1.a
a<-matrix(c(0,0,1,0,2,0,0,3,0,0,0,0,0,0,-.5,0),nrow = 4)
sigma=solve(diag(4)-a)%*%t(solve(diag(4)-a))
solve(sigma)
## [,1] [,2] [,3]
## [1,] 2.00000000000000044 -1.9999999999999947e+00 -1.0000000000000009e+00
## [2,] -1.99999999999999822 1.4000000000000007e+01 -1.3322676295501878e-15
## [3,] -1.00000000000000022 -3.9968028886505691e-15 1.0000000000000004e+00
## [4,] -0.50000000000000089 -3.0000000000000049e+00 5.0000000000000089e-01
## [,4]
## [1,] -0.50000000000000266
## [2,] -3.00000000000000133
## [3,] 0.50000000000000133
## [4,] 1.25000000000000178
datagenerate<-function(){
X2 = rnorm(1000)
X1=sapply(seq(1000),FUN = function(i) {e1=rnorm(1)
2*X2[i]+e1})
X4=sapply(seq(1000),FUN = function(i) {e4=rnorm(1)
3*X2[i]+e4})
X3 =sapply(seq(1000),FUN = function(i) {e3=rnorm(1)
X1[i]-0.5*X4[i]+e3})
return(data.frame(x1=X1,x2=X2,x3=X3,x4=X4))
}
dat<-lapply(seq(100),FUN = function(x) return(datagenerate()))
1.b
library(pcalg)
## Warning: package 'pcalg' was built under R version 3.2.5
library(combinat)
##
## Attaching package: 'combinat'
## The following object is masked from 'package:utils':
##
## combn
alpha <- 0.05
cutoff <- qnorm(1-alpha/2)
combination<-combn(x = seq(4),m = 2)
testconind<-function(dat){
corMatrix <- cor(dat)
testresult<-apply(combination,2,FUN = function(x){
return(condIndFisherZ(x = x[1],y = x[2],S = seq(4)[-x]
,corMatrix,n = dim(dat)[1],cutoff))})#(2,3)
return(combination[,testresult])
}
run100<-lapply(dat,FUN =function(x) return(testconind(x)) )
sum(unlist(lapply(run100,function(x){
if(sum(x==c(2,3))==2){return(1)}else{return(0)}
})))
## [1] 98
alpha <- 0.005
cutoff <- qnorm(1-alpha/2)
combination<-combn(x = seq(4),m = 2)
testconind<-function(dat){
corMatrix <- cor(dat)
testresult<-apply(combination,2,FUN = function(x){
return(condIndFisherZ(x = x[1],y = x[2],S = seq(4)[-x]
,corMatrix,n = dim(dat)[1],cutoff))})#(2,3)
return(combination[,testresult])
}
run100<-lapply(dat,FUN =function(x) return(testconind(x)) )
sum(unlist(lapply(run100,function(x){
if(sum(x==c(2,3))==2){return(1)}else{return(0)}
})))
## [1] 100
1.c
regselection<-function(dat){
bicselection<-function(responsei){
response=dat[,responsei]
full = lm(response ~ . , data = dat[,-responsei])
result<-step(full,direction="backward", k=log(dim(dat)[1]),trace = FALSE)
s=dim(result$anova)[1]
result$anova[s,1]
}
return(sapply(seq(4),FUN = bicselection))
}
r<-sapply(dat,FUN =function(x) return(regselection(x)))
sum(apply(r,2,FUN = function(x) {if(sum(x==c("","- x3","- x2",""))==4) return(TRUE)
else return(FALSE)}))
## [1] 100
1.d
library(glasso)
#Estimates a sparse inverse covariance matrix using a lasso (L1) penalty
lassoselection<-function(dat){
covMatrix<-cov(dat)
lassoinverse<-glasso(covMatrix,rho = 0.1)$wi
if(identical(setdiff(levels(factor(which(lassoinverse==0,arr.ind = T))) ,
c("2","3")),character(0)))return(TRUE)
else return(FALSE)
}
sum(sapply(dat,FUN =function(x) return(lassoselection(x))))
## [1] 100
2.a
library(glmnet)
## Loading required package: Matrix
## Warning: package 'Matrix' was built under R version 3.2.5
## Loading required package: foreach
## Loaded glmnet 2.0-5
HW3_DataSet<-read.table('HW3_DataSet.txt',colClasses = c('character','factor'),sep = ',')
y<-HW3_DataSet$V2
x<-unlist(strsplit(HW3_DataSet$V1,split = ""))
x<-matrix(x,byrow = TRUE,ncol=8)
colnames(x)<-paste('x',seq(8),sep = '')
createinteraction<-function(){
combination<-combn(8,2)
mat<-matrix(NA,nrow = dim(x)[1],ncol = ncol(combination))
colnames(mat)<-rep('hh',ncol(combination))
for(i in seq(ncol(combination))){
mat[,i]<-as.character(interaction(as.data.frame(x[,combination[,i]])))
colnames(mat)[i]<-paste('x',combination[,i][1],combination[,i][2],sep = '')
}
return(mat)
}
interterms<-createinteraction()
x<-cbind(x,interterms)
x[1:5,]
## x1 x2 x3 x4 x5 x6 x7 x8 x12 x13 x14 x15 x16 x17
## [1,] "1" "3" "2" "2" "2" "2" "1" "2" "1.3" "1.2" "1.2" "1.2" "1.2" "1.1"
## [2,] "2" "1" "3" "3" "2" "2" "3" "3" "2.1" "2.3" "2.3" "2.2" "2.2" "2.3"
## [3,] "2" "1" "2" "3" "2" "2" "2" "2" "2.1" "2.2" "2.3" "2.2" "2.2" "2.2"
## [4,] "1" "1" "2" "1" "3" "1" "3" "3" "1.1" "1.2" "1.1" "1.3" "1.1" "1.3"
## [5,] "2" "2" "1" "3" "1" "2" "2" "3" "2.2" "2.1" "2.3" "2.1" "2.2" "2.2"
## x18 x23 x24 x25 x26 x27 x28 x34 x35 x36 x37
## [1,] "1.2" "3.2" "3.2" "3.2" "3.2" "3.1" "3.2" "2.2" "2.2" "2.2" "2.1"
## [2,] "2.3" "1.3" "1.3" "1.2" "1.2" "1.3" "1.3" "3.3" "3.2" "3.2" "3.3"
## [3,] "2.2" "1.2" "1.3" "1.2" "1.2" "1.2" "1.2" "2.3" "2.2" "2.2" "2.2"
## [4,] "1.3" "1.2" "1.1" "1.3" "1.1" "1.3" "1.3" "2.1" "2.3" "2.1" "2.3"
## [5,] "2.3" "2.1" "2.3" "2.1" "2.2" "2.2" "2.3" "1.3" "1.1" "1.2" "1.2"
## x38 x45 x46 x47 x48 x56 x57 x58 x67 x68 x78
## [1,] "2.2" "2.2" "2.2" "2.1" "2.2" "2.2" "2.1" "2.2" "2.1" "2.2" "1.2"
## [2,] "3.3" "3.2" "3.2" "3.3" "3.3" "2.2" "2.3" "2.3" "2.3" "2.3" "3.3"
## [3,] "2.2" "3.2" "3.2" "3.2" "3.2" "2.2" "2.2" "2.2" "2.2" "2.2" "2.2"
## [4,] "2.3" "1.3" "1.1" "1.3" "1.3" "3.1" "3.3" "3.3" "1.3" "1.3" "3.3"
## [5,] "1.3" "3.1" "3.2" "3.2" "3.3" "1.2" "1.2" "1.3" "2.2" "2.3" "2.3"
fit = glmnet(x,y, family = "binomial")
fit$beta[,54]#chooose the tunning by largest %Dev:The fraction of (null) deviance explained
## x1 x2 x3
## 0.00000000000000000000 0.00000000000000000000 0.00000000000000000000
## x4 x5 x6
## -0.26780824428816774052 0.00000000000000000000 0.00000000000000000000
## x7 x8 x12
## 0.00000000000000000000 0.00623187031235798630 0.00000000000000000000
## x13 x14 x15
## 0.00000000000000000000 -0.78786379125861571993 0.00000000000000000000
## x16 x17 x18
## 0.00000000000000000000 0.00000000000000000000 0.00000000000000000000
## x23 x24 x25
## 0.00000000000000000000 -0.45648445886252342341 0.00000000000000000000
## x26 x27 x28
## 0.00000000000000000000 0.00000000000000000000 0.00000000000000000000
## x34 x35 x36
## 0.00000000000000000000 0.15321797660305888633 0.00000000000000000000
## x37 x38 x45
## 0.00000000000000000000 0.00022824204627049555 0.00000000000000000000
## x46 x47 x48
## 0.00000000000000000000 0.00000000000000000000 0.00000000000000000000
## x56 x57 x58
## 0.12282120433194361475 0.80835869496077128460 0.00268721891733512746
## x67 x68 x78
## 0.29195492913722281836 0.00296264587794060116 0.48359349142853547132
2.b
library(nnet)
y<-HW3_DataSet$V2
dat<-unlist(strsplit(HW3_DataSet$V1[y==" 1"],split = ""))
dat<-matrix(dat,byrow = TRUE,ncol=8)
colnames(dat)<-paste('x',seq(8),sep = '')
dat<-as.data.frame(dat)
selectionlist<-list()
for(i in seq(8)){
full <- multinom(dat[,i] ~ ., data = dat[,-i])
bicselect<-step(full,direction = 'backward'
,k=log(dim(dat)[1]),trace = 0)
selectionlist[[i]]<-(bicselect$coefnames)
}
## # weights: 48 (30 variable)
## initial value 721.788274
## iter 10 value 502.397312
## iter 20 value 491.265627
## iter 30 value 490.760234
## iter 40 value 490.699726
## final value 490.699633
## converged
## trying - x2
## trying - x3
## trying - x4
## trying - x5
## trying - x6
## trying - x7
## trying - x8
## # weights: 42 (26 variable)
## initial value 721.788274
## iter 10 value 501.981943
## iter 20 value 493.372342
## iter 30 value 492.801714
## iter 40 value 492.783306
## final value 492.783288
## converged
## trying - x2
## trying - x3
## trying - x4
## trying - x6
## trying - x7
## trying - x8
## # weights: 36 (22 variable)
## initial value 721.788274
## iter 10 value 504.503816
## iter 20 value 495.382130
## iter 30 value 495.076341
## final value 495.073689
## converged
## trying - x2
## trying - x3
## trying - x4
## trying - x7
## trying - x8
## # weights: 30 (18 variable)
## initial value 721.788274
## iter 10 value 505.653455
## iter 20 value 497.894219
## iter 30 value 497.765842
## final value 497.765540
## converged
## trying - x3
## trying - x4
## trying - x7
## trying - x8
## # weights: 24 (14 variable)
## initial value 721.788274
## iter 10 value 507.803007
## iter 20 value 500.292867
## iter 30 value 500.260850
## iter 30 value 500.260849
## final value 500.260849
## converged
## trying - x3
## trying - x4
## trying - x7
## # weights: 18 (10 variable)
## initial value 721.788274
## iter 10 value 510.054286
## final value 503.521894
## converged
## trying - x3
## trying - x7
## # weights: 12 (6 variable)
## initial value 721.788274
## iter 10 value 507.561241
## final value 507.449117
## converged
## trying - x7
## # weights: 48 (30 variable)
## initial value 721.788274
## iter 10 value 692.480246
## iter 20 value 690.005810
## iter 30 value 689.883026
## final value 689.882532
## converged
## trying - x1
## trying - x3
## trying - x4
## trying - x5
## trying - x6
## trying - x7
## trying - x8
## # weights: 42 (26 variable)
## initial value 721.788274
## iter 10 value 693.412983
## iter 20 value 691.171996
## iter 30 value 691.076745
## final value 691.076691
## converged
## trying - x1
## trying - x3
## trying - x4
## trying - x5
## trying - x7
## trying - x8
## # weights: 36 (22 variable)
## initial value 721.788274
## iter 10 value 695.004088
## iter 20 value 692.733691
## final value 692.676479
## converged
## trying - x1
## trying - x4
## trying - x5
## trying - x7
## trying - x8
## # weights: 30 (18 variable)
## initial value 721.788274
## iter 10 value 696.778446
## iter 20 value 694.925406
## final value 694.922239
## converged
## trying - x4
## trying - x5
## trying - x7
## trying - x8
## # weights: 24 (14 variable)
## initial value 721.788274
## iter 10 value 700.249659
## iter 20 value 698.036404
## iter 20 value 698.036403
## iter 20 value 698.036403
## final value 698.036403
## converged
## trying - x5
## trying - x7
## trying - x8
## # weights: 18 (10 variable)
## initial value 721.788274
## iter 10 value 702.445841
## final value 701.383331
## converged
## trying - x5
## trying - x8
## # weights: 12 (6 variable)
## initial value 721.788274
## iter 10 value 704.028805
## final value 704.028247
## converged
## trying - x5
## # weights: 48 (30 variable)
## initial value 721.788274
## iter 10 value 680.299236
## iter 20 value 677.434221
## iter 30 value 677.320747
## iter 30 value 677.320746
## iter 30 value 677.320743
## final value 677.320743
## converged
## trying - x1
## trying - x2
## trying - x4
## trying - x5
## trying - x6
## trying - x7
## trying - x8
## # weights: 42 (26 variable)
## initial value 721.788274
## iter 10 value 681.114708
## iter 20 value 678.068205
## iter 30 value 678.019519
## final value 678.019503
## converged
## trying - x1
## trying - x2
## trying - x4
## trying - x5
## trying - x7
## trying - x8
## # weights: 36 (22 variable)
## initial value 721.788274
## iter 10 value 682.510316
## iter 20 value 679.536995
## final value 679.458232
## converged
## trying - x1
## trying - x2
## trying - x5
## trying - x7
## trying - x8
## # weights: 30 (18 variable)
## initial value 721.788274
## iter 10 value 683.542375
## iter 20 value 681.119484
## final value 681.106992
## converged
## trying - x1
## trying - x5
## trying - x7
## trying - x8
## # weights: 24 (14 variable)
## initial value 721.788274
## iter 10 value 685.840297
## final value 682.878230
## converged
## trying - x1
## trying - x5
## trying - x8
## # weights: 48 (30 variable)
## initial value 721.788274
## iter 10 value 503.230561
## iter 20 value 478.933058
## iter 30 value 475.696540
## iter 40 value 475.371496
## iter 50 value 475.360365
## final value 475.360174
## converged
## trying - x1
## trying - x2
## trying - x3
## trying - x5
## trying - x6
## trying - x7
## trying - x8
## # weights: 42 (26 variable)
## initial value 721.788274
## iter 10 value 506.465205
## iter 20 value 478.731833
## iter 30 value 476.056672
## iter 40 value 475.823024
## iter 50 value 475.816739
## final value 475.816661
## converged
## trying - x1
## trying - x2
## trying - x3
## trying - x5
## trying - x7
## trying - x8
## # weights: 36 (22 variable)
## initial value 721.788274
## iter 10 value 506.498061
## iter 20 value 478.817797
## iter 30 value 476.972158
## iter 40 value 476.874031
## final value 476.872559
## converged
## trying - x1
## trying - x2
## trying - x3
## trying - x5
## trying - x7
## # weights: 30 (18 variable)
## initial value 721.788274
## iter 10 value 512.202703
## iter 20 value 479.482218
## iter 30 value 478.128648
## iter 40 value 478.048538
## final value 478.048360
## converged
## trying - x1
## trying - x2
## trying - x3
## trying - x5
## # weights: 24 (14 variable)
## initial value 721.788274
## iter 10 value 482.996503
## iter 20 value 479.560601
## iter 30 value 479.497532
## iter 40 value 479.494761
## iter 50 value 479.482489
## final value 479.481634
## converged
## trying - x1
## trying - x2
## trying - x5
## # weights: 18 (10 variable)
## initial value 721.788274
## iter 10 value 482.127579
## iter 20 value 482.036700
## final value 482.034706
## converged
## trying - x1
## trying - x2
## # weights: 12 (6 variable)
## initial value 721.788274
## iter 10 value 485.409165
## iter 20 value 485.185506
## final value 485.160859
## converged
## trying - x1
## # weights: 6 (2 variable)
## initial value 721.788274
## iter 10 value 489.149881
## iter 10 value 489.149880
## iter 10 value 489.149880
## final value 489.149880
## converged
## # weights: 48 (30 variable)
## initial value 721.788274
## iter 10 value 607.782838
## iter 20 value 594.419872
## iter 30 value 593.159940
## iter 40 value 593.014775
## final value 593.014133
## converged
## trying - x1
## trying - x2
## trying - x3
## trying - x4
## trying - x6
## trying - x7
## trying - x8
## # weights: 42 (26 variable)
## initial value 721.788274
## iter 10 value 601.078426
## iter 20 value 594.692676
## iter 30 value 594.432554
## iter 40 value 594.405325
## final value 594.405295
## converged
## trying - x2
## trying - x3
## trying - x4
## trying - x6
## trying - x7
## trying - x8
## # weights: 36 (22 variable)
## initial value 721.788274
## iter 10 value 601.209266
## iter 20 value 596.125326
## iter 30 value 595.910443
## iter 40 value 595.906440
## iter 40 value 595.906436
## iter 40 value 595.906436
## final value 595.906436
## converged
## trying - x2
## trying - x3
## trying - x4
## trying - x7
## trying - x8
## # weights: 30 (18 variable)
## initial value 721.788274
## iter 10 value 601.987541
## iter 20 value 597.975539
## final value 597.963136
## converged
## trying - x2
## trying - x3
## trying - x7
## trying - x8
## # weights: 48 (30 variable)
## initial value 721.788274
## iter 10 value 689.550913
## iter 20 value 681.638445
## iter 30 value 681.596455
## final value 681.596268
## converged
## trying - x1
## trying - x2
## trying - x3
## trying - x4
## trying - x5
## trying - x7
## trying - x8
## # weights: 42 (26 variable)
## initial value 721.788274
## iter 10 value 686.840098
## iter 20 value 682.203749
## iter 30 value 682.121113
## final value 682.121092
## converged
## trying - x1
## trying - x2
## trying - x3
## trying - x5
## trying - x7
## trying - x8
## # weights: 36 (22 variable)
## initial value 721.788274
## iter 10 value 687.661852
## iter 20 value 682.922570
## final value 682.866273
## converged
## trying - x1
## trying - x2
## trying - x5
## trying - x7
## trying - x8
## # weights: 30 (18 variable)
## initial value 721.788274
## iter 10 value 685.843318
## iter 20 value 684.155789
## final value 684.155779
## converged
## trying - x1
## trying - x5
## trying - x7
## trying - x8
## # weights: 24 (14 variable)
## initial value 721.788274
## iter 10 value 686.689268
## final value 685.759022
## converged
## trying - x1
## trying - x7
## trying - x8
## # weights: 18 (10 variable)
## initial value 721.788274
## iter 10 value 688.371377
## final value 687.886973
## converged
## trying - x7
## trying - x8
## # weights: 48 (30 variable)
## initial value 721.788274
## iter 10 value 615.182938
## iter 20 value 609.538848
## iter 30 value 609.241370
## final value 609.240081
## converged
## trying - x1
## trying - x2
## trying - x3
## trying - x4
## trying - x5
## trying - x6
## trying - x8
## # weights: 42 (26 variable)
## initial value 721.788274
## iter 10 value 616.573144
## iter 20 value 610.577916
## iter 30 value 610.425850
## final value 610.425521
## converged
## trying - x1
## trying - x2
## trying - x3
## trying - x5
## trying - x6
## trying - x8
## # weights: 36 (22 variable)
## initial value 721.788274
## iter 10 value 620.111444
## iter 20 value 612.180796
## final value 612.158885
## converged
## trying - x1
## trying - x2
## trying - x5
## trying - x6
## trying - x8
## # weights: 30 (18 variable)
## initial value 721.788274
## iter 10 value 627.787695
## iter 20 value 615.110084
## final value 615.093815
## converged
## trying - x1
## trying - x5
## trying - x6
## trying - x8
## # weights: 48 (30 variable)
## initial value 721.788274
## iter 10 value 671.417482
## iter 20 value 660.677239
## iter 30 value 660.496770
## final value 660.496320
## converged
## trying - x1
## trying - x2
## trying - x3
## trying - x4
## trying - x5
## trying - x6
## trying - x7
## # weights: 42 (26 variable)
## initial value 721.788274
## iter 10 value 671.202693
## iter 20 value 661.628284
## iter 30 value 661.437747
## final value 661.437510
## converged
## trying - x1
## trying - x2
## trying - x3
## trying - x5
## trying - x6
## trying - x7
## # weights: 36 (22 variable)
## initial value 721.788274
## iter 10 value 672.281204
## iter 20 value 663.658327
## final value 663.560963
## converged
## trying - x2
## trying - x3
## trying - x5
## trying - x6
## trying - x7
selectionlist
## [[1]]
## [1] "(Intercept)" "x72" "x73"
##
## [[2]]
## [1] "(Intercept)" "x52" "x53"
##
## [[3]]
## [1] "(Intercept)" "x12" "x13" "x52" "x53"
## [6] "x82" "x83"
##
## [[4]]
## [1] "(Intercept)"
##
## [[5]]
## [1] "(Intercept)" "x22" "x23" "x32" "x33"
## [6] "x72" "x73" "x82" "x83"
##
## [[6]]
## [1] "(Intercept)" "x72" "x73" "x82" "x83"
##
## [[7]]
## [1] "(Intercept)" "x12" "x13" "x52" "x53"
## [6] "x62" "x63" "x82" "x83"
##
## [[8]]
## [1] "(Intercept)" "x22" "x23" "x32" "x33"
## [6] "x52" "x53" "x62" "x63" "x72"
## [11] "x73"
##################################################
dat<-unlist(strsplit(HW3_DataSet$V1[y==" 0"],split = ""))
dat<-matrix(dat,byrow = TRUE,ncol=8)
colnames(dat)<-paste('x',seq(8),sep = '')
dat<-as.data.frame(dat)
selectionlist<-list()
for(i in seq(8)){
reg <- multinom(dat[,i] ~ ., data = dat[,-i])
bicselect<-step(reg,direction = 'backward'
,k=log(dim(dat)[1]),trace = -1)
selectionlist[[i]]<-(bicselect$coefnames)
}
## # weights: 48 (30 variable)
## initial value 363.640668
## iter 10 value 276.911440
## iter 20 value 270.832489
## iter 30 value 270.709404
## iter 40 value 270.673887
## final value 270.673795
## converged
## Start: AIC=715.40999999999997
## dat[, i] ~ x2 + x3 + x4 + x5 + x6 + x7 + x8
##
## trying - x2
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 279.900594
## iter 20 value 272.001526
## iter 30 value 271.888990
## iter 40 value 271.881484
## final value 271.881470
## converged
## trying - x3
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 276.462979
