.6282 0.4511 -0.2443 0.1814 -0.3976
## Par. lower-bounds: 4.6342 0.475 -0.6234 0.2775 -0.5288 0.4772 0.3059 -0.3726 -0.0013 -0.5592
## Par. upper-bounds: 5.9263 2.1017 -0.3595 0.5173 -0.1966 0.7792 0.5962 -0.1159 0.3641 -0.236
## Final Estimates: 5.766733 1.267958 -0.6233543 0.3319825 -0.3568218 0.6610428 0.5271596 -0.1158981 0.1418942 -0.4142125## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 5.7667 NaN NaN NaN
## loneliness_state_pmc 1.2680 NaN NaN NaN
## depressedmood_state -0.6234 NaN NaN NaN
## loneliness_state_pmc 0.3320 NaN NaN NaN
## depressedmood_state -0.3568 NaN NaN NaN
## loneliness_state_pmc 0.6610 0.1294 5.107 3.28e-07 ***
## 0.5272 NaN NaN NaN
## -0.1159 NaN NaN NaN
## 0.1419 NaN NaN NaN
## -0.4142 0.1329 -3.116 0.00184 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 5.766733 1.267958
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] -0.623 0.332
## [2,] -0.357 0.661
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] -0.527 0.116
## [2,] -0.142 0.414
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 67.89343 21.3770
## [2,] 21.37700 110.0128
## ----
## aic= 8.869688
## bic= 8.907147
## Number of parameters: 10
## initial estimates: 9.1642 -9.2919 0.4397 -0.201 0.5723 -0.0138 -0.3055 0.2777 -0.2962 0.1294
## Par. lower-bounds: 6.2254 -13.3562 0.2616 -0.3056 0.3261 -0.1584 -0.4975 0.1604 -0.5618 -0.0327
## Par. upper-bounds: 12.103 -5.2275 0.6177 -0.0965 0.8186 0.1308 -0.1135 0.3949 -0.0307 0.2915
## Final Estimates: 11.32749 -13.34286 0.3044601 -0.3055557 0.8185598 -0.1583673 -0.1135141 0.336812 -0.5037556 0.2664415## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 11.32749 0.38652 29.306 < 2e-16 ***
## loneliness_state_pmc -13.34286 NaN NaN NaN
## depressedmood_state 0.30446 0.01715 17.757 < 2e-16 ***
## loneliness_state_pmc -0.30556 NaN NaN NaN
## depressedmood_state 0.81856 NaN NaN NaN
## loneliness_state_pmc -0.15837 0.02254 -7.025 2.15e-12 ***
## -0.11351 NaN NaN NaN
## 0.33681 NaN NaN NaN
## -0.50376 NaN NaN NaN
## 0.26644 0.04826 5.521 3.36e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 11.32749 -13.34286
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.304 -0.306
## [2,] 0.819 -0.158
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.114 -0.337
## [2,] 0.504 -0.266
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 71.47679 58.7461
## [2,] 58.74610 136.3636
## ----
## aic= 8.761913
## bic= 8.799371
## Number of parameters: 10
## initial estimates: 32.1941 -23.2415 0.2729 -0.408 0.525 -0.3489 -0.0261 0.2801 -0.5431 0.3969
## Par. lower-bounds: 25.9868 -30.0668 0.1341 -0.573 0.3724 -0.5304 -0.1835 0.1034 -0.7162 0.2026
## Par. upper-bounds: 38.4015 -16.4161 0.4116 -0.2429 0.6776 -0.1674 0.1312 0.4568 -0.3701 0.5912
## Final Estimates: 26.58662 -23.55434 0.4007082 -0.2584072 0.5355769 -0.5303509 -0.183502 0.1047245 -0.4768972 0.5527806
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 26.5866 17.0166 1.562 0.11820
## loneliness_state_pmc -23.5543 7.5389 -3.124 0.00178 **
## depressedmood_state 0.4007 0.3863 1.037 0.29965
## loneliness_state_pmc -0.2584 0.7982 -0.324 0.74614
## depressedmood_state 0.5356 0.1696 3.157 0.00159 **
## loneliness_state_pmc -0.5304 0.7029 -0.755 0.45055
## -0.1835 0.4159 -0.441 0.65903
## 0.1047 0.8205 0.128 0.89844
## -0.4769 0.1883 -2.533 0.01132 *
## 0.5528 0.7388 0.748 0.45432
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 26.58662 -23.55434
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.401 -0.258
## [2,] 0.536 -0.530
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.184 -0.105
## [2,] 0.477 -0.553
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 270.8618 173.5352
## [2,] 173.5352 330.3352
## ----
## aic= 11.00567
## bic= 11.04313
## Number of parameters: 10
## initial estimates: 4.5649 -3.5734 0.8579 -0.3022 0.1111 0.2107 -0.6589 0.248 -0.0322 -0.1594
## Par. lower-bounds: 0.6196 -6.8155 0.736 -0.6227 0.0109 -0.0527 -0.7938 -0.0799 -0.143 -0.4288
## Par. upper-bounds: 8.5102 -0.3313 0.9798 0.0183 0.2113 0.4741 -0.524 0.5758 0.0787 0.11
## Final Estimates: 4.429476 -3.567211 0.8630077 0.01177566 0.1105371 0.3170698 -0.6089018 -0.07987372 -0.007294836 -0.2752489## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 4.429476 0.323532 13.69 <2e-16 ***
## loneliness_state_pmc -3.567211 NaN NaN NaN
## depressedmood_state 0.863008 0.009713 88.85 <2e-16 ***
## loneliness_state_pmc 0.011776 NaN NaN NaN
## depressedmood_state 0.110537 NaN NaN NaN
## loneliness_state_pmc 0.317070 NaN NaN NaN
## -0.608902 0.030409 -20.02 <2e-16 ***
## -0.079874 NaN NaN NaN
## -0.007295 NaN NaN NaN
## -0.275249 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 4.429476 -3.567211
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.863 0.0118
## [2,] 0.111 0.3171
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.60890 0.0799
## [2,] 0.00729 0.2752
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 56.30329 11.79923
## [2,] 11.79923 38.35008
## ----
## aic= 7.625145
## bic= 7.662604
## Number of parameters: 10
## initial estimates: 5.7839 -9.79 0.7797 -0.4801 0.3722 -0.0564 -0.59 0.5415 -0.2473 0.0979
## Par. lower-bounds: 1.7553 -13.795 0.6271 -0.6829 0.2204 -0.2581 -0.7544 0.3296 -0.4107 -0.1127
## Par. upper-bounds: 9.8125 -5.7851 0.9324 -0.2772 0.5239 0.1452 -0.4257 0.7533 -0.0839 0.3085
## Final Estimates: 5.68042 -9.976642 0.7842351 -0.3851042 0.3809818 0.01667749 -0.5236217 0.3779977 -0.2447848 0.02373888## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 5.68042 NaN NaN NaN
## loneliness_state_pmc -9.97664 NaN NaN NaN
## depressedmood_state 0.78424 NaN NaN NaN
## loneliness_state_pmc -0.38510 NaN NaN NaN
## depressedmood_state 0.38098 NaN NaN NaN
## loneliness_state_pmc 0.01668 NaN NaN NaN
## -0.52362 NaN NaN NaN
## 0.37800 NaN NaN NaN
## -0.24478 NaN NaN NaN
## 0.02374 NaN NaN NaN
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 5.68042 -9.976642
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.784 -0.3851
## [2,] 0.381 0.0167
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.524 -0.3780
## [2,] 0.245 -0.0237
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 51.91170 19.69873
## [2,] 19.69873 50.01053
## ----
## aic= 7.71417
## bic= 7.751628
## Number of parameters: 10
## initial estimates: 11.4312 -6.5553 0.553 0.1534 0.2576 0.1465 -0.2301 -0.2131 -0.0312 -0.0738
## Par. lower-bounds: 7.9676 -9.5949 0.4196 -0.0435 0.1406 -0.0262 -0.3785 -0.4226 -0.1613 -0.2577
## Par. upper-bounds: 14.8948 -3.5156 0.6863 0.3502 0.3746 0.3193 -0.0818 -0.0035 0.099 0.1101
## Final Estimates: 10.2261 -4.942636 0.5998537 0.3502336 0.1932659 0.1888023 -0.2880179 -0.3903283 0.0439298 -0.08227453
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 10.22610 1.96418 5.206 1.93e-07 ***
## loneliness_state_pmc -4.94264 2.76995 -1.784 0.074363 .
## depressedmood_state 0.59985 0.07649 7.842 4.44e-15 ***
## loneliness_state_pmc 0.35023 0.15091 2.321 0.020294 *
## depressedmood_state 0.19327 0.10796 1.790 0.073425 .
## loneliness_state_pmc 0.18880 0.16636 1.135 0.256428
## -0.28802 0.07574 -3.803 0.000143 ***
## -0.39033 0.15975 -2.443 0.014550 *
## 0.04393 0.11462 0.383 0.701534
## -0.08227 0.17753 -0.463 0.643051
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 10.2261 -4.942636
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.600 0.350
## [2,] 0.193 0.189
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.2880 0.3903
## [2,] -0.0439 0.0823
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 130.91298 54.71713
## [2,] 54.71713 105.36093
## ----
## aic= 9.301508
## bic= 9.338967
## Number of parameters: 10
## initial estimates: 10.1716 -5.0354 0.4038 0.0113 0.2958 0.0232 -0.2995 -0.0139 -0.3162 0.0152
## Par. lower-bounds: 6.2347 -9.4143 0.1737 -0.2774 0.0399 -0.298 -0.5366 -0.3071 -0.5798 -0.311
## Par. upper-bounds: 14.1085 -0.6566 0.6338 0.3 0.5516 0.3443 -0.0625 0.2793 -0.0525 0.3413
## Final Estimates: 11.24065 -9.409091 0.3414189 -0.2750877 0.5514542 0.07326299 -0.2336736 0.27934 -0.5681405 -0.03188752
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 11.24065 3.28956 3.417 0.000633 ***
