第Q回（12月11日） Task Check and Weekly Assignment
To Do
□ 因子分析の様々なオプションを試してみる。
Assignment
□ 検査データを因子分析し，因子軸の回転をした上で，因子に命名しなさい。
因子負荷量とともにレポートすること。
前回同様，5教科
いつものファイルの読み込みと下処理。済んでいる場合はやらなくてよいです。
※Workspaceにsampleが入っている場合＝済んでいる場合です。
sample <- read.csv("sample(mac).csv", na.strings = "*")
sample$sex <- factor(sample$sex, labels = c("male", "female"))
因子分析に使うところだけサブセットを作っておきましょうか。
fac_data <- subset(sample, select = c("kokugo", "sansuu", "rika", "eigo", "syakai"))
plot(fac_data)
因子分析は次のようにするのでした。
library(psych)
fa(fac_data, nfactors = 2)
## Loading required package: GPArotation
## Factor Analysis using method = minres
## Call: fa(r = fac_data, nfactors = 2)
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR2 MR1 h2 u2
## kokugo 0.99 -0.04 0.99 0.0082
## sansuu 0.03 1.00 1.00 0.0050
## rika -0.10 0.69 0.49 0.5090
## eigo 0.93 -0.01 0.86 0.1388
## syakai 0.68 0.16 0.47 0.5314
##
## MR2 MR1
## SS loadings 2.31 1.50
## Proportion Var 0.46 0.30
## Cumulative Var 0.46 0.76
## Proportion Explained 0.61 0.39
## Cumulative Proportion 0.61 1.00
##
## With factor correlations of
## MR2 MR1
## MR2 1.00 -0.08
## MR1 -0.08 1.00
##
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 10 and the objective function was 3.31 with Chi Square of 319.4
## The degrees of freedom for the model are 1 and the objective function was 0.08
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.12
## The number of observations was 100 with Chi Square = 7.36 with prob < 0.0067
##
## Tucker Lewis Index of factoring reliability = 0.791
## RMSEA index = 0.259 and the 90 % confidence intervals are 0.107 0.436
## BIC = 2.76
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## MR2 MR1
## Correlation of scores with factors 1.00 1.00
## Multiple R square of scores with factors 0.99 1.00
## Minimum correlation of possible factor scores 0.98 0.99
推定オプションを追加
fa(fac_data, nfactors = 2, fm = "gls")
## Factor Analysis using method = gls
## Call: fa(r = fac_data, nfactors = 2, fm = "gls")
## Standardized loadings (pattern matrix) based upon correlation matrix
## GLS1 GLS2 h2 u2
## kokugo 0.99 -0.05 0.98 0.0162
## sansuu 0.03 1.00 1.00 0.0021
## rika -0.11 0.69 0.50 0.5022
## eigo 0.93 0.01 0.86 0.1422
## syakai 0.69 0.12 0.47 0.5277
##
## GLS1 GLS2
## SS loadings 2.32 1.49
## Proportion Var 0.46 0.30
## Cumulative Var 0.46 0.76
## Proportion Explained 0.61 0.39
## Cumulative Proportion 0.61 1.00
##
## With factor correlations of
## GLS1 GLS2
## GLS1 1.00 -0.07
## GLS2 -0.07 1.00
##
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 10 and the objective function was 3.31 with Chi Square of 319.4
## The degrees of freedom for the model are 1 and the objective function was 0.09
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.1
## The number of observations was 100 with Chi Square = 8.47 with prob < 0.0036
##
## Tucker Lewis Index of factoring reliability = 0.755
## RMSEA index = 0.281 and the 90 % confidence intervals are 0.127 0.455
## BIC = 3.86
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## GLS1 GLS2
## Correlation of scores with factors 0.99 1.00
## Multiple R square of scores with factors 0.99 1.01
## Minimum correlation of possible factor scores 0.97 1.01
##
## WARNING, the factor score fit indices suggest that the solution is degenerate. Try a different method of factor extraction.