## iter 20 value 272.204016
## iter 30 value 272.083174
## iter 40 value 272.081138
## iter 40 value 272.081136
## iter 40 value 272.081136
## final value 272.081136
## converged
## trying - x4
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 275.686420
## iter 20 value 271.894988
## final value 271.862890
## converged
## trying - x5
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 291.132777
## iter 20 value 283.242512
## iter 30 value 283.104760
## iter 40 value 283.099347
## final value 283.099340
## converged
## trying - x6
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 276.629748
## iter 20 value 272.757065
## iter 30 value 272.660652
## iter 40 value 272.657269
## iter 40 value 272.657266
## iter 40 value 272.657266
## final value 272.657266
## converged
## trying - x7
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 288.296043
## iter 20 value 277.956722
## iter 30 value 277.856325
## iter 40 value 277.849387
## final value 277.849376
## converged
## trying - x8
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 289.694251
## iter 20 value 279.227228
## iter 30 value 279.094306
## iter 40 value 279.082600
## final value 279.082582
## converged
## Df AIC
## - x4 26 595.72577947624040
## - x2 26 595.76294082114566
## - x3 26 596.16227167936574
## - x6 26 597.31453202552348
## <none> 30 601.34759048578189
## - x7 26 607.69875253687826
## - x8 26 610.16516377768664
## - x5 26 618.19868076789794
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 275.686420
## iter 20 value 271.894988
## final value 271.862890
## converged
##
## Step: AIC=694.58000000000004
## dat[, i] ~ x2 + x3 + x5 + x6 + x7 + x8
##
## trying - x2
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 275.119901
## iter 20 value 272.995224
## final value 272.977590
## converged
## trying - x3
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 275.999903
## iter 20 value 273.356297
## final value 273.340675
## converged
## trying - x5
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 286.907625
## iter 20 value 284.866879
## final value 284.861520
## converged
## trying - x6
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 276.189200
## iter 20 value 274.007940
## final value 274.001737
## converged
## trying - x7
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 290.088652
## iter 20 value 279.729879
## final value 279.727094
## converged
## trying - x8
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 285.006607
## iter 20 value 281.206140
## final value 281.199356
## converged
## Df AIC
## - x2 22 589.95518027236369
## - x3 22 590.68135096774972
## - x6 22 592.00347498313465
## <none> 26 595.72577947624040
## - x7 22 603.45418896834769
## - x8 22 606.39871147664940
## - x5 22 613.72303972070654
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 275.119901
## iter 20 value 272.995224
## final value 272.977590
## converged
##
## Step: AIC=673.60000000000002
## dat[, i] ~ x3 + x5 + x6 + x7 + x8
##
## trying - x3
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 275.534563
## iter 20 value 274.425325
## final value 274.422304
## converged
## trying - x5
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 297.826875
## iter 20 value 285.752278
## final value 285.749939
## converged
## trying - x6
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 276.919823
## iter 20 value 275.278704
## final value 275.278124
## converged
## trying - x7
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 285.254178
## iter 20 value 280.887484
## final value 280.886054
## converged
## trying - x8
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 285.288082
## iter 20 value 282.376125
## final value 282.375586
## converged
## Df AIC
## - x3 18 584.84460778826417
## - x6 18 586.55624720770618
## <none> 22 589.95518027236369
## - x7 18 597.77210885569843
## - x8 18 600.75117251769530
## - x5 18 607.49987746703039
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 275.534563
## iter 20 value 274.425325
## final value 274.422304
## converged
##
## Step: AIC=653.27999999999997
## dat[, i] ~ x5 + x6 + x7 + x8
##
## trying - x5
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 287.728636
## iter 20 value 286.591807
## iter 20 value 286.591806
## iter 20 value 286.591806
## final value 286.591806
## converged
## trying - x6
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 277.237085
## iter 20 value 276.572521
## iter 20 value 276.572521
## iter 20 value 276.572521
## final value 276.572521
## converged
## trying - x7
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 284.267858
## iter 20 value 282.264433
## iter 20 value 282.264433
## iter 20 value 282.264433
## final value 282.264433
## converged
## trying - x8
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 285.501410
## iter 20 value 283.544041
## iter 20 value 283.544040
## iter 20 value 283.544040
## final value 283.544040
## converged
## Df AIC
## - x6 14 581.14504235092613
## <none> 18 584.84460778826417
## - x7 14 592.52886624110852
## - x8 14 595.08808090766638
## - x5 14 601.18361102981862
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 277.237085
## iter 20 value 276.572521
## iter 20 value 276.572521
## iter 20 value 276.572521
## final value 276.572521
## converged
##
## Step: AIC=634.37
## dat[, i] ~ x5 + x7 + x8
##
## trying - x5
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 288.766908
## final value 288.711098
## converged
## trying - x7
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 285.226192
## final value 284.278119
## converged
## trying - x8
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 285.624089
## final value 285.240321
## converged
## Df AIC
## <none> 14 581.14504235092613
## - x7 10 588.55623731596359
## - x8 10 590.48064249120011
## - x5 10 597.42219593998891
## # weights: 48 (30 variable)
## initial value 363.640668
## iter 10 value 338.611673
## iter 20 value 337.435622
## iter 30 value 337.294190
## iter 40 value 337.283081
## final value 337.283010
## converged
## Start: AIC=848.63
## dat[, i] ~ x1 + x3 + x4 + x5 + x6 + x7 + x8
##
## trying - x1
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 339.739876
## iter 20 value 338.926669
## iter 30 value 338.800907
## iter 40 value 338.793633
## final value 338.793616
## converged
## trying - x3
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 340.363776
## iter 20 value 339.217667
## iter 30 value 339.092456
## iter 40 value 339.088408
## iter 40 value 339.088405
## iter 40 value 339.088405
## final value 339.088405
## converged
## trying - x4
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 340.201160
## iter 20 value 339.796053
## final value 339.795867
## converged
## trying - x5
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 342.008044
## iter 20 value 340.805604
## iter 30 value 340.690591
## iter 40 value 340.687145
## iter 40 value 340.687142
## iter 40 value 340.687142
## final value 340.687142
## converged
## trying - x6
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 344.093539
## iter 20 value 343.337508
## iter 30 value 343.241086
## iter 40 value 343.235921
## final value 343.235914
## converged
## trying - x7
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 343.875912
## iter 20 value 342.910754
## iter 30 value 342.846625
## final value 342.843702
## converged
## trying - x8
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 340.462257
## iter 20 value 339.310074
## iter 30 value 339.243342
## iter 40 value 339.240120
## iter 40 value 339.240117
## iter 40 value 339.240117
## final value 339.240117
## converged
## Df AIC
## - x1 26 729.58723105243052
## - x3 26 730.17680972506491
## - x8 26 730.48023347037167
## - x4 26 731.59173329473037
## - x5 26 733.37428480025505
## <none> 30 734.56602063590935
## - x7 26 737.68740343765342
## - x6 26 738.47182842716074
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 339.739876
## iter 20 value 338.926669
## iter 30 value 338.800907
## iter 40 value 338.793633
## final value 338.793616
## converged
##
## Step: AIC=828.44000000000005
## dat[, i] ~ x3 + x4 + x5 + x6 + x7 + x8
##
## trying - x3
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 341.460773
## iter 20 value 340.687624
## iter 30 value 340.598526
## final value 340.597554
## converged
## trying - x4
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 341.426878
## iter 20 value 341.149739
## final value 341.149638
## converged
## trying - x5
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 342.635318
## iter 20 value 341.967657
## iter 30 value 341.879782
## final value 341.878512
## converged
## trying - x6
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 345.660263
## iter 20 value 344.968894
## iter 30 value 344.884189
## final value 344.883247
## converged
## trying - x7
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 345.128929
## iter 20 value 344.356446
## iter 30 value 344.294818
## final value 344.293663
## converged
## trying - x8
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 342.116745
## iter 20 value 341.036825
## iter 30 value 340.946497
## final value 340.944438
## converged
## Df AIC
## - x3 22 725.19510738699182
## - x8 22 725.88887677676394
## - x4 22 726.29927661858187
## - x5 22 727.75702490506035
## <none> 26 729.58723105243052
## - x7 22 732.58732574499686
## - x6 22 733.76649397963388
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 341.460773
## iter 20 value 340.687624
## iter 30 value 340.598526
## final value 340.597554
## converged
##
## Step: AIC=808.84000000000003
## dat[, i] ~ x4 + x5 + x6 + x7 + x8
##
## trying - x4
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 343.125631