## loneliness_state_pmc -9.40909 5.40793 -1.740 0.081882 .
## depressedmood_state 0.34142 0.19256 1.773 0.076224 .
## loneliness_state_pmc -0.27509 0.34794 -0.791 0.429170
## depressedmood_state 0.55145 0.31663 1.742 0.081574 .
## loneliness_state_pmc 0.07326 0.42045 0.174 0.861670
## -0.23367 0.20123 -1.161 0.245549
## 0.27934 0.35675 0.783 0.433619
## -0.56814 0.32284 -1.760 0.078438 .
## -0.03189 0.41882 -0.076 0.939311
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 11.24065 -9.409091
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.341 -0.2751
## [2,] 0.551 0.0733
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.234 -0.2793
## [2,] 0.568 0.0319
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 34.47135 10.98817
## [2,] 10.98817 42.07941
## ----
## aic= 7.207065
## bic= 7.244524
## Number of parameters: 10
## initial estimates: 2.1207 -2.09 0.8895 -0.0429 0.1128 0.643 -0.8407 0.0902 -0.093 -0.542
## Par. lower-bounds: -1.6276 -5.4983 0.6961 -0.3021 -0.063 0.4074 -1.0458 -0.1795 -0.2794 -0.7872
## Par. upper-bounds: 5.8691 1.3184 1.083 0.2162 0.2887 0.8787 -0.6357 0.36 0.0934 -0.2967
## Final Estimates: 0.1702928 -0.3875144 0.9932136 -0.1871162 0.02226408 0.7954598 -0.8516299 0.2421591 0.048684 -0.6712349## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 0.17029 NaN NaN NaN
## loneliness_state_pmc -0.38751 NaN NaN NaN
## depressedmood_state 0.99321 NaN NaN NaN
## loneliness_state_pmc -0.18712 NaN NaN NaN
## depressedmood_state 0.02226 NaN NaN NaN
## loneliness_state_pmc 0.79546 NaN NaN NaN
## -0.85163 NaN NaN NaN
## 0.24216 NaN NaN NaN
## 0.04868 NaN NaN NaN
## -0.67123 NaN NaN NaN
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 0.1702928 -0.3875144
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.9932 -0.187
## [2,] 0.0223 0.795
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.8516 -0.242
## [2,] -0.0487 0.671
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 259.2157 139.8788
## [2,] 139.8788 213.1087
## ----
## aic= 10.49649
## bic= 10.53395
## Number of parameters: 10
## initial estimates: 15.9036 2.2154 0.6744 -0.1007 -0.045 -0.1283 -0.3624 0.08 0.1204 0.1118
## Par. lower-bounds: 11.5482 -2.3719 0.5855 -0.3942 -0.1387 -0.4374 -0.4686 -0.2181 0.0086 -0.2022
## Par. upper-bounds: 20.259 6.8026 0.7633 0.1928 0.0486 0.1809 -0.2563 0.3781 0.2322 0.4257
## Final Estimates: 15.736 2.178934 0.678566 0.1190287 -0.04451166 -0.03911719 -0.3318054 -0.1748543 0.09933122 -0.002071697## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 15.736001 2.317753 6.789 1.13e-11 ***
## loneliness_state_pmc 2.178934 1.614186 1.350 0.1771
## depressedmood_state 0.678566 0.047325 14.338 < 2e-16 ***
## loneliness_state_pmc 0.119029 NaN NaN NaN
## depressedmood_state -0.044512 0.033085 -1.345 0.1785
## loneliness_state_pmc -0.039117 0.390775 -0.100 0.9203
## -0.331805 0.059100 -5.614 1.97e-08 ***
## -0.174854 NaN NaN NaN
## 0.099331 0.049484 2.007 0.0447 *
## -0.002072 0.385678 -0.005 0.9957
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 15.736 2.178934
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.6786 0.1190
## [2,] -0.0445 -0.0391
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.3318 0.17485
## [2,] -0.0993 0.00207
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 37.014091 4.521907
## [2,] 4.521907 41.084650
## ----
## aic= 7.327682
## bic= 7.36514
## Number of parameters: 10
## initial estimates: 13.0358 -10.225 0.6965 -0.1297 0.2385 -0.1027 -0.5026 0.1735 -0.2177 0.0429
## Par. lower-bounds: 7.5273 -14.2325 0.5693 -0.4379 0.1459 -0.327 -0.6516 -0.1509 -0.3262 -0.1931
## Par. upper-bounds: 18.5444 -6.2175 0.8238 0.1786 0.331 0.1215 -0.3536 0.4979 -0.1093 0.2789
## Final Estimates: 12.46318 -9.670447 0.7098114 0.1213011 0.2247378 -0.3269935 -0.3871728 -0.1509307 -0.1093271 0.2160486
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 12.46318 6.69467 1.862 0.0627 .
## loneliness_state_pmc -9.67045 5.32100 -1.817 0.0692 .
## depressedmood_state 0.70981 0.15564 4.561 5.1e-06 ***
## loneliness_state_pmc 0.12130 0.65592 0.185 0.8533
## depressedmood_state 0.22474 0.12358 1.819 0.0690 .
## loneliness_state_pmc -0.32699 0.79616 -0.411 0.6813
## -0.38717 0.16291 -2.377 0.0175 *
## -0.15093 0.64080 -0.236 0.8138
## -0.10933 0.09544 -1.145 0.2520
## 0.21605 0.80467 0.268 0.7883
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 12.46318 -9.670447
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.710 0.121
## [2,] 0.225 -0.327
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.387 0.151
## [2,] 0.109 -0.216
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 186.16833 89.51495
## [2,] 89.51495 98.53340
## ----
## aic= 9.257178
## bic= 9.294636
## Number of parameters: 10
## initial estimates: 8.7521 0.1301 0.2678 0.2824 -0.0096 0.1961 -0.1093 -0.2444 0.0996 -0.1906
## Par. lower-bounds: 6.7612 -1.7964 0.1107 0.0754 -0.1616 -0.0042 -0.2798 -0.4619 -0.0654 -0.4011
## Par. upper-bounds: 10.743 2.0565 0.4249 0.4894 0.1424 0.3964 0.0612 -0.0268 0.2645 0.0199
## Final Estimates: 9.128457 0.3475358 0.2028714 0.07924046 -0.05950525 0.008451067 0.05509695 -0.02683382 0.1868908 -0.002489353## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 9.128457 0.561631 16.253 < 2e-16 ***
## loneliness_state_pmc 0.347536 NaN NaN NaN
## depressedmood_state 0.202871 0.065373 3.103 0.00191 **
## loneliness_state_pmc 0.079240 NaN NaN NaN
## depressedmood_state -0.059505 NaN NaN NaN
## loneliness_state_pmc 0.008451 NaN NaN NaN
## 0.055097 0.080207 0.687 0.49212
## -0.026834 NaN NaN NaN
## 0.186891 NaN NaN NaN
## -0.002489 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 9.128457 0.3475358
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.2029 0.07924
## [2,] -0.0595 0.00845
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] -0.0551 0.02683
## [2,] -0.1869 0.00249
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 156.77819 71.73716
## [2,] 71.73716 142.84937
## ----
## aic= 9.769821
## bic= 9.80728
## Number of parameters: 10
## initial estimates: 40.1349 10.57 0.2015 -0.039 -0.2112 0.3958 -0.066 0.2774 0.1355 -0.0432
## Par. lower-bounds: 31.9238 2.8778 0.0403 -0.211 -0.3622 0.2346 -0.252 0.0785 -0.0388 -0.2295
## Par. upper-bounds: 48.346 18.2621 0.3628 0.1331 -0.0602 0.557 0.12 0.4763 0.3098 0.1432
## Final Estimates: 44.76236 18.20071 0.1099747 0.05856476 -0.3622296 0.3387861 0.07439274 0.07853535 0.2950754 -0.002576346
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 44.762359 14.471485 3.093 0.00198 **