## Warning: the factor score fit indices suggest that the solution is
## degenerate
fa(fac_data, nfactors = 2, fm = "ml")
## Factor Analysis using method = ml
## Call: fa(r = fac_data, nfactors = 2, fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 ML2 h2 u2
## kokugo 0.99 -0.04 1.00 0.005
## sansuu 0.03 1.00 1.00 0.005
## rika -0.10 0.69 0.49 0.509
## eigo 0.93 -0.01 0.86 0.141
## syakai 0.68 0.16 0.47 0.533
##
## ML1 ML2
## SS loadings 2.31 1.50
## Proportion Var 0.46 0.30
## Cumulative Var 0.46 0.76
## Proportion Explained 0.61 0.39
## Cumulative Proportion 0.61 1.00
##
## With factor correlations of
## ML1 ML2
## ML1 1.00 -0.08
## ML2 -0.08 1.00
##
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 10 and the objective function was 3.31 with Chi Square of 319.4
## The degrees of freedom for the model are 1 and the objective function was 0.08
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.12
## The number of observations was 100 with Chi Square = 7.33 with prob < 0.0068
##
## Tucker Lewis Index of factoring reliability = 0.792
## RMSEA index = 0.259 and the 90 % confidence intervals are 0.106 0.435
## BIC = 2.72
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## ML1 ML2
## Correlation of scores with factors 1.00 1.00
## Multiple R square of scores with factors 1.00 1.00
## Minimum correlation of possible factor scores 0.99 0.99
fa(fac_data, nfactors = 2, fm = "pa")
## maximum iteration exceeded
## Factor Analysis using method = pa
## Call: fa(r = fac_data, nfactors = 2, fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 h2 u2
## kokugo 1.00 -0.04 1.00 6.9e-05
## sansuu 0.02 1.06 1.13 -1.3e-01
## rika -0.12 0.64 0.43 5.7e-01
## eigo 0.92 0.01 0.84 1.6e-01
## syakai 0.68 0.12 0.46 5.4e-01
##
## PA1 PA2
## SS loadings 2.31 1.56
## Proportion Var 0.46 0.31
## Cumulative Var 0.46 0.77
## Proportion Explained 0.60 0.40
## Cumulative Proportion 0.60 1.00
##
## With factor correlations of
## PA1 PA2
## PA1 1.00 -0.06
## PA2 -0.06 1.00
##
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 10 and the objective function was 3.31 with Chi Square of 319.4
## The degrees of freedom for the model are 1 and the objective function was 0.08
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.09
## The number of observations was 100 with Chi Square = 7.71 with prob < 0.0055
##
## Tucker Lewis Index of factoring reliability = 0.78
## RMSEA index = 0.266 and the 90 % confidence intervals are 0.113 0.442
## BIC = 3.1
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2
## Correlation of scores with factors 1 1.08
## Multiple R square of scores with factors 1 1.16
## Minimum correlation of possible factor scores 1 1.33
##
## WARNING, the factor score fit indices suggest that the solution is degenerate. Try a different method of factor extraction.