## iter 20 value 342.892498
## final value 342.892463
## converged
## trying - x5
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 344.217731
## iter 20 value 343.541930
## iter 30 value 343.500402
## final value 343.500323
## converged
## trying - x6
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 347.010726
## iter 20 value 346.473414
## iter 30 value 346.454270
## final value 346.454235
## converged
## trying - x7
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 347.133591
## iter 20 value 346.341061
## iter 30 value 346.306572
## final value 346.306518
## converged
## trying - x8
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 343.489284
## iter 20 value 342.647056
## iter 30 value 342.601638
## final value 342.601556
## converged
## Df AIC
## - x8 18 721.20311208955195
## - x4 18 721.78492534748784
## - x5 18 723.00064574402074
## <none> 22 725.19510738699182
## - x7 18 728.61303652727565
## - x6 18 728.90846962705484
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 343.489284
## iter 20 value 342.647056
## iter 30 value 342.601638
## final value 342.601556
## converged
##
## Step: AIC=789.63999999999999
## dat[, i] ~ x4 + x5 + x6 + x7
##
## trying - x4
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 345.194053
## iter 20 value 344.926663
## iter 20 value 344.926660
## iter 20 value 344.926660
## final value 344.926660
## converged
## trying - x5
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 346.468240
## iter 20 value 345.891448
## iter 30 value 345.868522
## iter 30 value 345.868522
## final value 345.868522
## converged
## trying - x6
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 348.430392
## iter 20 value 348.044262
## iter 30 value 348.033316
## iter 30 value 348.033316
## final value 348.033316
## converged
## trying - x7
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 350.019028
## iter 20 value 349.510652
## iter 30 value 349.503975
## iter 30 value 349.503975
## final value 349.503975
## converged
## Df AIC
## - x4 14 717.85332094291653
## - x5 14 719.73704471007795
## <none> 18 721.20311208955195
## - x6 14 724.06663208537259
## - x7 14 727.00794936769182
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 345.194053
## iter 20 value 344.926663
## iter 20 value 344.926660
## iter 20 value 344.926660
## final value 344.926660
## converged
##
## Step: AIC=771.08000000000004
## dat[, i] ~ x5 + x6 + x7
##
## trying - x5
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 347.942027
## final value 347.810896
## converged
## trying - x6
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 350.038708
## final value 349.997568
## converged
## trying - x7
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 351.763752
## final value 351.673003
## converged
## Df AIC
## - x5 10 715.62179101398465
## <none> 14 717.85332094291653
## - x6 10 719.99513669405428
## - x7 10 723.34600681324639
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 347.942027
## final value 347.810896
## converged
##
## Step: AIC=753.63999999999999
## dat[, i] ~ x6 + x7
##
## trying - x6
## # weights: 12 (6 variable)
## initial value 363.640668
## iter 10 value 352.675904
## final value 352.675599
## converged
## trying - x7
## # weights: 12 (6 variable)
## initial value 363.640668
## iter 10 value 356.127858
## iter 10 value 356.127857
## iter 10 value 356.127857
## final value 356.127857
## converged
## Df AIC
## <none> 10 715.62179101398465
## - x6 6 717.35119801149608
## - x7 6 724.25571495750842
## # weights: 48 (30 variable)
## initial value 363.640668
## iter 10 value 351.008998
## iter 20 value 349.256339
## iter 30 value 348.809471
## iter 40 value 348.792635
## final value 348.792338
## converged
## Start: AIC=871.64999999999998
## dat[, i] ~ x1 + x2 + x4 + x5 + x6 + x7 + x8
##
## trying - x1
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 351.708967
## iter 20 value 350.352326
## iter 30 value 350.072772
## iter 40 value 350.064407
## final value 350.064394
## converged
## trying - x2
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 352.945449
## iter 20 value 351.027261
## iter 30 value 350.608858
## iter 40 value 350.601835
## final value 350.601828
## converged
## trying - x4
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 352.041023
## iter 20 value 351.062675
## final value 351.061446
## converged
## trying - x5
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 354.212757
## iter 20 value 352.669257
## iter 30 value 352.339050
## iter 40 value 352.330500
## final value 352.330490
## converged
## trying - x6
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 351.962217
## iter 20 value 350.247318
## iter 30 value 349.815778
## iter 40 value 349.809196
## final value 349.809189
## converged
## trying - x7
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 351.873349
## iter 20 value 350.425595
## iter 30 value 350.215801
## iter 40 value 350.209488
## final value 350.209481
## converged
## trying - x8
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 352.291678
## iter 20 value 350.692043
## iter 30 value 350.319000
## iter 40 value 350.298287
## final value 350.298227
## converged
## Df AIC
## - x6 26 751.61837745710795
## - x1 26 752.12878730158411
## - x7 26 752.41896161694012
## - x8 26 752.59645349624202
## - x2 26 753.20365603255505
## - x4 26 754.12289130223633
## - x5 26 756.66098098394309
## <none> 30 757.58467578741602
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 351.962217
## iter 20 value 350.247318
## iter 30 value 349.815778
## iter 40 value 349.809196
## final value 349.809189
## converged
##
## Step: AIC=850.47000000000003
## dat[, i] ~ x1 + x2 + x4 + x5 + x7 + x8
##
## trying - x1
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 352.828305
## iter 20 value 351.107987
## iter 30 value 350.960751
## final value 350.960089
## converged
## trying - x2
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 353.373050
## iter 20 value 351.578014
## iter 30 value 351.372842
## final value 351.370820
## converged
## trying - x4
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 352.727857
## iter 20 value 352.188080
## final value 352.187708
## converged
## trying - x5
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 354.681581
## iter 20 value 353.258725
## iter 30 value 353.136244
## final value 353.135629
## converged
## trying - x7
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 352.906880
## iter 20 value 351.536092
## iter 30 value 351.286893
## final value 351.284505
## converged
## trying - x8
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 352.870983
## iter 20 value 351.404904
## iter 30 value 351.118585
## final value 351.117390
## converged
## Df AIC
## - x1 22 745.92017871593180
## - x8 22 746.23477959563377
## - x7 22 746.56901066068110
## - x2 22 746.74163983391622
## - x4 22 748.37541670356609
## - x5 22 750.27125781879977
## <none> 26 751.61837745710795
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 352.828305
## iter 20 value 351.107987
## iter 30 value 350.960751
## final value 350.960089
## converged
##
## Step: AIC=829.57000000000005
## dat[, i] ~ x2 + x4 + x5 + x7 + x8
##
## trying - x2
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 354.206716
## iter 20 value 352.547681
## iter 30 value 352.507653
## final value 352.507564
## converged
## trying - x4
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 353.652432
## iter 20 value 353.458063
## final value 353.458049
## converged
## trying - x5
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 355.259579
## iter 20 value 353.748618
## iter 30 value 353.714477
## final value 353.714424
## converged
## trying - x7
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 353.877110
## iter 20 value 352.545773
## iter 30 value 352.436968
## final value 352.436702
## converged
## trying - x8
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 353.588884
## iter 20 value 352.071760
## iter 30 value 351.991674
## final value 351.991578
## converged
## Df AIC
## - x8 18 739.98315558167985
## - x7 18 740.87340301496590
## - x2 18 741.01512748394123
## - x4 18 742.91609890883433
## - x5 18 743.42884728891875
## <none> 22 745.92017871593180
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 353.588884
## iter 20 value 352.071760
## iter 30 value 351.991674
## final value 351.991578
## converged
##
## Step: AIC=808.41999999999996
## dat[, i] ~ x2 + x4 + x5 + x7
##
## trying - x2
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 354.669853
## iter 20 value 353.427363
## iter 30 value 353.419892
## iter 30 value 353.419892
## final value 353.419892
## converged
## trying - x4
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 354.381820
## final value 354.305108
## converged
## trying - x5
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 356.028191
## iter 20 value 354.894530
## iter 30 value 354.881424
## iter 30 value 354.881424
## final value 354.881424
## converged
## trying - x7
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 354.373375
## iter 20 value 353.329787
## iter 30 value 353.320171
## iter 30 value 353.320171
## final value 353.320171
## converged
## Df AIC
## - x7 14 734.64034148125290
## - x2 14 734.83978345045057
## - x4 14 736.61021543373386
## - x5 14 737.76284709457730
## <none> 18 739.98315558167985
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 354.373375