## loneliness_state_pmc 18.200713 12.034913 1.512 0.13045
## depressedmood_state 0.109975 0.287397 0.383 0.70197
## loneliness_state_pmc 0.058565 0.239042 0.245 0.80646
## depressedmood_state -0.362230 0.238824 -1.517 0.12934
## loneliness_state_pmc 0.338786 0.181855 1.863 0.06247 .
## 0.074393 0.306839 0.242 0.80843
## 0.078535 0.254133 0.309 0.75730
## 0.295075 0.245468 1.202 0.22933
## -0.002576 0.176380 -0.015 0.98835
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 44.76236 18.20071
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.110 0.0586
## [2,] -0.362 0.3388
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] -0.0744 -0.07854
## [2,] -0.2951 0.00258
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 555.7442 397.4550
## [2,] 397.4550 480.3947
## ----
## aic= 11.61344
## bic= 11.6509
## Number of parameters: 10
## initial estimates: 8.2443 -5.4879 0.2777 -0.0251 0.478 0.1434 -0.2226 0.1087 -0.359 0.12
## Par. lower-bounds: 6.0714 -9.8365 0.0906 -0.1171 0.1037 -0.0406 -0.4219 0.0109 -0.7577 -0.0757
## Par. upper-bounds: 10.4172 -1.1393 0.4647 0.0668 0.8524 0.3275 -0.0234 0.2065 0.0397 0.3158
## Final Estimates: 6.11209 -1.282903 0.4647191 -0.1170984 0.1076322 0.1232802 -0.3527158 0.1877779 0.002769736 0.170341## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 6.11209 NaN NaN NaN
## loneliness_state_pmc -1.28290 NaN NaN NaN
## depressedmood_state 0.46472 NaN NaN NaN
## loneliness_state_pmc -0.11710 NaN NaN NaN
## depressedmood_state 0.10763 NaN NaN NaN
## loneliness_state_pmc 0.12328 NaN NaN NaN
## -0.35272 NaN NaN NaN
## 0.18778 NaN NaN NaN
## 0.00277 NaN NaN NaN
## 0.17034 NaN NaN NaN
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 6.11209 -1.282903
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.465 -0.117
## [2,] 0.108 0.123
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.35272 -0.188
## [2,] -0.00277 -0.170
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 53.51192 58.37542
## [2,] 58.37542 215.19187
## ----
## aic= 9.014848
## bic= 9.052307
## Number of parameters: 10
## initial estimates: 8.1582 0.5653 0.7819 -0.492 -0.0137 0.2957 -0.7594 0.6668 -0.0789 -0.0617
## Par. lower-bounds: -2.721 -9.6008 0.49 -0.8466 -0.2865 -0.0357 -1.0624 0.3018 -0.362 -0.4028
## Par. upper-bounds: 19.0374 10.7315 1.0738 -0.1374 0.2591 0.6271 -0.4565 1.0318 0.2042 0.2794
## Final Estimates: 4.429083 0.2057079 0.8822468 -0.4597684 -0.004377745 0.4806957 -0.8653481 0.6457299 -0.07518173 -0.2418838
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 4.429083 4.318866 1.026 0.305118
## loneliness_state_pmc 0.205708 3.846184 0.053 0.957347
## depressedmood_state 0.882247 0.116228 7.591 3.18e-14 ***
## loneliness_state_pmc -0.459768 0.150458 -3.056 0.002245 **
## depressedmood_state -0.004378 0.103445 -0.042 0.966244
## loneliness_state_pmc 0.480696 0.127671 3.765 0.000166 ***
## -0.865348 0.127069 -6.810 9.75e-12 ***
## 0.645730 0.159881 4.039 5.37e-05 ***
## -0.075182 0.109666 -0.686 0.492998
## -0.241884 0.135505 -1.785 0.074252 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 4.429083 0.2057079
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.88225 -0.460
## [2,] -0.00438 0.481
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.8653 -0.646
## [2,] 0.0752 0.242
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 343.2441 236.2725
## [2,] 236.2725 298.3978
## ----
## aic= 10.76361
## bic= 10.80107
## Number of parameters: 10
## initial estimates: 11.7458 -1.8556 0.3872 0.0567 0.1006 0.1663 -0.0808 -0.191 -0.0714 0.073
## Par. lower-bounds: 9.3545 -4.3407 0.2822 -0.0478 -0.0085 0.0577 -0.2184 -0.3271 -0.2144 -0.0684
## Par. upper-bounds: 14.1372 0.6295 0.4921 0.1613 0.2096 0.2749 0.0568 -0.055 0.0716 0.2143
## Final Estimates: 13.69113 -3.988257 0.2822417 0.01921189 0.2095842 0.2749475 0.05676253 -0.05500597 -0.2131778 -0.03651005## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 13.69113 1.18979 11.507 < 2e-16 ***
## loneliness_state_pmc -3.98826 NaN NaN NaN
## depressedmood_state 0.28224 0.05174 5.455 4.89e-08 ***
## loneliness_state_pmc 0.01921 NaN NaN NaN
## depressedmood_state 0.20958 NaN NaN NaN
## loneliness_state_pmc 0.27495 NaN NaN NaN
## 0.05676 0.05533 1.026 0.305
## -0.05501 NaN NaN NaN
## -0.21318 NaN NaN NaN
## -0.03651 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 13.69113 -3.988257
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.282 0.0192
## [2,] 0.210 0.2749
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] -0.0568 0.0550
## [2,] 0.2132 0.0365
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 595.7173 411.6795
## [2,] 411.6795 629.6883
## ----
## aic= 12.24815
## bic= 12.28561
## Number of parameters: 10
## initial estimates: 4.809 -3.6334 0.6979 -0.0524 0.2272 0.3184 -0.6544 0.0902 -0.1734 -0.2343
## Par. lower-bounds: 2.2516 -5.9864 0.543 -0.2205 0.0847 0.1638 -0.8248 -0.0952 -0.3301 -0.4049
## Par. upper-bounds: 7.3663 -1.2803 0.8528 0.1157 0.3698 0.4731 -0.4841 0.2757 -0.0167 -0.0637
## Final Estimates: 4.731059 -3.89262 0.7064067 0.1156642 0.2489312 0.4730793 -0.5531003 -0.07967368 -0.1878221 -0.3497868## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 4.73106 NaN NaN NaN
## loneliness_state_pmc -3.89262 NaN NaN NaN
## depressedmood_state 0.70641 NaN NaN NaN
## loneliness_state_pmc 0.11566 NaN NaN NaN
## depressedmood_state 0.24893 NaN NaN NaN
## loneliness_state_pmc 0.47308 NaN NaN NaN
## -0.55310 NaN NaN NaN
## -0.07967 NaN NaN NaN
## -0.18782 NaN NaN NaN
## -0.34979 NaN NaN NaN
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 4.731059 -3.89262
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.706 0.116
## [2,] 0.249 0.473
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.553 0.0797
## [2,] 0.188 0.3498
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 157.57945 83.22609
## [2,] 83.22609 132.52161
## ----
## aic= 9.557958
## bic= 9.595416
## Number of parameters: 10
## initial estimates: 18.1949 -31.7604 0.6089 0.0142 0.6805 -0.0488 -0.2868 0.0153 -0.4811 0.0386
## Par. lower-bounds: 12.3823 -38.6272 0.4845 -0.0935 0.5335 -0.176 -0.4246 -0.1047 -0.6439 -0.1032
## Par. upper-bounds: 24.0075 -24.8935 0.7334 0.122 0.8276 0.0785 -0.1489 0.1353 -0.3182 0.1803
## Final Estimates: 18.1792 -31.79967 0.609955 0.06936098 0.6829853 0.07849981 -0.2605704 -0.02939565 -0.4791251 -0.1031775## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 18.17920 NaN NaN NaN
## loneliness_state_pmc -31.79967 NaN NaN NaN
## depressedmood_state 0.60995 NaN NaN NaN
## loneliness_state_pmc 0.06936 0.04048 1.714 0.0866 .
## depressedmood_state 0.68299 NaN NaN NaN
## loneliness_state_pmc 0.07850 NaN NaN NaN
## -0.26057 0.01918 -13.586 <2e-16 ***
## -0.02940 0.06467 -0.455 0.6494
## -0.47913 NaN NaN NaN
## -0.10318 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 18.1792 -31.79967
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.610 0.0694
## [2,] 0.683 0.0785
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.261 0.0294
## [2,] 0.479 0.1032
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 58.68077 20.38888
## [2,] 20.38888 77.76478
## ----
## aic= 8.344569
## bic= 8.382027
## Number of parameters: 10
## initial estimates: 11.7484 8.2811 0.3616 0.1576 -0.4516 0.81 -0.177 0.0365 0.4013 -0.3336
## Par. lower-bounds: 8.9824 4.5788 0.2163 0.0591 -0.6461 0.6781 -0.3425 -0.0787 0.1798 -0.4879
## Par. upper-bounds: 14.5145 11.9835 0.5068 0.2561 -0.2572 0.9418 -0.0115 0.1518 0.6229 -0.1793
## Final Estimates: 9.260638 9.560213 0.4956265 0.06057023 -0.5212188 0.9418475 -0.3159932 0.1516078 0.456303 -0.4878794
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 9.26064 1.41929 6.525 6.81e-11 ***
## loneliness_state_pmc 9.56021 2.01979 4.733 2.21e-06 ***
## depressedmood_state 0.49563 0.07562 6.554 5.61e-11 ***
## loneliness_state_pmc 0.06057 0.05284 1.146 0.251634
## depressedmood_state -0.52122 0.10813 -4.820 1.43e-06 ***
## loneliness_state_pmc 0.94185 0.07515 12.533 < 2e-16 ***
## -0.31599 0.08529 -3.705 0.000212 ***
## 0.15161 0.06087 2.491 0.012753 *
## 0.45630 0.12677 3.599 0.000319 ***
## -0.48788 0.09340 -5.224 1.75e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 9.260638 9.560213
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.496 0.0606
## [2,] -0.521 0.9418
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.316 -0.152
## [2,] -0.456 0.488
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 166.8268 154.7888