## Warning: the factor score fit indices suggest that the solution is
## degenerate
回転オプションを追加
fa(fac_data, nfactors = 2, fm = "ml", rotate = "promax")
## Factor Analysis using method = ml
## Call: fa(r = fac_data, nfactors = 2, rotate = "promax", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML2 ML1 h2 u2
## kokugo 0.99 -0.05 1.00 0.005
## sansuu 0.01 1.00 1.00 0.005
## rika -0.12 0.68 0.49 0.509
## eigo 0.93 -0.02 0.86 0.141
## syakai 0.67 0.16 0.47 0.533
##
## ML2 ML1
## SS loadings 2.31 1.49
## Proportion Var 0.46 0.30
## Cumulative Var 0.46 0.76
## Proportion Explained 0.61 0.39
## Cumulative Proportion 0.61 1.00
##
## With factor correlations of
## ML2 ML1
## ML2 1.00 -0.05
## ML1 -0.05 1.00
##
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 10 and the objective function was 3.31 with Chi Square of 319.4
## The degrees of freedom for the model are 1 and the objective function was 0.08
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.12
## The number of observations was 100 with Chi Square = 7.33 with prob < 0.0068
##
## Tucker Lewis Index of factoring reliability = 0.792
## RMSEA index = 0.259 and the 90 % confidence intervals are 0.106 0.435
## BIC = 2.72
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## ML2 ML1
## Correlation of scores with factors 1.00 1.00
## Multiple R square of scores with factors 1.00 1.00
## Minimum correlation of possible factor scores 0.99 0.99
fa(fac_data, nfactors = 2, fm = "ml", rotate = "varimax")
## Factor Analysis using method = ml
## Call: fa(r = fac_data, nfactors = 2, rotate = "varimax", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML2 ML1 h2 u2
## kokugo 0.99 -0.14 1.00 0.005
## sansuu 0.05 1.00 1.00 0.005
## rika -0.08 0.70 0.49 0.509
## eigo 0.92 -0.10 0.86 0.141
## syakai 0.68 0.09 0.47 0.533
##
## ML2 ML1
## SS loadings 2.29 1.52
## Proportion Var 0.46 0.30
## Cumulative Var 0.46 0.76
## Proportion Explained 0.60 0.40
## Cumulative Proportion 0.60 1.00
##
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 10 and the objective function was 3.31 with Chi Square of 319.4
## The degrees of freedom for the model are 1 and the objective function was 0.08
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.12
## The number of observations was 100 with Chi Square = 7.33 with prob < 0.0068
##
## Tucker Lewis Index of factoring reliability = 0.792
## RMSEA index = 0.259 and the 90 % confidence intervals are 0.106 0.435
## BIC = 2.72
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## ML2 ML1
## Correlation of scores with factors 1.00 1.00
## Multiple R square of scores with factors 1.00 1.00
## Minimum correlation of possible factor scores 0.99 0.99
出力用に整えて
result.fa <- fa(fac_data, nfactors = 2, fm = "ml", rotate = "varimax")
print(result.fa, digit = 3, sort = T)
## Factor Analysis using method = ml
## Call: fa(r = fac_data, nfactors = 2, rotate = "varimax", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item ML2 ML1 h2 u2
## kokugo 1 0.987 -0.144 0.995 0.005
## eigo 4 0.921 -0.105 0.859 0.141
## syakai 5 0.677 0.095 0.467 0.533
## sansuu 2 0.053 0.996 0.995 0.005
## rika 3 -0.085 0.696 0.491 0.509
##
## ML2 ML1
## SS loadings 2.290 1.517
## Proportion Var 0.458 0.303
## Cumulative Var 0.458 0.761
## Proportion Explained 0.602 0.398
## Cumulative Proportion 0.602 1.000
##
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 10 and the objective function was 3.309 with Chi Square of 319.4