## iter 20 value 353.329787
## iter 30 value 353.320171
## iter 30 value 353.320171
## final value 353.320171
## converged
##
## Step: AIC=787.87
## dat[, i] ~ x2 + x4 + x5
##
## trying - x2
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 355.988688
## iter 20 value 354.951710
## final value 354.950099
## converged
## trying - x4
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 355.493532
## final value 355.418445
## converged
## trying - x5
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 356.977087
## iter 20 value 356.202021
## final value 356.201630
## converged
## Df AIC
## - x2 10 729.90019892624014
## - x4 10 730.83688917302072
## - x5 10 732.40326094897182
## <none> 14 734.64034148125290
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 355.988688
## iter 20 value 354.951710
## final value 354.950099
## converged
##
## Step: AIC=767.91999999999996
## dat[, i] ~ x4 + x5
##
## trying - x4
## # weights: 12 (6 variable)
## initial value 363.640668
## iter 10 value 356.982643
## iter 10 value 356.982640
## iter 10 value 356.982640
## final value 356.982640
## converged
## trying - x5
## # weights: 12 (6 variable)
## initial value 363.640668
## iter 10 value 357.694393
## final value 357.665284
## converged
## Df AIC
## - x4 6 725.96528007374673
## - x5 6 727.33056801166299
## <none> 10 729.90019892624014
## # weights: 12 (6 variable)
## initial value 363.640668
## iter 10 value 356.982643
## iter 10 value 356.982640
## iter 10 value 356.982640
## final value 356.982640
## converged
##
## Step: AIC=748.77999999999997
## dat[, i] ~ x5
##
## trying - x5
## # weights: 6 (2 variable)
## initial value 363.640668
## final value 359.521241
## converged
## Df AIC
## - x5 2 723.04248100406937
## <none> 6 725.96528007374673
## # weights: 6 (2 variable)
## initial value 363.640668
## final value 359.521241
## converged
##
## Step: AIC=730.64999999999998
## dat[, i] ~ 1
##
## # weights: 48 (30 variable)
## initial value 363.640668
## iter 10 value 214.634467
## iter 20 value 205.575076
## iter 30 value 203.648255
## iter 40 value 202.951004
## iter 50 value 202.943058
## final value 202.943042
## converged
## Start: AIC=579.95000000000005
## dat[, i] ~ x1 + x2 + x3 + x5 + x6 + x7 + x8
##
## trying - x1
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 210.053701
## iter 20 value 206.571885
## iter 30 value 203.953870
## iter 40 value 203.896570
## final value 203.896378
## converged
## trying - x2
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 209.858749
## iter 20 value 206.975306
## iter 30 value 204.574192
## iter 40 value 204.559356
## final value 204.559338
## converged
## trying - x3
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 212.289566
## iter 20 value 207.115678
## iter 30 value 205.103537
## iter 40 value 205.007490
## final value 205.007337
## converged
## trying - x5
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 213.301742
## iter 20 value 209.492763
## iter 30 value 206.953598
## iter 40 value 206.882781
## final value 206.882529
## converged
## trying - x6
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 211.872145
## iter 20 value 206.629779
## iter 30 value 204.869789
## iter 40 value 204.829970
## final value 204.829915
## converged
## trying - x7
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 212.771953
## iter 20 value 206.403400
## iter 30 value 204.490162
## iter 40 value 204.460693
## final value 204.460648
## converged
## trying - x8
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 210.819189
## iter 20 value 208.089711
## iter 30 value 205.262548
## iter 40 value 205.194424
## final value 205.194285
## converged
## Df AIC
## - x1 26 459.79275558862571
## - x7 26 460.92129539599154
## - x2 26 461.11867537751840
## - x6 26 461.65982966962770
## - x3 26 462.01467320284502
## - x8 26 462.38856948323365
## - x5 26 465.76505772802665
## <none> 30 465.88608349938659
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 210.053701
## iter 20 value 206.571885
## iter 30 value 203.953870
## iter 40 value 203.896570
## final value 203.896378
## converged
##
## Step: AIC=558.64999999999998
## dat[, i] ~ x2 + x3 + x5 + x6 + x7 + x8
##
## trying - x2
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 211.537142
## iter 20 value 207.410468
## iter 30 value 205.433949
## iter 40 value 205.428323
## final value 205.428318
## converged
## trying - x3
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 212.079436
## iter 20 value 207.699191
## iter 30 value 205.983896
## iter 40 value 205.955263
## final value 205.955228
## converged
## trying - x5
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 214.154813
## iter 20 value 210.291669
## iter 30 value 208.346039
## iter 40 value 208.336925
## final value 208.336904
## converged
## trying - x6
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 210.937606
## iter 20 value 207.445015
## iter 30 value 205.919552
## iter 40 value 205.913315
## final value 205.913309
## converged
## trying - x7
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 210.524516
## iter 20 value 207.252358
## iter 30 value 206.397799
## iter 40 value 206.394224
## final value 206.394220
## converged
## trying - x8
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 214.310667
## iter 20 value 209.695834
## iter 30 value 206.991054
## iter 40 value 206.970686
## final value 206.970665
## converged
## Df AIC
## - x2 22 454.85663579424045
## - x6 22 455.82661867635863
## - x3 22 455.91045576021412
## - x7 22 456.78844047293728
## - x8 22 457.94133074312339
## <none> 26 459.79275558862571
## - x5 22 460.67380828134793
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 211.537142
## iter 20 value 207.410468
## iter 30 value 205.433949
## iter 40 value 205.428323
## final value 205.428318
## converged
##
## Step: AIC=538.5
## dat[, i] ~ x3 + x5 + x6 + x7 + x8
##
## trying - x3
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 213.312790
## iter 20 value 208.460126
## iter 30 value 207.940357
## final value 207.937823
## converged
## trying - x5
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 216.360431
## iter 20 value 210.538332
## iter 30 value 209.426174
## final value 209.424213
## converged
## trying - x6
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 212.299154
## iter 20 value 207.635124
## iter 30 value 207.264924
## final value 207.264064
## converged
## trying - x7
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 212.868252
## iter 20 value 208.481787
## iter 30 value 208.161438
## final value 208.159581
## converged
## trying - x8
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 215.273816
## iter 20 value 210.775226
## iter 30 value 210.223578
## final value 210.221855
## converged
## Df AIC
## - x6 18 450.52812852919516
## - x3 18 451.87564570639393
## - x7 18 452.31916266836799
## - x5 18 454.84842573688962
## <none> 22 454.85663579424045
## - x8 18 456.44370981322459
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 212.299154
## iter 20 value 207.635124
## iter 30 value 207.264924
## final value 207.264064
## converged
##
## Step: AIC=518.97000000000003
## dat[, i] ~ x3 + x5 + x7 + x8
##
## trying - x3
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 215.244449
## iter 20 value 209.548972
## iter 30 value 209.485637
## iter 30 value 209.485637
## final value 209.485637
## converged
## trying - x5
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 217.749615
## iter 20 value 211.396744
## iter 30 value 211.254444
## iter 30 value 211.254444
## final value 211.254444
## converged
## trying - x7
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 214.286016
## iter 20 value 209.459837
## iter 30 value 209.380668
## iter 30 value 209.380668
## final value 209.380668
## converged
## trying - x8
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 216.685397
## iter 20 value 211.525322
## iter 30 value 211.452342
## iter 30 value 211.452342
## final value 211.452342
## converged
## Df AIC
## - x7 14 446.76133520700046
## - x3 14 446.97127443046099
## - x5 14 450.50888806444459
## <none> 18 450.52812852919516
## - x8 14 450.90468483689864
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 214.286016
## iter 20 value 209.459837
## iter 30 value 209.380668
## iter 30 value 209.380668
## final value 209.380668
## converged
##
## Step: AIC=499.99000000000001
## dat[, i] ~ x3 + x5 + x8
##
## trying - x3
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 214.398167
## iter 20 value 211.564413
## iter 30 value 211.554399
## iter 40 value 211.550932
## final value 211.550676
## converged
## trying - x5
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 217.202128
## iter 20 value 214.280724
## iter 30 value 214.272866
## iter 40 value 214.269993
## final value 214.269761
## converged
## trying - x8
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 217.640024
## iter 20 value 214.017841
## iter 30 value 214.006970
## iter 40 value 214.002709
## final value 214.002685
## converged
## Df AIC
## - x3 10 443.10135280051907
## <none> 14 446.76133520700046
## - x8 10 448.00537016474021
## - x5 10 448.53952216003842
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 214.398167