## [2,] 154.7888 294.4387
## ----
## aic= 10.14732
## bic= 10.18478
## Number of parameters: 10
## initial estimates: 8.9166 -0.6842 0.4917 0.0136 0.041 0.3511 -0.3739 0.0924 -0.0194 -0.1295
## Par. lower-bounds: 6.0366 -4.8944 0.3289 -0.1064 -0.1969 0.1758 -0.5504 -0.0364 -0.2775 -0.3177
## Par. upper-bounds: 11.7966 3.526 0.6544 0.1335 0.2789 0.5264 -0.1973 0.2211 0.2386 0.0587
## Final Estimates: 8.830139 -0.6947409 0.495976 0.1321911 0.03996679 0.188179 -0.3370204 -0.03635543 0.01379091 0.05750577## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 8.83014 NaN NaN NaN
## loneliness_state_pmc -0.69474 NaN NaN NaN
## depressedmood_state 0.49598 NaN NaN NaN
## loneliness_state_pmc 0.13219 NaN NaN NaN
## depressedmood_state 0.03997 NaN NaN NaN
## loneliness_state_pmc 0.18818 NaN NaN NaN
## -0.33702 NaN NaN NaN
## -0.03636 NaN NaN NaN
## 0.01379 NaN NaN NaN
## 0.05751 NaN NaN NaN
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 8.830139 -0.6947409
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.496 0.132
## [2,] 0.040 0.188
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.3370 0.0364
## [2,] -0.0138 -0.0575
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 61.03991 50.82827
## [2,] 50.82827 133.94248
## ----
## aic= 8.643436
## bic= 8.680895
## Number of parameters: 10
## initial estimates: 8.6022 -2.0531 0.2219 -0.1459 0.1866 0.1349 -0.0188 0.0689 -0.1505 -0.1673
## Par. lower-bounds: 7.0263 -3.3921 0.0872 -0.2948 0.0721 0.0084 -0.1667 -0.0973 -0.2762 -0.3086
## Par. upper-bounds: 10.1781 -0.714 0.3566 0.003 0.3011 0.2615 0.1292 0.2352 -0.0248 -0.026
## Final Estimates: 7.088569 -2.735471 0.3566425 -0.04231962 0.248478 0.2608032 -0.1595536 -0.09733377 -0.2033257 -0.3085856## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 7.08857 NaN NaN NaN
## loneliness_state_pmc -2.73547 0.76550 -3.573 0.000352 ***
## depressedmood_state 0.35664 NaN NaN NaN
## loneliness_state_pmc -0.04232 NaN NaN NaN
## depressedmood_state 0.24848 0.06799 3.654 0.000258 ***
## loneliness_state_pmc 0.26080 NaN NaN NaN
## -0.15955 NaN NaN NaN
## -0.09733 NaN NaN NaN
## -0.20333 0.07947 -2.558 0.010516 *
## -0.30859 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 7.088569 -2.735471
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.357 -0.0423
## [2,] 0.248 0.2608
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.160 0.0973
## [2,] 0.203 0.3086
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 92.35680 24.96223
## [2,] 24.96223 67.59561
## ----
## aic= 8.648337
## bic= 8.685796
## Number of parameters: 10
## initial estimates: 9.7297 -6.6156 0.749 0.027 0.1693 0.1825 -0.5794 0.1384 -0.0162 -0.0095
## Par. lower-bounds: 6.3946 -9.2846 0.6679 -0.1159 0.1044 0.0681 -0.6864 -0.0279 -0.1017 -0.1426
## Par. upper-bounds: 13.0648 -3.9466 0.8301 0.1698 0.2342 0.2968 -0.4725 0.3047 0.0694 0.1236
## Final Estimates: 7.073936 -7.16284 0.8194612 0.01663371 0.1865116 0.06812785 -0.4725221 0.01160262 -0.00346838 0.08829978## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 7.073936 NaN NaN NaN
## loneliness_state_pmc -7.162840 2.478920 -2.889 0.00386 **
## depressedmood_state 0.819461 NaN NaN NaN
## loneliness_state_pmc 0.016634 NaN NaN NaN
## depressedmood_state 0.186512 0.062956 2.963 0.00305 **
## loneliness_state_pmc 0.068128 NaN NaN NaN
## -0.472522 NaN NaN NaN
## 0.011603 NaN NaN NaN
## -0.003468 0.049648 -0.070 0.94431
## 0.088300 0.056279 1.569 0.11666
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 7.073936 -7.16284
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.819 0.0166
## [2,] 0.187 0.0681
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.47252 -0.0116
## [2,] 0.00347 -0.0883
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 426.2441 150.8224
## [2,] 150.8224 269.8294
## ----
## aic= 11.44671
## bic= 11.48417
## Number of parameters: 10
## initial estimates: 22.9177 -25.1358 0.6553 0.1496 0.3785 0.2377 -0.4326 0.0212 -0.4349 -0.0098
## Par. lower-bounds: 16.0053 -32.2729 0.5518 0.0184 0.2716 0.1022 -0.5553 -0.1242 -0.5616 -0.16
## Par. upper-bounds: 29.8302 -17.9986 0.7589 0.2808 0.4854 0.3731 -0.3099 0.1667 -0.3082 0.1403
## Final Estimates: 16.01265 -32.18333 0.7588926 0.07131845 0.4854362 0.272751 -0.4166187 0.01305352 -0.4994687 -0.08362607
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 16.01265 14.08987 1.136 0.255762
## loneliness_state_pmc -32.18333 5.83850 -5.512 3.54e-08 ***
## depressedmood_state 0.75889 0.21245 3.572 0.000354 ***
## loneliness_state_pmc 0.07132 0.27820 0.256 0.797673
## depressedmood_state 0.48544 0.08799 5.517 3.45e-08 ***
## loneliness_state_pmc 0.27275 0.15185 1.796 0.072460 .
## -0.41662 0.24277 -1.716 0.086146 .
## 0.01305 0.29327 0.045 0.964498
## -0.49947 0.14626 -3.415 0.000638 ***
## -0.08363 0.22266 -0.376 0.707225
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 16.01265 -32.18333
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.759 0.0713
## [2,] 0.485 0.2728
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.417 -0.0131
## [2,] 0.499 0.0836
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 151.30726 65.15303
## [2,] 65.15303 155.63496
## ----
## aic= 9.882342
## bic= 9.919801
## Number of parameters: 10
## initial estimates: 6.3836 6.159 0.332 0.1258 -0.64 0.5305 -0.2071 -0.2014 0.586 -0.4261
## Par. lower-bounds: 4.9349 3.551 0.1844 0.029 -0.9058 0.3562 -0.3652 -0.3029 0.3015 -0.6088
## Par. upper-bounds: 7.8323 8.767 0.4797 0.2227 -0.3742 0.7049 -0.0491 -0.0999 0.8705 -0.2434
## Final Estimates: 7.770282 8.685628 0.1906041 0.2223508 -0.9057594 0.4922895 -0.04912707 -0.3028722 0.8196476 -0.3388488
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 7.77028 1.13025 6.875 6.21e-12 ***
## loneliness_state_pmc 8.68563 2.17635 3.991 6.58e-05 ***
## depressedmood_state 0.19060 0.11645 1.637 0.101676
## loneliness_state_pmc 0.22235 0.07082 3.140 0.001691 **
## depressedmood_state -0.90576 0.22567 -4.014 5.98e-05 ***
## loneliness_state_pmc 0.49229 0.08964 5.492 3.98e-08 ***
## -0.04913 0.12422 -0.395 0.692482
## -0.30287 0.07158 -4.231 2.32e-05 ***
## 0.81965 0.24307 3.372 0.000746 ***
## -0.33885 0.09477 -3.576 0.000349 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 7.770282 8.685628
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.191 0.222
## [2,] -0.906 0.492
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.0491 0.303
## [2,] -0.8196 0.339
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 35.3322944 -0.1801644
## [2,] -0.1801644 117.0371579
## ----
## aic= 8.341567
## bic= 8.379026
## Number of parameters: 10
## initial estimates: 33.2104 1.5012 -0.4167 0.1888 -0.0613 0.064 0.3593 -0.0907 0.0122 0.0403
## Par. lower-bounds: 29.4853 -2.2225 -0.5742 0.0168 -0.2188 -0.1079 0.1914 -0.2723 -0.1556 -0.1413
## Par. upper-bounds: 36.9355 5.2249 -0.2592 0.3608 0.0961 0.2359 0.5271 0.091 0.18 0.2219
## Final Estimates: 33.86773 -2.222466 -0.4445253 0.04377891 0.09517565 0.2359471 0.3751558 0.09097406 -0.1325797 -0.1242528## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 33.86773 2.44575 13.848 < 2e-16 ***
## loneliness_state_pmc -2.22247 7.69350 -0.289 0.77268
## depressedmood_state -0.44453 0.10345 -4.297 1.73e-05 ***
## loneliness_state_pmc 0.04378 0.33964 0.129 0.89744
## depressedmood_state 0.09518 0.32789 0.290 0.77161
## loneliness_state_pmc 0.23595 NaN NaN NaN
## 0.37516 0.13045 2.876 0.00403 **
## 0.09097 0.32141 0.283 0.77714
## -0.13258 0.31557 -0.420 0.67439
## -0.12425 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 33.86773 -2.222466
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] -0.4445 0.0438
## [2,] 0.0952 0.2359
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] -0.375 -0.091
## [2,] 0.133 0.124
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 94.19682 21.93326
## [2,] 21.93326 94.32568
## ----
## aic= 9.050762
## bic= 9.088221
## Number of parameters: 10
## initial estimates: 24.3662 -7.5477 0.2657 0.2255 0.2272 0.1952 -0.0825 -0.0766 -0.0235 -0.0114
## Par. lower-bounds: 17.6887 -14.1697 0.0652 0.0296 0.0284 9e-04 -0.2951 -0.2852 -0.2344 -0.2183
## Par. upper-bounds: 31.0436 -0.9258 0.4661 0.4214 0.4259 0.3895 0.1302 0.1319 0.1874 0.1954
## Final Estimates: 24.70345 -4.057794 0.2554063 0.4056108 0.122172 0.3894897 -0.07802021 -0.2664624 0.08037353 -0.2182577
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 24.70345 10.21161 2.419 0.0156 *
## loneliness_state_pmc -4.05779 19.54862 -0.208 0.8356
## depressedmood_state 0.25541 0.30782 0.830 0.4067
## loneliness_state_pmc 0.40561 0.36186 1.121 0.2623
## depressedmood_state 0.12217 0.58921 0.207 0.8357
## loneliness_state_pmc 0.38949 0.56328 0.691 0.4893
## -0.07802 0.31019 -0.252 0.8014
## -0.26646 0.38623 -0.690 0.4902
## 0.08037 0.59873 0.134 0.8932
## -0.21826 0.57081 -0.382 0.7022
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 24.70345 -4.057794