## The degrees of freedom for the model are 1 and the objective function was 0.077
##
## The root mean square of the residuals (RMSR) is 0.026
## The df corrected root mean square of the residuals is 0.118
## The number of observations was 100 with Chi Square = 7.328 with prob < 0.00679
##
## Tucker Lewis Index of factoring reliability = 0.7925
## RMSEA index = 0.2587 and the 90 % confidence intervals are 0.1061 0.4352
## BIC = 2.723
## Fit based upon off diagonal values = 0.994
## Measures of factor score adequacy
## ML2 ML1
## Correlation of scores with factors 0.998 0.998
## Multiple R square of scores with factors 0.995 0.995
## Minimum correlation of possible factor scores 0.990 0.990
因子得点の算出
result.fa <- fa(fac_data, nfactors = 2, fm = "ml", rotate = "varimax", scores = T)
result.fa$scores
## ML2 ML1
## 1 -2.28782 0.52135
## 2 1.12618 -1.49112
## 3 -1.06278 0.47028
## 4 -0.50931 0.60941
## 5 0.74822 0.20653
## 6 NA NA
## 7 NA NA
## 8 0.42126 -1.28433
## 9 -1.12771 0.64371
## 10 -0.66403 2.12267
## 11 0.59562 -0.45290
## 12 NA NA
## 13 -0.77437 0.29396
## 14 0.02907 1.41534
## 15 0.35936 1.07128
## 16 0.73045 1.04833
## 17 0.13312 -0.60439
## 18 -1.13081 -2.20637
## 19 1.65254 -1.18254
## 20 0.64307 1.04547
## 21 0.30235 1.22896
## 22 0.83031 0.04123
## 23 0.63148 -1.29447
## 24 -0.55542 0.27383
## 25 -0.53745 1.94844
## 26 0.91697 -0.81596
## 27 -1.07856 -0.35986
## 28 -1.26689 0.98694
## 29 0.55806 -1.12788
## 30 0.70725 0.37142
## 31 2.01168 -0.37008
## 32 1.26971 -0.49705
## 33 1.27007 -0.15337
## 34 0.05609 -0.43770
## 35 0.17384 0.89896
## 36 0.33584 -0.61067
## 37 0.10210 0.41413
## 38 -0.87525 0.46217
## 39 -1.45305 0.99816
## 40 0.83226 0.19536
## 41 0.50208 0.55683
## 42 0.58750 -0.11684
## 43 0.08960 -1.26746
## 44 -0.88458 -0.04719
## 45 1.12299 -0.48915
## 46 -0.22051 0.25278
## 47 -0.95712 -1.38464
## 48 -0.79556 -0.37866
## 49 -0.41955 -0.40051
## 50 -0.37485 -0.23528
## 51 -0.30681 -0.23504
## 52 -1.03326 0.46792
## 53 0.12013 -1.09653
## 54 1.30800 0.84119
## 55 1.04386 -0.64571
## 56 1.80835 0.98677
## 57 -2.03813 -0.31921
## 58 -0.11617 0.58135
## 59 0.96493 -0.48143
## 60 -1.24427 -1.87774
## 61 -0.45939 0.93894
## 62 -1.40031 0.81961
## 63 -1.62075 0.16412
## 64 -0.80704 0.62569
## 65 -0.58404 0.44376
## 66 -1.92619 -0.14980
## 67 -0.46867 0.11211
## 68 -0.58661 -1.56832
## 69 0.34264 0.89019
## 70 -0.45484 -1.24249
## 71 0.10153 2.41090
## 72 -0.31991 -0.40537
## 73 1.23657 -0.31912
## 74 -0.20601 -1.25083
## 75 -0.21821 -0.57870
## 76 -0.61668 -1.22526
## 77 1.92370 0.14825
## 78 0.84758 0.20493
## 79 2.13928 -1.03818
## 80 -0.34168 1.59565
## 81 1.75009 1.15797
## 82 -1.67828 -1.83542
## 83 0.66776 1.21894
## 84 1.10882 1.36359
## 85 1.89139 0.47861
## 86 -0.09089 -0.41141
## 87 -0.55280 -0.89432
## 88 0.37035 -1.95369
## 89 -0.42903 -0.57637
## 90 0.57338 -1.12336
## 91 -1.16208 0.80913
## 92 -0.64795 0.44817
## 93 -1.30917 0.32045
## 94 -0.20495 0.58666
## 95 0.15207 0.90547
## 96 -0.11280 -0.92334
## 97 -0.14831 0.92208
## 98 2.20477 0.96461
## 99 -1.33279 1.83117
## 100 -0.81582 -1.21169
因子得点の基本的な特徴を再確認
summary(result.fa$scores)
## ML2 ML1
## Min. :-2.2878 Min. :-2.206
## 1st Qu.:-0.6640 1st Qu.:-0.604
## Median :-0.1128 Median : 0.148
## Mean :-0.0094 Mean : 0.018
## 3rd Qu.: 0.6678 3rd Qu.: 0.809
## Max. : 2.2048 Max. : 2.411
## NA's :3 NA's :3
hist(result.fa$scores[, 1])
hist(result.fa$scores[, 2])
plot(result.fa$scores[, 1], result.fa$scores[, 2])
cor(result.fa$scores[, 1], result.fa$scores[, 2], use = "complete.obs")
## [1] -0.007582
今日はここまで。
課題は，http://www1.doshisha.ac.jp/~mjin/data/ にある職業適性能力検査データをつかって，因子分析をし（抽出方法の指定，回転の指定もする），因子に命名してください。