## iter 20 value 211.564413
## iter 30 value 211.554399
## iter 40 value 211.550932
## final value 211.550676
## converged
##
## Step: AIC=481.12
## dat[, i] ~ x5 + x8
##
## trying - x5
## # weights: 12 (6 variable)
## initial value 363.640668
## iter 10 value 217.143287
## iter 20 value 216.331924
## final value 216.269873
## converged
## trying - x8
## # weights: 12 (6 variable)
## initial value 363.640668
## iter 10 value 216.560417
## iter 20 value 216.103337
## final value 216.036732
## converged
## Df AIC
## <none> 10 443.10135280051907
## - x8 6 444.07346483423260
## - x5 6 444.53974505812408
## # weights: 48 (30 variable)
## initial value 363.640668
## iter 10 value 317.199035
## iter 20 value 314.997842
## iter 30 value 314.910465
## iter 40 value 314.882025
## final value 314.881829
## converged
## Start: AIC=803.83000000000004
## dat[, i] ~ x1 + x2 + x3 + x4 + x6 + x7 + x8
##
## trying - x1
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 328.296565
## iter 20 value 327.396385
## iter 30 value 327.238297
## iter 40 value 327.227990
## final value 327.227959
## converged
## trying - x2
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 320.617882
## iter 20 value 318.455011
## iter 30 value 318.322342
## iter 40 value 318.313541
## final value 318.313532
## converged
## trying - x3
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 321.518854
## iter 20 value 318.494339
## iter 30 value 318.418152
## iter 40 value 318.405575
## final value 318.405549
## converged
## trying - x4
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 321.602045
## iter 20 value 319.098509
## final value 319.093103
## converged
## trying - x6
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 317.990550
## iter 20 value 316.355074
## iter 30 value 316.241476
## iter 40 value 316.236008
## final value 316.235999
## converged
## trying - x7
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 321.869693
## iter 20 value 320.108333
## iter 30 value 319.982209
## iter 40 value 319.975133
## final value 319.975119
## converged
## trying - x8
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 319.407265
## iter 20 value 317.214401
## iter 30 value 317.116032
## iter 40 value 317.100055
## final value 317.100004
## converged
## Df AIC
## - x6 26 684.47199759822763
## - x8 26 686.20000858760011
## - x2 26 688.62706489521770
## - x3 26 688.81109766911311
## <none> 30 689.76365709379468
## - x4 26 690.18620592323475
## - x7 26 691.95023747606990
## - x1 26 706.45591840910993
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 317.990550
## iter 20 value 316.355074
## iter 30 value 316.241476
## iter 40 value 316.236008
## final value 316.235999
## converged
##
## Step: AIC=783.33000000000004
## dat[, i] ~ x1 + x2 + x3 + x4 + x7 + x8
##
## trying - x1
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 329.583700
## iter 20 value 328.549673
## iter 30 value 328.381636
## final value 328.378886
## converged
## trying - x2
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 321.484683
## iter 20 value 319.434206
## iter 30 value 319.294579
## final value 319.293616
## converged
## trying - x3
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 320.998664
## iter 20 value 319.656178
## iter 30 value 319.563961
## final value 319.561615
## converged
## trying - x4
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 322.425615
## iter 20 value 320.469946
## final value 320.466912
## converged
## trying - x7
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 322.497203
## iter 20 value 321.832612
## iter 30 value 321.689363
## final value 321.688774
## converged
## trying - x8
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 320.927940
## iter 20 value 318.552726
## iter 30 value 318.433937
## iter 40 value 318.428458
## final value 318.428453
## converged
## Df AIC
## - x8 22 680.85690586866588
## - x2 22 682.58723160998568
## - x3 22 683.12322987556956
## <none> 26 684.47199759822763
## - x4 22 684.93382354034622
## - x7 22 687.37754736264299
## - x1 22 700.75777192977375
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 320.927940
## iter 20 value 318.552726
## iter 30 value 318.433937
## iter 40 value 318.428458
## final value 318.428453
## converged
##
## Step: AIC=764.5
## dat[, i] ~ x1 + x2 + x3 + x4 + x7
##
## trying - x1
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 332.703591
## iter 20 value 332.262201
## iter 30 value 332.153018
## final value 332.152798
## converged
## trying - x2
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 322.916768
## iter 20 value 321.680454
## iter 30 value 321.557721
## final value 321.557330
## converged
## trying - x3
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 322.653165
## iter 20 value 321.855488
## iter 30 value 321.772348
## final value 321.771908
## converged
## trying - x4
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 324.037826
## iter 20 value 323.334687
## final value 323.334199
## converged
## trying - x7
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 325.745451
## iter 20 value 324.916859
## iter 30 value 324.800377
## final value 324.800121
## converged
## Df AIC
## - x2 18 679.11465999194661
## - x3 18 679.54381596372468
## <none> 22 680.85690586866588
## - x4 18 682.66839748586517
## - x7 18 685.60024282706695
## - x1 18 700.30559648141718
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 322.916768
## iter 20 value 321.680454
## iter 30 value 321.557721
## final value 321.557330
## converged
##
## Step: AIC=747.54999999999995
## dat[, i] ~ x1 + x3 + x4 + x7
##
## trying - x1
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 335.725577
## iter 20 value 335.280836
## iter 30 value 335.269144
## iter 30 value 335.269144
## final value 335.269144
## converged
## trying - x3
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 325.278821
## iter 20 value 324.837717
## iter 30 value 324.827503
## iter 30 value 324.827503
## final value 324.827503
## converged
## trying - x4
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 326.603581
## final value 326.053898
## converged
## trying - x7
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 329.609851
## iter 20 value 328.953876
## iter 30 value 328.937089
## iter 30 value 328.937089
## final value 328.937089
## converged
## Df AIC
## - x3 14 677.65500694898401
## <none> 18 679.11465999194661
## - x4 14 680.10779629049739
## - x7 14 685.87417794448231
## - x1 14 698.53828856933774
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 325.278821
## iter 20 value 324.837717
## iter 30 value 324.827503
## iter 30 value 324.827503
## final value 324.827503
## converged
##
## Step: AIC=730.88
## dat[, i] ~ x1 + x4 + x7
##
## trying - x1
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 338.394977
## iter 20 value 338.071721
## final value 338.070652
## converged
## trying - x4
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 329.625072
## final value 329.201548
## converged
## trying - x7
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 332.767359
## iter 20 value 332.189446
## final value 332.188722
## converged
## Df AIC
## <none> 14 677.65500694898401
## - x4 10 678.40309597085411
## - x7 10 684.37744324669143
## - x1 10 696.14130344130922
## # weights: 48 (30 variable)
## initial value 363.640668
## iter 10 value 350.156020
## iter 20 value 348.272911
## iter 30 value 348.076259
## iter 40 value 348.062134
## final value 348.061982
## converged
## Start: AIC=870.19000000000005
## dat[, i] ~ x1 + x2 + x3 + x4 + x5 + x7 + x8
##
## trying - x1
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 352.179188
## iter 20 value 350.024625
## iter 30 value 349.851013
## iter 40 value 349.843162
## final value 349.843148
## converged
## trying - x2
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 354.922559
## iter 20 value 354.037557
## iter 30 value 353.902077
## iter 40 value 353.894536
## final value 353.894523
## converged
## trying - x3
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 350.910413
## iter 20 value 349.287020
## iter 30 value 349.123969
## iter 40 value 349.117106
## final value 349.117092
## converged
## trying - x4
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 351.188060
## iter 20 value 349.398671
## final value 349.393777
## converged
## trying - x5
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 351.042148
## iter 20 value 349.435879
## iter 30 value 349.262837
## iter 40 value 349.251331
## final value 349.251308
## converged
## trying - x7
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 353.295928
## iter 20 value 351.761107
## iter 30 value 351.589281
## iter 40 value 351.581631
## final value 351.581623
## converged
## trying - x8
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 351.943143
## iter 20 value 350.496269
## iter 30 value 350.319477
## iter 40 value 350.306789
## final value 350.306763
## converged
## Df AIC
## - x3 26 750.23418303476546
## - x5 26 750.50261585552630
## - x4 26 750.78755303674359
## - x1 26 751.68629555610653
## - x8 26 752.61352538126994
## - x7 26 755.16324530039935
## <none> 30 756.12396407750998
## - x2 26 759.78904530726550
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 350.910413
## iter 20 value 349.287020
## iter 30 value 349.123969
## iter 40 value 349.117106
## final value 349.117092
## converged
##
## Step: AIC=849.09000000000003
## dat[, i] ~ x1 + x2 + x4 + x5 + x7 + x8
##
## trying - x1
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 352.255937
## iter 20 value 350.908998
## iter 30 value 350.793691
## final value 350.791670
## converged
## trying - x2
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 355.636458
## iter 20 value 354.767547
## iter 30 value 354.670169
## final value 354.669083
## converged
## trying - x4
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 351.983761