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.255 0.406
## [2,] 0.122 0.389
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.0780 0.266
## [2,] -0.0804 0.218
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 122.67824 73.10313
## [2,] 73.10313 120.68619
## ----
## aic= 9.169272
## bic= 9.206731
## Number of parameters: 10
## initial estimates: 3.1814 -5.3321 0.9145 -0.697 0.1425 0.2038 -0.4132 0.8885 0.1658 -0.095
## Par. lower-bounds: -3.305 -10.075 0.7423 -1.0203 0.0166 -0.0326 -0.6023 0.5491 0.0276 -0.3432
## Par. upper-bounds: 9.6679 -0.5892 1.0867 -0.3736 0.2684 0.4403 -0.2242 1.2279 0.304 0.1531
## Final Estimates: 3.191398 -5.362336 0.9166504 -0.7590839 0.1448441 0.166748 -0.3586188 0.8848197 0.1784498 -0.1071262## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 3.1914 NaN NaN NaN
## loneliness_state_pmc -5.3623 NaN NaN NaN
## depressedmood_state 0.9167 NaN NaN NaN
## loneliness_state_pmc -0.7591 NaN NaN NaN
## depressedmood_state 0.1448 NaN NaN NaN
## loneliness_state_pmc 0.1667 NaN NaN NaN
## -0.3586 NaN NaN NaN
## 0.8848 NaN NaN NaN
## 0.1784 NaN NaN NaN
## -0.1071 NaN NaN NaN
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 3.191398 -5.362336
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.917 -0.759
## [2,] 0.145 0.167
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.359 -0.885
## [2,] -0.178 0.107
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 257.1970 125.7048
## [2,] 125.7048 137.0117
## ----
## aic= 9.889235
## bic= 9.926694
## Number of parameters: 10
## initial estimates: 1.6072 -1.2895 0.4857 0.2004 0.408 0.122 -0.3691 0.0331 -0.2163 -0.0667
## Par. lower-bounds: 1.112 -1.9112 0.3658 0.0718 0.2575 -0.0394 -0.5025 -0.1038 -0.3837 -0.2386
## Par. upper-bounds: 2.1024 -0.6677 0.6056 0.3289 0.5585 0.2834 -0.2358 0.1699 -0.0489 0.1051
## Final Estimates: 1.477307 -1.742771 0.5254192 0.3048121 0.5584928 0.0001394639 -0.3871182 -0.1037956 -0.3610405 0.04259184## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 1.4773073 0.5589626 2.643 0.00822 **
## loneliness_state_pmc -1.7427709 0.3168181 -5.501 3.78e-08 ***
## depressedmood_state 0.5254192 0.1767480 2.973 0.00295 **
## loneliness_state_pmc 0.3048121 0.2377815 1.282 0.19988
## depressedmood_state 0.5584928 0.0785516 7.110 1.16e-12 ***
## loneliness_state_pmc 0.0001395 NaN NaN NaN
## -0.3871182 0.1671790 -2.316 0.02058 *
## -0.1037956 0.2269677 -0.457 0.64745
## -0.3610405 0.0928055 -3.890 0.00010 ***
## 0.0425918 0.0140152 3.039 0.00237 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 1.477307 -1.742771
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.525 0.304812
## [2,] 0.558 0.000139
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.387 0.1038
## [2,] 0.361 -0.0426
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 35.7978 12.52460
## [2,] 12.5246 56.44195
## ----
## aic= 7.544568
## bic= 7.582027
## Number of parameters: 10
## initial estimates: 4.9631 2.4107 0.038 0.1272 -0.4635 0.7424 0.0239 -0.0646 0.4426 -0.5265
## Par. lower-bounds: 3.9715 0.8551 -0.1391 0.0447 -0.7414 0.6129 -0.1643 -0.1565 0.1474 -0.6707
## Par. upper-bounds: 5.9548 3.9663 0.2152 0.2097 -0.1857 0.8718 0.2121 0.0274 0.7379 -0.3822
## Final Estimates: 4.04999 1.186325 0.2151753 0.1318175 -0.2288097 0.8718013 -0.151903 -0.07552375 0.1474373 -0.6433282## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 4.04999 NaN NaN NaN
## loneliness_state_pmc 1.18632 NaN NaN NaN
## depressedmood_state 0.21518 NaN NaN NaN
## loneliness_state_pmc 0.13182 0.02105 6.261 3.83e-10 ***
## depressedmood_state -0.22881 NaN NaN NaN
## loneliness_state_pmc 0.87180 NaN NaN NaN
## -0.15190 NaN NaN NaN
## -0.07552 0.01151 -6.559 5.40e-11 ***
## 0.14744 NaN NaN NaN
## -0.64333 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 4.04999 1.186325
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.215 0.132
## [2,] -0.229 0.872
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.152 0.0755
## [2,] -0.147 0.6433
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 51.30879 35.86481
## [2,] 35.86481 126.40412
## ----
## aic= 8.570576
## bic= 8.608035
## Number of parameters: 10
## initial estimates: 12.2367 0.4399 0.4974 -0.0083 -0.0172 0.3629 -0.0225 -0.1088 0.3086 -0.4768
## Par. lower-bounds: 7.8757 -3.0934 0.3207 -0.2986 -0.1604 0.1278 -0.2173 -0.4153 0.1508 -0.725
## Par. upper-bounds: 16.5977 3.9731 0.6741 0.2819 0.1259 0.5981 0.1723 0.1976 0.4665 -0.2285
## Final Estimates: 8.064475 -0.481776 0.6674469 -0.2632865 0.01926785 0.4170957 -0.2149829 0.197581 0.23757 -0.5007352## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 8.06448 NaN NaN NaN
## loneliness_state_pmc -0.48178 NaN NaN NaN
## depressedmood_state 0.66745 NaN NaN NaN
## loneliness_state_pmc -0.26329 NaN NaN NaN
## depressedmood_state 0.01927 NaN NaN NaN
## loneliness_state_pmc 0.41710 NaN NaN NaN
## -0.21498 NaN NaN NaN
## 0.19758 NaN NaN NaN
## 0.23757 NaN NaN NaN
## -0.50074 NaN NaN NaN
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 8.064475 -0.481776
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.6674 -0.263
## [2,] 0.0193 0.417
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.215 -0.198
## [2,] -0.238 0.501
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 219.1343 126.9517
## [2,] 126.9517 146.2195
## ----
## aic= 9.68993
## bic= 9.727388
## Number of parameters: 10
## initial estimates: 9.87 -4.441 0.4598 -0.385 0.2425 0.1462 -0.386 0.3221 -0.2544 -0.1906
## Par. lower-bounds: 5.8816 -8.9621 0.2423 -0.7423 -0.0041 -0.2588 -0.6106 -0.0384 -0.5089 -0.5993
## Par. upper-bounds: 13.8585 0.08 0.6774 -0.0277 0.4891 0.5512 -0.1614 0.6827 2e-04 0.2182
## Final Estimates: 13.69732 -8.854963 0.2513796 -0.7299796 0.4839359 -0.04853868 -0.1614087 0.6826917 -0.5089466 0.01747677## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 13.69732 3.56666 3.840 0.000123 ***
## loneliness_state_pmc -8.85496 2.56799 -3.448 0.000564 ***
## depressedmood_state 0.25138 0.19466 1.291 0.196562
## loneliness_state_pmc -0.72998 NaN NaN NaN
## depressedmood_state 0.48394 0.14004 3.456 0.000549 ***
## loneliness_state_pmc -0.04854 0.23806 -0.204 0.838438
## -0.16141 0.19271 -0.838 0.402277
## 0.68269 NaN NaN NaN
## -0.50895 0.12275 -4.146 3.38e-05 ***
## 0.01748 0.22928 0.076 0.939240
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 13.69732 -8.854963
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.251 -0.7300
## [2,] 0.484 -0.0485
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.161 -0.6827
## [2,] 0.509 -0.0175
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 29.177031 6.587714
## [2,] 6.587714 37.290047
## ----
## aic= 6.965689
## bic= 7.003148
## Number of parameters: 10
## initial estimates: 23.3628 -14.6947 0.5168 0.1095 0.3032 -0.0538 -0.123 -0.2994 -0.2406 -0.0771
## Par. lower-bounds: 18.1354 -18.9695 0.4102 -0.0781 0.2159 -0.2073 -0.2519 -0.5053 -0.3459 -0.2454
## Par. upper-bounds: 28.5903 -10.42 0.6235 0.2972 0.3904 0.0996 0.0058 -0.0936 -0.1352 0.0913
## Final Estimates: 18.26077 -15.3678 0.6235056 0.2971662 0.3178907 0.09269218 -0.251894 -0.4542399 -0.1882475 -0.2260387## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 18.26077 NaN NaN NaN
## loneliness_state_pmc -15.36780 NaN NaN NaN
## depressedmood_state 0.62351 NaN NaN NaN
## loneliness_state_pmc 0.29717 NaN NaN NaN
## depressedmood_state 0.31789 NaN NaN NaN
## loneliness_state_pmc 0.09269 NaN NaN NaN
## -0.25189 NaN NaN NaN
## -0.45424 NaN NaN NaN
## -0.18825 NaN NaN NaN
## -0.22604 NaN NaN NaN
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 18.26077 -15.3678
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.624 0.2972
## [2,] 0.318 0.0927
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.252 0.454
## [2,] 0.188 0.226
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 224.9553 100.1882
## [2,] 100.1882 159.3804
## ----
## aic= 10.17303
## bic= 10.21049
## Number of parameters: 10
## initial estimates: 17.3349 -20.7423 0.5455 0.2395 0.5416 0.0488 -0.1685 -0.1287 -0.4068 0.1464
## Par. lower-bounds: 13.036 -24.7781 0.4345 0.1127 0.4373 -0.0702 -0.2981 -0.2765 -0.5285 0.0076
## Par. upper-bounds: 21.6338 -16.7064 0.6565 0.3662 0.6458 0.1678 -0.0388 0.019 -0.2851 0.2851
## Final Estimates: 19.92942 -24.71465 0.4789561 0.3662342 0.6457997 0.09315452 -0.09791956 -0.2562903 -0.4955371 0.007643019## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 19.929422 4.772387 4.176 2.97e-05 ***
## loneliness_state_pmc -24.714653 5.443958 -4.540 5.63e-06 ***
## depressedmood_state 0.478956 0.124444 3.849 0.000119 ***
## loneliness_state_pmc 0.366234 0.209291 1.750 0.080139 .
## depressedmood_state 0.645800 0.142189 4.542 5.58e-06 ***
## loneliness_state_pmc 0.093155 0.053640 1.737 0.082448 .
## -0.097920 0.113140 -0.865 0.386778
## -0.256290 0.236654 -1.083 0.278819
## -0.495537 0.156358 -3.169 0.001528 **
## 0.007643 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 19.92942 -24.71465
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.479 0.3662
## [2,] 0.646 0.0932
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.0979 0.25629
## [2,] 0.4955 -0.00764
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 172.34161 80.33808
## [2,] 80.33808 145.16265
## ----
## aic= 9.843231
## bic= 9.880689
## Number of parameters: 10
## initial estimates: 33.4577 -4.6644 0.2408 -0.6887 0.1064 -0.1811 -0.1892 0.6876 -0.0535 0.2945
## Par. lower-bounds: 27.6767 -8.7726 0.1121 -0.9755 0.015 -0.3849 -0.3353 0.3874 -0.1573 0.0812
## Par. upper-bounds: 39.2388 -0.5561 0.3695 -0.4018 0.1979 0.0227 -0.0432 0.9877 0.0502 0.5078
## Final Estimates: 27.73102 -0.6499881 0.3694879 -0.4066202 0.01496265 -0.3685255 -0.278384 0.3874363 0.01834199 0.5077897## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 27.73102 NaN NaN NaN
## loneliness_state_pmc -0.64999 11.07066 -0.059 0.95318
## depressedmood_state 0.36949 NaN NaN NaN
## loneliness_state_pmc -0.40662 NaN NaN NaN
## depressedmood_state 0.01496 0.25135 0.060 0.95253
## loneliness_state_pmc -0.36853 0.13747 -2.681 0.00734 **
## -0.27838 NaN NaN NaN
## 0.38744 NaN NaN NaN
## 0.01834 0.22055 0.083 0.93372
## 0.50779 0.12105 4.195 2.73e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 27.73102 -0.6499881
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.369 -0.407
## [2,] 0.015 -0.369
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.2784 -0.387
## [2,] -0.0183 -0.508
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 467.275 157.5240
## [2,] 157.524 232.5929
## ----
## aic= 11.35132
## bic= 11.38878
## Number of parameters: 10
## initial estimates: 18.9805 -2.2041 0.1521 0.2345 0.0959 0.0063 0.0247 0.0242 -0.0933 0.2484
## Par. lower-bounds: 16.1788 -5.5604 0.0323 0.0939 -0.0477 -0.1621 -0.1173 -0.1293 -0.2634 0.0645
## Par. upper-bounds: 21.7822 1.1522 0.272 0.3751 0.2395 0.1747 0.1667 0.1776 0.0768 0.4322
## Final Estimates: 17.79647 -5.356932 0.2078998 0.3750835 0.2381969 -0.1621211 -0.06077672 -0.1209029 -0.26336 0.4069851## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 17.79647 NaN NaN NaN
## loneliness_state_pmc -5.35693 2.30907 -2.320 0.02034 *
## depressedmood_state 0.20790 NaN NaN NaN
## loneliness_state_pmc 0.37508 NaN NaN NaN
## depressedmood_state 0.23820 0.09922 2.401 0.01636 *
## loneliness_state_pmc -0.16212 0.13861 -1.170 0.24217
## -0.06078 NaN NaN NaN
## -0.12090 NaN NaN NaN
## -0.26336 0.08608 -3.059 0.00222 **
## 0.40699 0.12941 3.145 0.00166 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 17.79647 -5.356932
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.208 0.375
## [2,] 0.238 -0.162
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.0608 0.121
## [2,] 0.2634 -0.407
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 211.9204 155.8755
## [2,] 155.8755 306.0602
## ----
## aic= 10.6249
## bic= 10.66236
## Number of parameters: 10
## initial estimates: 6.6675 -5.1649 0.4017 0.1592 0.4565 0.6215 -0.2695 -0.0871 -0.4066 -0.239
## Par. lower-bounds: 5.2423 -6.9855 0.2847 0.0968 0.3071 0.5417 -0.4044 -0.1678 -0.5788 -0.3421
## Par. upper-bounds: 8.0928 -3.3444 0.5187 0.2217 0.606 0.7013 -0.1347 -0.0063 -0.2344 -0.1359
## Final Estimates: 5.377319 -5.048864 0.5187283 0.1382649 0.4522449 0.7012723 -0.3180371 -0.06013163 -0.3125228 -0.3343591## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 5.37732 NaN NaN NaN
## loneliness_state_pmc -5.04886 2.10583 -2.398 0.016504 *
## depressedmood_state 0.51873 NaN NaN NaN
## loneliness_state_pmc 0.13826 NaN NaN NaN
## depressedmood_state 0.45224 0.18756 2.411 0.015899 *
## loneliness_state_pmc 0.70127 0.07734 9.067 < 2e-16 ***
## -0.31804 NaN NaN NaN
## -0.06013 NaN NaN NaN
## -0.31252 0.20189 -1.548 0.121620
## -0.33436 0.08716 -3.836 0.000125 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 5.377319 -5.048864
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.519 0.138
## [2,] 0.452 0.701
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.318 0.0601
## [2,] 0.313 0.3344
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 111.26580 56.14824
## [2,] 56.14824 179.71760
## ----
## aic= 9.746023
## bic= 9.783482
## Number of parameters: 10
## initial estimates: 22.7954 2.7036 0.2541 0.1137 -0.0858 0.3333 0.0858 -0.2302 0.298 -0.3467
## Par. lower-bounds: 19.2372 -0.4166 0.1417 -0.0461 -0.1843 0.1932 -0.0493 -0.4093 0.1794 -0.5038
## Par. upper-bounds: 26.3537 5.8238 0.3664 0.2735 0.0127 0.4735 0.221 -0.051 0.4165 -0.1896
## Final Estimates: 19.31828 5.621133 0.3664132 0.08539555 -0.1842795 0.4734675 -0.04934451 -0.1747442 0.3464255 -0.424785## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 19.31828 NaN NaN NaN
## loneliness_state_pmc 5.62113 NaN NaN NaN
## depressedmood_state 0.36641 NaN NaN NaN
## loneliness_state_pmc 0.08540 0.10866 0.786 0.432
## depressedmood_state -0.18428 NaN NaN NaN
## loneliness_state_pmc 0.47347 NaN NaN NaN
## -0.04934 NaN NaN NaN
## -0.17474 0.09469 -1.845 0.065 .
## 0.34643 NaN NaN NaN
## -0.42479 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 19.31828 5.621133
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.366 0.0854
## [2,] -0.184 0.4735
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.0493 0.175
## [2,] -0.3464 0.425
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 336.4144 163.6505
## [2,] 163.6505 260.0121
## ----
## aic= 11.02783
## bic= 11.06528
## Number of parameters: 10
## initial estimates: 48.9655 -57.3473 0.4558 -0.2029 0.6374 -0.2719 -0.1896 0.324 -0.4317 0.3609
## Par. lower-bounds: 30.516 -78.885 0.2509 -0.3863 0.3981 -0.486 -0.4036 0.1327 -0.6816 0.1376
## Par. upper-bounds: 67.415 -35.8097 0.6608 -0.0194 0.8766 -0.0577 0.0244 0.5152 -0.1819 0.5841
## Final Estimates: 48.9197 -57.29459 0.4562269 -0.01938978 0.6371777 -0.06851369 -0.232729 0.1327372 -0.4516935 0.1376304## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 48.91970 17.07155 2.866 0.00416 **
## loneliness_state_pmc -57.29459 NaN NaN NaN
## depressedmood_state 0.45623 0.18977 2.404 0.01621 *
## loneliness_state_pmc -0.01939 0.22712 -0.085 0.93197
## depressedmood_state 0.63718 NaN NaN NaN
## loneliness_state_pmc -0.06851 NaN NaN NaN
## -0.23273 0.18738 -1.242 0.21423
## 0.13274 0.23055 0.576 0.56479
## -0.45169 NaN NaN NaN
## 0.13763 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 48.9197 -57.29459
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.456 -0.0194
## [2,] 0.637 -0.0685
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.233 -0.133
## [2,] 0.452 -0.138
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 90.36416 47.07466
## [2,] 47.07466 120.77201
## ----
## aic= 9.085069
## bic= 9.122528
## Number of parameters: 10
## initial estimates: 9.6645 -9.9273 0.6441 0.0735 0.3667 0.1152 -0.3731 0.002 -0.2384 -0.2286
## Par. lower-bounds: 7.0664 -13.1215 0.5498 -0.0474 0.2507 -0.0334 -0.4872 -0.1286 -0.3787 -0.3891
## Par. upper-bounds: 12.2625 -6.7331 0.7385 0.1944 0.4827 0.2638 -0.259 0.1325 -0.0982 -0.0681
## Final Estimates: 7.105157 -9.945948 0.738475 0.194361 0.3674601 0.2638427 -0.4681867 -0.1275683 -0.2169623 -0.3459143## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 7.10516 2.05770 3.453 0.000554 ***