## iter 20 value 350.570710
## final value 350.569489
## converged
## trying - x5
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 351.955463
## iter 20 value 350.269001
## iter 30 value 350.100169
## final value 350.098319
## converged
## trying - x7
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 354.015628
## iter 20 value 352.791871
## iter 30 value 352.658785
## final value 352.657629
## converged
## trying - x8
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 352.428509
## iter 20 value 351.253506
## iter 30 value 351.159263
## final value 351.158604
## converged
## Df AIC
## - x5 22 744.19663808270036
## - x4 22 745.13897710177366
## - x1 22 745.58334047657206
## - x8 22 746.31720700384017
## - x7 22 749.31525861214425
## <none> 26 750.23418303476546
## - x2 22 753.33816581899259
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 351.955463
## iter 20 value 350.269001
## iter 30 value 350.100169
## final value 350.098319
## converged
##
## Step: AIC=827.84000000000003
## dat[, i] ~ x1 + x2 + x4 + x7 + x8
##
## trying - x1
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 353.208930
## iter 20 value 351.849772
## iter 30 value 351.726124
## final value 351.725944
## converged
## trying - x2
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 356.269664
## iter 20 value 355.509356
## iter 30 value 355.484449
## final value 355.484398
## converged
## trying - x4
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 352.976999
## iter 20 value 351.512164
## final value 351.511664
## converged
## trying - x7
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 355.114717
## iter 20 value 354.116696
## iter 30 value 354.061247
## final value 354.061198
## converged
## trying - x8
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 353.101244
## iter 20 value 352.183102
## iter 30 value 352.161821
## final value 352.161780
## converged
## Df AIC
## - x4 18 739.02332713148371
## - x1 18 739.45188830504912
## - x8 18 740.32356018738824
## - x7 18 744.12239667638903
## <none> 22 744.19663808270036
## - x2 18 746.96879613749695
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 352.976999
## iter 20 value 351.512164
## final value 351.511664
## converged
##
## Step: AIC=807.46000000000004
## dat[, i] ~ x1 + x2 + x7 + x8
##
## trying - x1
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 353.410794
## final value 353.258462
## converged
## trying - x2
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 356.859263
## final value 356.574916
## converged
## trying - x7
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 355.947334
## iter 20 value 355.633131
## iter 20 value 355.633131
## iter 20 value 355.633131
## final value 355.633131
## converged
## trying - x8
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 353.792918
## final value 353.723330
## converged
## Df AIC
## - x1 14 734.51692454524323
## - x8 14 735.44666026588084
## <none> 18 739.02332713148371
## - x7 14 739.26626115973693
## - x2 14 741.14983260843849
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 353.410794
## final value 353.258462
## converged
##
## Step: AIC=787.75
## dat[, i] ~ x2 + x7 + x8
##
## trying - x2
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 358.621793
## final value 358.617631
## converged
## trying - x7
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 357.475544
## final value 357.441069
## converged
## trying - x8
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 355.206295
## final value 355.127038
## converged
## Df AIC
## - x8 10 730.25407578752390
## <none> 14 734.51692454524323
## - x7 10 734.88213890123200
## - x2 10 737.23526287993684
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 355.206295
## final value 355.127038
## converged
##
## Step: AIC=768.27999999999997
## dat[, i] ~ x2 + x7
##
## trying - x2
## # weights: 12 (6 variable)
## initial value 363.640668
## iter 10 value 359.992474
## final value 359.991741
## converged
## trying - x7
## # weights: 12 (6 variable)
## initial value 363.640668
## iter 10 value 359.288634
## iter 10 value 359.288633
## iter 10 value 359.288633
## final value 359.288633
## converged
## Df AIC
## <none> 10 730.25407578752390
## - x7 6 730.57726584589284
## - x2 6 731.98348278844264
## # weights: 48 (30 variable)
## initial value 363.640668
## iter 10 value 302.849184
## iter 20 value 297.485439
## iter 30 value 297.220602
## iter 40 value 297.206634
## final value 297.206504
## converged
## Start: AIC=768.48000000000002
## dat[, i] ~ x1 + x2 + x3 + x4 + x5 + x6 + x8
##
## trying - x1
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 310.299307
## iter 20 value 304.689619
## iter 30 value 304.442781
## iter 40 value 304.431190
## final value 304.431166
## converged
## trying - x2
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 309.497373
## iter 20 value 302.884455
## iter 30 value 302.620140
## iter 40 value 302.609157
## final value 302.609134
## converged
## trying - x3
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 304.222827
## iter 20 value 298.813279
## iter 30 value 298.590789
## iter 40 value 298.580436
## final value 298.580406
## converged
## trying - x4
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 308.141637
## iter 20 value 298.893982
## final value 298.884283
## converged
## trying - x5
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 306.317842
## iter 20 value 302.670622
## iter 30 value 302.425530
## iter 40 value 302.419436
## final value 302.419429
## converged
## trying - x6
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 305.438023
## iter 20 value 300.962934
## iter 30 value 300.711943
## iter 40 value 300.705713
## final value 300.705703
## converged
## trying - x8
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 311.352993
## iter 20 value 307.260938
## iter 30 value 307.038874
## iter 40 value 307.030275
## final value 307.030261
## converged
## Df AIC
## - x3 26 649.16081197949529
## - x4 26 649.76856608502567
## - x6 26 653.41140527092841
## <none> 30 654.41300896492044
## - x5 26 656.83885726176834
## - x2 26 657.21826811819631
## - x1 26 660.86233154292472
## - x8 26 666.06052271379883
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 304.222827
## iter 20 value 298.813279
## iter 30 value 298.590789
## iter 40 value 298.580436
## final value 298.580406
## converged
##
## Step: AIC=748.01999999999998
## dat[, i] ~ x1 + x2 + x4 + x5 + x6 + x8
##
## trying - x1
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 310.264523
## iter 20 value 306.023521
## iter 30 value 305.855165
## iter 40 value 305.851585
## iter 40 value 305.851583
## iter 40 value 305.851583
## final value 305.851583
## converged
## trying - x2
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 312.096051
## iter 20 value 304.316185
## iter 30 value 304.123516
## iter 40 value 304.120163
## iter 40 value 304.120161
## iter 40 value 304.120161
## final value 304.120161
## converged
## trying - x4
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 306.667261
## iter 20 value 300.041064
## final value 300.037481
## converged
## trying - x5
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 309.398416
## iter 20 value 304.228018
## iter 30 value 304.021333
## iter 40 value 304.018038
## iter 40 value 304.018036
## iter 40 value 304.018036
## final value 304.018036
## converged
## trying - x6
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 309.476587
## iter 20 value 302.328898
## iter 30 value 302.134667
## final value 302.132852
## converged
## trying - x8
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 315.683707
## iter 20 value 308.357438
## iter 30 value 308.145637
## final value 308.143345
## converged
## Df AIC
## - x4 22 644.07496202445134
## - x6 22 648.26570367057036
## <none> 26 649.16081197949529
## - x5 22 652.03607245656599
## - x2 22 652.24032168537985
## - x1 22 655.70316694478652
## - x8 22 660.28669072976913
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 306.667261
## iter 20 value 300.041064
## final value 300.037481
## converged
##
## Step: AIC=727.72000000000003
## dat[, i] ~ x1 + x2 + x5 + x6 + x8
##
## trying - x1
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 310.694017
## iter 20 value 307.727678
## final value 307.726394
## converged
## trying - x2
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 309.511337
## iter 20 value 305.601396
## final value 305.600509
## converged
## trying - x5
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 309.075319
## iter 20 value 305.651599
## final value 305.651149
## converged
## trying - x6
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 307.180176
## iter 20 value 303.754230
## final value 303.752525
## converged
## trying - x8
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 313.144665
## iter 20 value 309.697924
## final value 309.697448
## converged
## Df AIC
## - x6 18 643.50505073450677
## <none> 22 644.07496202445134
## - x2 18 647.20101857457325
## - x5 18 647.30229714605821
## - x1 18 651.45278733423550
## - x8 18 655.39489536339931
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 307.180176
## iter 20 value 303.754230
## final value 303.752525
## converged
##
## Step: AIC=711.94000000000005
## dat[, i] ~ x1 + x2 + x5 + x8
##
## trying - x1
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 311.782657
## final value 311.450909
## converged
## trying - x2
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 309.643168
## iter 20 value 308.474321
## iter 20 value 308.474319
## iter 20 value 308.474319
## final value 308.474319
## converged
## trying - x5
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 311.002012