## loneliness_state_pmc -9.94595 2.22024 -4.480 7.48e-06 ***
## depressedmood_state 0.73847 0.07581 9.741 < 2e-16 ***
## loneliness_state_pmc 0.19436 0.11073 1.755 0.079226 .
## depressedmood_state 0.36746 0.08142 4.513 6.39e-06 ***
## loneliness_state_pmc 0.26384 NaN NaN NaN
## -0.46819 0.08562 -5.468 4.55e-08 ***
## -0.12757 0.10524 -1.212 0.225437
## -0.21696 0.08876 -2.444 0.014507 *
## -0.34591 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 7.105157 -9.945948
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.738 0.194
## [2,] 0.367 0.264
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.468 0.128
## [2,] 0.217 0.346
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 63.31642 25.63513
## [2,] 25.63513 102.10357
## ----
## aic= 8.681221
## bic= 8.71868
## Number of parameters: 10
## initial estimates: 16.983 -7.0498 0.57 0.2417 0.179 0.387 -0.1739 -0.1381 0.1483 -0.4097
## Par. lower-bounds: 13.2044 -11.062 0.4758 0.1092 0.0789 0.2463 -0.2885 -0.2834 0.0267 -0.5639
## Par. upper-bounds: 20.7616 -3.0376 0.6642 0.3743 0.279 0.5278 -0.0594 0.0072 0.2699 -0.2554
## Final Estimates: 14.31046 -5.8178 0.6368425 0.3585573 0.1469277 0.4203946 -0.2679645 -0.280191 0.1812833 -0.4049348## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 14.31046 3.70235 3.865 0.000111 ***
## loneliness_state_pmc -5.81780 NaN NaN NaN
## depressedmood_state 0.63684 0.09381 6.789 1.13e-11 ***
## loneliness_state_pmc 0.35856 0.18070 1.984 0.047220 *
## depressedmood_state 0.14693 NaN NaN NaN
## loneliness_state_pmc 0.42039 NaN NaN NaN
## -0.26796 0.08640 -3.102 0.001925 **
## -0.28019 0.17911 -1.564 0.117730
## 0.18128 NaN NaN NaN
## -0.40493 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 14.31046 -5.8178
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.637 0.359
## [2,] 0.147 0.420
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.268 0.280
## [2,] -0.181 0.405
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 151.87015 66.17968
## [2,] 66.17968 178.16525
## ----
## aic= 10.04345
## bic= 10.08091
## Number of parameters: 10
## initial estimates: 25.0443 12.2092 0.3728 0.0467 -0.3057 0.8363 -0.1382 -0.0365 0.4155 -0.665
## Par. lower-bounds: 18.9414 5.346 0.2206 -0.0726 -0.4768 0.7022 -0.3039 -0.1688 0.2292 -0.8137
## Par. upper-bounds: 31.1472 19.0724 0.5249 0.1659 -0.1346 0.9704 0.0274 0.0957 0.6017 -0.5163
## Final Estimates: 24.40115 10.05307 0.3903441 0.1659489 -0.2511797 0.9515961 -0.1607479 -0.1687829 0.313735 -0.7473469## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 24.40115 NaN NaN NaN
## loneliness_state_pmc 10.05307 NaN NaN NaN
## depressedmood_state 0.39034 NaN NaN NaN
## loneliness_state_pmc 0.16595 NaN NaN NaN
## depressedmood_state -0.25118 NaN NaN NaN
## loneliness_state_pmc 0.95160 0.04216 22.568 < 2e-16 ***
## -0.16075 NaN NaN NaN
## -0.16878 0.02291 -7.369 1.72e-13 ***
## 0.31373 NaN NaN NaN
## -0.74735 0.05731 -13.040 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 24.40115 10.05307
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.390 0.166
## [2,] -0.251 0.952
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.161 0.169
## [2,] -0.314 0.747
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 90.36415 48.93631
## [2,] 48.93631 112.21902
## ----
## aic= 8.969194
## bic= 9.006652
## Number of parameters: 10
## initial estimates: 7.0517 -6.8225 0.7225 0.0492 0.2692 0.1443 -0.4003 0.2151 -0.2088 0.0254
## Par. lower-bounds: 4.4365 -9.0458 0.624 -0.1304 0.1855 -0.0084 -0.5196 0.0187 -0.3102 -0.1415
## Par. upper-bounds: 9.667 -4.5991 0.821 0.2288 0.3529 0.2969 -0.2809 0.4114 -0.1073 0.1923
## Final Estimates: 6.786658 -8.964867 0.7324847 0.09353856 0.3529061 -0.008402866 -0.3329846 0.08008712 -0.2930078 0.1922861
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 6.786658 22.339344 0.304 0.761
## loneliness_state_pmc -8.964867 6.762730 -1.326 0.185
## depressedmood_state 0.732485 0.879660 0.833 0.405
## loneliness_state_pmc 0.093539 2.023137 0.046 0.963
## depressedmood_state 0.352906 0.265785 1.328 0.184
## loneliness_state_pmc -0.008403 0.839010 -0.010 0.992
## -0.332985 0.999617 -0.333 0.739
## 0.080087 2.137439 0.037 0.970
## -0.293008 0.355328 -0.825 0.410
## 0.192286 1.075759 0.179 0.858
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 6.786658 -8.964867
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.732 0.0935
## [2,] 0.353 -0.0084
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.333 -0.0801
## [2,] 0.293 -0.1923
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 202.72929 84.48587
## [2,] 84.48587 142.40007
## ----
## aic= 10.00077
## bic= 10.03823
## Number of parameters: 10
## initial estimates: 11.6824 3.2301 0.379 0.2163 -0.1697 0.5129 -0.3937 0.2002 0.1464 -0.161
## Par. lower-bounds: 9.164 0.5108 0.2485 0.0532 -0.3106 0.3368 -0.5411 0.0257 -0.0127 -0.3494
## Par. upper-bounds: 14.2008 5.9493 0.5096 0.3794 -0.0287 0.6891 -0.2463 0.3747 0.3056 0.0274
## Final Estimates: 13.26708 4.677934 0.2939497 0.3433521 -0.2487498 0.4919479 -0.2462932 0.03448958 0.2249603 -0.1211295
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 13.26708 2.32935 5.696 1.23e-08 ***
## loneliness_state_pmc 4.67793 3.49953 1.337 0.18131
## depressedmood_state 0.29395 0.12358 2.379 0.01737 *
## loneliness_state_pmc 0.34335 0.19217 1.787 0.07398 .
## depressedmood_state -0.24875 0.18569 -1.340 0.18038
## loneliness_state_pmc 0.49195 0.19030 2.585 0.00974 **
## -0.24629 0.14172 -1.738 0.08223 .
## 0.03449 0.21551 0.160 0.87285
## 0.22496 0.18988 1.185 0.23612
## -0.12113 0.19411 -0.624 0.53261
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 13.26708 4.677934
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.294 0.343
## [2,] -0.249 0.492
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.246 -0.0345
## [2,] -0.225 0.1211
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 121.32316 70.93369
## [2,] 70.93369 137.12206
## ----
## aic= 9.373433
## bic= 9.410892
## Number of parameters: 10
## initial estimates: 4.1548 -1.3023 0.869 -0.8786 0.0421 0.2127 -0.3139 0.7324 0.0457 -0.1802
## Par. lower-bounds: 2.3008 -2.9158 0.8131 -1.0775 -0.0066 0.0395 -0.3946 0.5222 -0.0246 -0.3631
## Par. upper-bounds: 6.0088 0.3112 0.925 -0.6796 0.0908 0.3858 -0.2331 0.9426 0.116 0.0027
## Final Estimates: 3.791563 -0.4637659 0.8796199 -1.077547 0.01383004 0.2625873 -0.2827196 0.874059 0.1019388 -0.3631462## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 3.791563 1.504508 2.520 0.011731 *
## loneliness_state_pmc -0.463766 0.246828 -1.879 0.060258 .
## depressedmood_state 0.879620 0.046529 18.905 < 2e-16 ***
## loneliness_state_pmc -1.077547 0.279198 -3.859 0.000114 ***
## depressedmood_state 0.013830 0.008121 1.703 0.088565 .
## loneliness_state_pmc 0.262587 0.025690 10.222 < 2e-16 ***
## -0.282720 0.057087 -4.952 7.33e-07 ***
## 0.874059 0.276251 3.164 0.001556 **
## 0.101939 0.022628 4.505 6.64e-06 ***
## -0.363146 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 3.791563 -0.4637659
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.8796 -1.078
## [2,] 0.0138 0.263
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.283 -0.874
## [2,] -0.102 0.363
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 126.75975 32.55736
## [2,] 32.55736 95.00644
## ----
## aic= 9.318391
## bic= 9.355849
## Number of parameters: 10
## initial estimates: 2.062 -8.3898 0.9227 -0.1757 0.316 0.304 -0.5799 0.2978 -0.2471 -0.2963
## Par. lower-bounds: -1.0445 -10.5767 0.8083 -0.3833 0.2354 0.1579 -0.7125 0.0687 -0.3404 -0.4576
## Par. upper-bounds: 5.1685 -6.2029 1.0372 0.0318 0.3966 0.4501 -0.4473 0.5268 -0.1537 -0.1351
## Final Estimates: -0.3285593 -8.146462 1.012946 -0.2176116 0.3077414 0.4501499 -0.7124753 0.3971807 -0.2543848 -0.4575799
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state -0.32856 1.40879 -0.233 0.815590
## loneliness_state_pmc -8.14646 2.12997 -3.825 0.000131 ***
## depressedmood_state 1.01295 0.05289 19.154 < 2e-16 ***
## loneliness_state_pmc -0.21761 0.09086 -2.395 0.016614 *
## depressedmood_state 0.30774 0.08033 3.831 0.000128 ***
## loneliness_state_pmc 0.45015 0.14495 3.105 0.001900 **
## -0.71248 0.06901 -10.324 < 2e-16 ***
## 0.39718 0.09789 4.057 4.96e-05 ***
## -0.25438 0.10439 -2.437 0.014815 *
## -0.45758 0.15784 -2.899 0.003744 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: -0.3285593 -8.146462
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 1.013 -0.218
## [2,] 0.308 0.450
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.712 -0.397
## [2,] 0.254 0.458
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 136.36663 49.77029
## [2,] 49.77029 64.96201
## ----
## aic= 8.775455
## bic= 8.812914
## Number of parameters: 10
## initial estimates: 3.6702 1.8993 0.1822 0.2039 -0.4232 0.5403 -0.229 -0.1113 0.3461 -0.4278
## Par. lower-bounds: 2.2176 0.2051 -0.1257 -0.0312 -0.7824 0.266 -0.543 -0.3521 -0.02 -0.7088
## Par. upper-bounds: 5.1229 3.5935 0.4902 0.4391 -0.064 0.8145 0.0849 0.1296 0.7123 -0.1468
## Final Estimates: 2.297416 2.876562 0.490199 -0.01296353 -0.6389866 0.8145332 -0.5070488 0.1142545 0.5715398 -0.6925034## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 2.29742 0.91544 2.510 0.012085 *
## loneliness_state_pmc 2.87656 1.42946 2.012 0.044184 *
## depressedmood_state 0.49020 0.20188 2.428 0.015176 *
## loneliness_state_pmc -0.01296 NaN NaN NaN
## depressedmood_state -0.63899 0.31571 -2.024 0.042973 *
## loneliness_state_pmc 0.81453 0.18997 4.288 1.81e-05 ***
## -0.50705 0.19087 -2.656 0.007896 **
## 0.11425 NaN NaN NaN
## 0.57154 0.32188 1.776 0.075795 .
## -0.69250 0.19685 -3.518 0.000435 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 2.297416 2.876562
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.490 -0.013
## [2,] -0.639 0.815
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.507 -0.114
## [2,] -0.572 0.693
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 68.08790 35.41162
## [2,] 35.41162 92.16609
## ----
## aic= 8.535752
## bic= 8.573211
## Number of parameters: 10
## initial estimates: 16.9356 3.9788 0.2126 0.2386 -0.1849 0.7043 -0.0178 -0.1933 0.2483 -0.4469
## Par. lower-bounds: 13.2382 0.1537 0.0435 0.0986 -0.3599 0.5595 -0.1999 -0.3474 0.06 -0.6063
## Par. upper-bounds: 20.6329 7.8039 0.3818 0.3786 -0.0099 0.8492 0.1642 -0.0393 0.4367 -0.2875
## Final Estimates: 20.56273 5.668057 0.04357141 0.3056581 -0.2635931 0.6165054 0.1642446 -0.2411379 0.2903255 -0.2875466
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 20.56273 11.00397 1.869 0.061670 .
## loneliness_state_pmc 5.66806 7.28061 0.779 0.436266
## depressedmood_state 0.04357 0.51178 0.085 0.932153
## loneliness_state_pmc 0.30566 0.34145 0.895 0.370694
## depressedmood_state -0.26359 0.33844 -0.779 0.436072
## loneliness_state_pmc 0.61651 0.18312 3.367 0.000761 ***
## 0.16424 0.56151 0.293 0.769899
## -0.24114 0.37978 -0.635 0.525468
## 0.29033 0.35366 0.821 0.411698
## -0.28755 0.18747 -1.534 0.125071
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 20.56273 5.668057
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.0436 0.306
## [2,] -0.2636 0.617
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] -0.164 0.241
## [2,] -0.290 0.288
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 149.09789 83.47118
## [2,] 83.47118 163.07011
## ----
## aic= 9.775401
## bic= 9.81286
## Number of parameters: 10
## initial estimates: 4.4497 -25.4477 0.9009 -0.4082 0.5566 -0.2947 -0.6476 0.3253 -0.452 0.3098
## Par. lower-bounds: -4.4372 -32.283 0.7071 -0.7428 0.4076 -0.552 -0.8543 -0.021 -0.6109 0.0435
## Par. upper-bounds: 13.3367 -18.6123 1.0947 -0.0736 0.7057 -0.0373 -0.4409 0.6716 -0.293 0.5762
## Final Estimates: 4.738265 -29.52358 0.8962188 -0.07363697 0.6464021 -0.5061178 -0.5869371 0.02584877 -0.4831747 0.5761577## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 4.73826 NaN NaN NaN
## loneliness_state_pmc -29.52358 NaN NaN NaN
## depressedmood_state 0.89622 NaN NaN NaN
## loneliness_state_pmc -0.07364 NaN NaN NaN
## depressedmood_state 0.64640 NaN NaN NaN
## loneliness_state_pmc -0.50612 NaN NaN NaN
## -0.58694 NaN NaN NaN
## 0.02585 NaN NaN NaN
## -0.48317 NaN NaN NaN
## 0.57616 NaN NaN NaN
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 4.738265 -29.52358
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.896 -0.0736
## [2,] 0.646 -0.5061
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.587 -0.0258
## [2,] 0.483 -0.5762
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 238.0644 113.7730
## [2,] 113.7730 148.0178
## ----
## aic= 10.02633
## bic= 10.06379
## Number of parameters: 10
## initial estimates: 5.8492 -4.0409 0.4454 0.1718 0.3773 0.2426 0.0977 -0.0825 -0.204 -0.0752
## Par. lower-bounds: 4.6464 -5.7755 0.3472 0.0806 0.2356 0.1109 -0.025 -0.1879 -0.3809 -0.2272
## Par. upper-bounds: 7.0519 -2.3063 0.5437 0.2631 0.519 0.3742 0.2203 0.0229 -0.0271 0.0768
## Final Estimates: 5.878664 -4.927653 0.4426647 0.1262543 0.4647239 0.1321414 0.08681995 -0.008783663 -0.27499 0.07680688## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 5.878664 0.808652 7.270 3.60e-13 ***
## loneliness_state_pmc -4.927653 NaN NaN NaN
## depressedmood_state 0.442665 0.070004 6.323 2.56e-10 ***
## loneliness_state_pmc 0.126254 0.081240 1.554 0.120
## depressedmood_state 0.464724 NaN NaN NaN
## loneliness_state_pmc 0.132141 NaN NaN NaN
## 0.086820 0.063409 1.369 0.171
## -0.008784 0.072855 -0.121 0.904
## -0.274990 NaN NaN NaN
## 0.076807 NaN NaN NaN
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 5.878664 -4.927653
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.443 0.126
## [2,] 0.465 0.132
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] -0.0868 0.00878
## [2,] 0.2750 -0.07681
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 127.2828 109.8139
## [2,] 109.8139 263.8374
## ----
## aic= 9.991157
## bic= 10.02862
## Number of parameters: 10
## initial estimates: 10.3189 -7.0596 0.4737 0.1301 0.3604 -0.0584 -0.216 -0.219 -0.3462 -0.0316
## Par. lower-bounds: 7.2425 -10.7269 0.3178 -0.0646 0.1746 -0.2904 -0.3836 -0.4203 -0.5461 -0.2716
## Par. upper-bounds: 13.3953 -3.3922 0.6295 0.3247 0.5462 0.1737 -0.0483 -0.0178 -0.1463 0.2083
## Final Estimates: 7.269305 -10.68752 0.6289825 0.3247304 0.5461944 -0.1846805 -0.3836495 -0.3346471 -0.5287274 0.1449557
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 7.2693 6.7787 1.072 0.283552
## loneliness_state_pmc -10.6875 2.3011 -4.645 3.41e-06 ***
## depressedmood_state 0.6290 0.3463 1.816 0.069356 .
## loneliness_state_pmc 0.3247 0.6760 0.480 0.630952
## depressedmood_state 0.5462 0.1170 4.669 3.02e-06 ***
## loneliness_state_pmc -0.1847 0.2409 -0.767 0.443230
## -0.3836 0.3772 -1.017 0.309112
## -0.3346 0.6707 -0.499 0.617811
## -0.5287 0.1390 -3.804 0.000142 ***
## 0.1450 0.2159 0.671 0.502049
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 7.269305 -10.68752
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.629 0.325
## [2,] 0.546 -0.185
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.384 0.335
## [2,] 0.529 -0.145
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 47.15119 24.25717
## [2,] 24.25717 67.55546
## ----
## aic= 7.876363
## bic= 7.913822
## Number of parameters: 10
## initial estimates: 16.6339 -18.4133 0.6542 -0.1739 0.3817 -0.26 -0.2054 0.1054 -0.2806 0.3787
## Par. lower-bounds: 10.1107 -23.0057 0.5203 -0.4262 0.2874 -0.4376 -0.3575 -0.166 -0.3877 0.1877
## Par. upper-bounds: 23.1572 -13.821 0.7881 0.0784 0.4759 -0.0824 -0.0533 0.3768 -0.1736 0.5698
## Final Estimates: 13.5508 -17.5113 0.7181452 -0.4261569 0.3639289 -0.2292379 -0.2311963 0.3767606 -0.2313484 0.3204161## Warning in sqrt(diag(solve(Hessian))): NaNs produced##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## depressedmood_state 13.5508 NaN NaN NaN
## loneliness_state_pmc -17.5113 1.5018 -11.660 < 2e-16 ***
## depressedmood_state 0.7181 NaN NaN NaN
## loneliness_state_pmc -0.4262 NaN NaN NaN
## depressedmood_state 0.3639 0.0300 12.132 < 2e-16 ***
## loneliness_state_pmc -0.2292 0.1320 -1.737 0.08233 .
## -0.2312 NaN NaN NaN
## 0.3768 NaN NaN NaN
## -0.2314 NaN NaN NaN
## 0.3204 0.1235 2.594 0.00947 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ---
## Estimates in matrix form:
## Constant term:
## Estimates: 13.5508 -17.5113
## AR coefficient matrix
## AR( 1 )-matrix
## [,1] [,2]
## [1,] 0.718 -0.426
## [2,] 0.364 -0.229
## MA coefficient matrix
## MA( 1 )-matrix
## [,1] [,2]
## [1,] 0.231 -0.377
## [2,] 0.231 -0.320
##
## Residuals cov-matrix:
## [,1] [,2]
## [1,] 319.4000 132.1469
## [2,] 132.1469 160.1808
## ----
## aic= 10.43951
## bic= 10.47697# Extract fit results and noisy simulated series into separate lists
fit_results_list <- lapply(simulated_data_list, function(x) x$fit)
noisy_simulated_data_list <- lapply(simulated_data_list, function(x) x$noisy_simulated_series)
head(noisy_simulated_data_list[[2]])## [,1] [,2]
## [1,] -21.416277 -17.725189
## [2,] -3.567117 -14.181161
## [3,] 9.901681 11.494652
## [4,] -3.084147 -34.573236
## [5,] 4.223676 2.742824
## [6,] -10.839556 -2.273094Lastly we can plot a specific individual’s data (eg., individual 2) We can also combine the list into a data frame for easier analysis in the future.
plot.ts(noisy_simulated_data_list[[2]], xlab = "Time", main = "Time Series Data")
#turning it into one large data frame for analysis
combined_noisy_simulated_df <- do.call(rbind, lapply(1:length(noisy_simulated_data_list), function(i) {
individual_df <- as.data.frame(noisy_simulated_data_list[[i]])
individual_df$ID <- i
individual_df$time <- 1:nrow(individual_df)
return(individual_df)
}))
head(combined_noisy_simulated_df)## V1 V2 ID time
## 1 -20.6887321 -14.0768312 1 1
## 2 1.7708411 -7.0322110 1 2
## 3 5.3934847 12.0572885 1 3
## 4 5.4853600 -35.2848444 1 4
## 5 -0.6238122 -4.8033292 1 5
## 6 -10.0310852 -0.4980432 1 6