## iter 20 value 309.620939
## iter 20 value 309.620936
## iter 20 value 309.620936
## final value 309.620936
## converged
## trying - x8
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 315.094852
## iter 20 value 313.578321
## iter 20 value 313.578319
## iter 20 value 313.578319
## final value 313.578319
## converged
## Df AIC
## <none> 18 643.50505073450677
## - x2 14 644.94863887024314
## - x5 14 647.24187288633539
## - x1 14 650.90181841764479
## - x8 14 655.15663889864038
## # weights: 48 (30 variable)
## initial value 363.640668
## iter 10 value 317.160352
## iter 20 value 313.723532
## iter 30 value 313.367198
## iter 40 value 313.326693
## final value 313.326332
## converged
## Start: AIC=800.72000000000003
## dat[, i] ~ x1 + x2 + x3 + x4 + x5 + x6 + x7
##
## trying - x1
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 325.367538
## iter 20 value 321.817475
## iter 30 value 321.451354
## iter 40 value 321.436533
## final value 321.436480
## converged
## trying - x2
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 318.532464
## iter 20 value 315.472498
## iter 30 value 315.146105
## iter 40 value 315.134346
## final value 315.134330
## converged
## trying - x3
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 318.158147
## iter 20 value 315.048746
## iter 30 value 314.713705
## iter 40 value 314.692630
## final value 314.692592
## converged
## trying - x4
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 321.046949
## iter 20 value 316.349243
## final value 316.346227
## converged
## trying - x5
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 319.707560
## iter 20 value 315.953916
## iter 30 value 315.605644
## iter 40 value 315.591525
## final value 315.591503
## converged
## trying - x6
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 319.467786
## iter 20 value 316.188466
## iter 30 value 315.803498
## iter 40 value 315.777912
## final value 315.777869
## converged
## trying - x7
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 325.351188
## iter 20 value 323.354565
## iter 30 value 323.145083
## iter 40 value 323.127055
## final value 323.127017
## converged
## Df AIC
## - x3 26 681.38518457617977
## - x2 26 682.26866019895238
## - x5 26 683.18300627514407
## - x6 26 683.55573897371744
## - x4 26 684.69245424372218
## <none> 30 686.65266311605365
## - x1 26 694.87295942536434
## - x7 26 698.25403467098704
## # weights: 42 (26 variable)
## initial value 363.640668
## iter 10 value 318.158147
## iter 20 value 315.048746
## iter 30 value 314.713705
## iter 40 value 314.692630
## final value 314.692592
## converged
##
## Step: AIC=780.24000000000001
## dat[, i] ~ x1 + x2 + x4 + x5 + x6 + x7
##
## trying - x1
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 325.165345
## iter 20 value 322.769673
## iter 30 value 322.534597
## iter 40 value 322.531311
## iter 40 value 322.531309
## iter 40 value 322.531309
## final value 322.531309
## converged
## trying - x2
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 318.348337
## iter 20 value 316.571551
## iter 30 value 316.335827
## final value 316.334288
## converged
## trying - x4
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 319.575596
## iter 20 value 317.595148
## final value 317.594581
## converged
## trying - x5
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 320.224735
## iter 20 value 317.345691
## iter 30 value 317.039360
## final value 317.037449
## converged
## trying - x6
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 319.633061
## iter 20 value 317.172026
## iter 30 value 316.924860
## final value 316.923611
## converged
## trying - x7
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 326.772647
## iter 20 value 324.589036
## iter 30 value 324.393152
## iter 40 value 324.389965
## iter 40 value 324.389964
## iter 40 value 324.389964
## final value 324.389964
## converged
## Df AIC
## - x2 22 676.66857552050294
## - x6 22 677.84722188601415
## - x5 22 678.07489729235419
## - x4 22 679.18916192369636
## <none> 26 681.38518457617977
## - x1 22 689.06261869597233
## - x7 22 692.77992703126267
## # weights: 36 (22 variable)
## initial value 363.640668
## iter 10 value 318.348337
## iter 20 value 316.571551
## iter 30 value 316.335827
## final value 316.334288
## converged
##
## Step: AIC=760.32000000000005
## dat[, i] ~ x1 + x4 + x5 + x6 + x7
##
## trying - x1
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 325.953992
## iter 20 value 324.321982
## iter 30 value 324.271560
## final value 324.271411
## converged
## trying - x4
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 319.786226
## iter 20 value 319.456012
## final value 319.455656
## converged
## trying - x5
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 320.800070
## iter 20 value 318.828068
## iter 30 value 318.763731
## final value 318.763619
## converged
## trying - x6
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 319.788189
## iter 20 value 318.105640
## iter 30 value 318.045987
## final value 318.045891
## converged
## trying - x7
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 328.999934
## iter 20 value 326.970615
## iter 30 value 326.822679
## final value 326.822398
## converged
## Df AIC
## - x6 18 672.09178155610289
## - x5 18 673.52723715862021
## - x4 18 674.91131205185798
## <none> 22 676.66857552050294
## - x1 18 684.54282289039884
## - x7 18 689.64479553050728
## # weights: 30 (18 variable)
## initial value 363.640668
## iter 10 value 319.788189
## iter 20 value 318.105640
## iter 30 value 318.045987
## final value 318.045891
## converged
##
## Step: AIC=740.52999999999997
## dat[, i] ~ x1 + x4 + x5 + x7
##
## trying - x1
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 326.848121
## iter 20 value 325.646447
## iter 30 value 325.626494
## iter 30 value 325.626494
## final value 325.626494
## converged
## trying - x4
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 321.843934
## final value 321.253940
## converged
## trying - x5
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 321.675266
## iter 20 value 320.431314
## iter 30 value 320.420848
## iter 30 value 320.420848
## final value 320.420848
## converged
## trying - x7
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 329.173539
## iter 20 value 328.409561
## iter 30 value 328.389711
## iter 30 value 328.389711
## final value 328.389711
## converged
## Df AIC
## - x5 14 668.84169510668153
## - x4 14 670.50788006223263
## <none> 18 672.09178155610289
## - x1 14 679.25298854744904
## - x7 14 684.77942100800215
## # weights: 24 (14 variable)
## initial value 363.640668
## iter 10 value 321.675266
## iter 20 value 320.431314
## iter 30 value 320.420848
## iter 30 value 320.420848
## final value 320.420848
## converged
##
## Step: AIC=722.07000000000005
## dat[, i] ~ x1 + x4 + x7
##
## trying - x1
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 330.833613
## iter 20 value 329.755958
## final value 329.754835
## converged
## trying - x4
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 324.384888
## final value 324.271674
## converged
## trying - x7
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 332.285672
## iter 20 value 331.774002
## final value 331.773370
## converged
## Df AIC
## - x4 10 668.54334764415967
## <none> 14 668.84169510668153
## - x1 10 679.50967014820833
## - x7 10 683.54674059357876
## # weights: 18 (10 variable)
## initial value 363.640668
## iter 10 value 324.384888
## final value 324.271674
## converged
##
## Step: AIC=706.55999999999995
## dat[, i] ~ x1 + x7
##
## trying - x1
## # weights: 12 (6 variable)
## initial value 363.640668
## iter 10 value 335.370218
## final value 335.370149
## converged
## trying - x7
## # weights: 12 (6 variable)
## initial value 363.640668
## iter 10 value 335.933686
## iter 10 value 335.933683
## iter 10 value 335.933683
## final value 335.933683
## converged
## Df AIC
## <none> 10 668.54334764415967
## - x1 6 682.74029898321112
## - x7 6 683.86736557738175
selectionlist
## [[1]]
## [1] "(Intercept)" "x52" "x53" "x72" "x73"
## [6] "x82" "x83"
##
## [[2]]
## [1] "(Intercept)" "x62" "x63" "x72" "x73"
##
## [[3]]
## [1] "(Intercept)"
##
## [[4]]
## [1] "(Intercept)" "x52" "x53" "x82" "x83"
##
## [[5]]
## [1] "(Intercept)" "x12" "x13" "x42" "x43"
## [6] "x72" "x73"
##
## [[6]]
## [1] "(Intercept)" "x22" "x23" "x72" "x73"
##
## [[7]]
## [1] "(Intercept)" "x12" "x13" "x22" "x23"
## [6] "x52" "x53" "x82" "x83"
##
## [[8]]
## [1] "(Intercept)" "x12" "x13" "x72" "x73"
3.c
library(pcalg)
dat<-lapply(seq(100),FUN = function(x) return(datagenerate()))#100sample
mec<-function(dat){
score<-new("GaussL0penObsScore",data=dat)
ges.fit <- ges(score)
g<-ges.fit$essgraph$.in.edges
if(g$x1==2 && g$x4==2 && sum(g$x3 %in%c(1,4))==2 &&
sum(g$x2 %in%c(1,4))==2) return(TRUE)
else return(FALSE)
}
sum(sapply(dat,FUN =function(x) return(mec(x))))
## [1] 98
#plot(ges.fit$essgraph, main = "Estimated CPDAG")
3.d
library(bnlearn)
## Warning: package 'bnlearn' was built under R version 3.2.5
##
## Attaching package: 'bnlearn'
## The following objects are masked from 'package:pcalg':
##
## dsep, pdag2dag, shd, skeleton
mmhcfit<-function(dat){
score<-new("GaussL0penObsScore",data=dat)
g<-mmhc(x = dat, debug = FALSE)
if(sum(c("x1",'x4') %in% g$nodes$x3$parents)==2 &&
sum(c("x1",'x4') %in% g$nodes$x2$nbr)==2) return(TRUE)
else return(FALSE)
}
sum(sapply(dat,FUN =function(x) return(mmhcfit(x))))
## [1] 100