library(lavaan) # HolzingerSwineford1939 データを読み込む data(HolzingerSwineford1939) head(HolzingerSwineford1939)
データはこのような感じ
id sex ageyr agemo school grade x1 x2 x3 x4 x5 x6
1 1 1 13 1 Pasteur 7 3.333333 7.75 0.375 2.333333 5.75 1.2857143
2 2 2 13 7 Pasteur 7 5.333333 5.25 2.125 1.666667 3.00 1.2857143
3 3 2 13 1 Pasteur 7 4.500000 5.25 1.875 1.000000 1.75 0.4285714
4 4 1 13 2 Pasteur 7 5.333333 7.75 3.000 2.666667 4.50 2.4285714
5 5 2 12 2 Pasteur 7 4.833333 4.75 0.875 2.666667 4.00 2.5714286
6 6 2 14 1 Pasteur 7 5.333333 5.00 2.250 1.000000 3.00 0.8571429
x7 x8 x9
1 3.391304 5.75 6.361111
2 3.782609 6.25 7.916667
3 3.260870 3.90 4.416667
4 3.000000 5.30 4.861111
5 3.695652 6.30 5.916667
6 4.347826 6.65 7.500000
とりあえず、schoolごとの平均点を計算してみよう。
library(dplyr) HolzingerSwineford1939 %>% group_by(school) %>% summarise(across(x1:x9, mean))
school x1 x2 x3 x4 x5 x6 x7 x8 x9 1 Grant-White 4.93 6.2 2.00 3.32 4.71 2.47 3.92 5.49 5.33 2 Pasteur 4.94 5.98 2.49 2.82 4.00 1.92 4.43 5.56 5.42
データの説明
- 被験者: 7歳から12歳の子供301人
- 検査: 知能検査
- 変数:
id: 被験者IDsex: 性別 (1 = 男性, 2 = 女性)ageyr: 年齢（年）agemo: 年齢（月）school: 学校名 (Pasteur, Grant-White)grade: 学年x1-x9: 知能検査の各項目の得点x1: Visual Perception (視覚的知覚)x2: Cubes (立方体)x3: Lozenges (菱形)x4: Paragraph Comprehension (段落理解)x5: Sentence Completion (文章完成)x6: Word Meaning (単語の意味)x7: Addition (加算)x8: Counting Dots (点の数え上げ)x9: Straight and Curved Capitals (直線と曲線の首都)
多母集団同時分析
# モデルを定義する
model.HS <- '
visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9
'
# モデルをPasteur校とGrant-White校に同時に当てはめる
fit <- sem(model.HS,
data = HolzingerSwineford1939,
missing = "ML",
group = "school",
estimator = "MLR")
# 結果を表示
summary(fit, standardized = TRUE)
結果。
lavaan 0.6-19 ended normally after 60 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 63
Number of equality constraints 15
Number of observations per group:
Pasteur 156
Grant-White 145
Number of missing patterns per group:
Pasteur 1
Grant-White 1
Model Test User Model:
Standard Scaled
Test Statistic 164.103 166.748
Degrees of freedom 60 60
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.984
Yuan-Bentler correction (Mplus variant)
Test statistic for each group:
Pasteur 91.665 91.665
Grant-White 75.084 75.084
Parameter Estimates:
Standard errors Sandwich
Information bread Observed
Observed information based on Hessian
Group 1 [Pasteur]:
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
visual =~
x1 1.000 0.892 0.768
x2 (.p2.) 0.576 0.131 4.395 0.000 0.514 0.411
x3 (.p3.) 0.798 0.173 4.627 0.000 0.712 0.591
textual =~
x4 1.000 0.938 0.815
x5 (.p5.) 1.120 0.067 16.623 0.000 1.050 0.829
x6 (.p6.) 0.932 0.064 14.652 0.000 0.874 0.862
speed =~
x7 1.000 0.568 0.516
x8 (.p8.) 1.130 0.133 8.488 0.000 0.641 0.657
x9 (.p9.) 1.009 0.207 4.864 0.000 0.573 0.578
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
visual ~~
textual 0.410 0.135 3.043 0.002 0.490 0.490
speed 0.178 0.067 2.661 0.008 0.351 0.351
textual ~~
speed 0.180 0.062 2.889 0.004 0.338 0.338
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.x1 (.25.) 5.001 0.094 53.050 0.000 5.001 4.302
.x2 (.26.) 6.151 0.087 70.867 0.000 6.151 4.925
.x3 (.27.) 2.271 0.095 24.016 0.000 2.271 1.885
.x4 (.28.) 2.778 0.086 32.173 0.000 2.778 2.413
.x5 (.29.) 4.035 0.103 39.095 0.000 4.035 3.184
.x6 (.30.) 1.926 0.075 25.751 0.000 1.926 1.900
.x7 (.31.) 4.242 0.079 53.702 0.000 4.242 3.855
.x8 (.32.) 5.630 0.075 75.002 0.000 5.630 5.771
.x9 (.33.) 5.465 0.072 76.114 0.000 5.465 5.516
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.x1 0.555 0.184 3.017 0.003 0.555 0.411
.x2 1.296 0.161 8.047 0.000 1.296 0.831
.x3 0.944 0.147 6.446 0.000 0.944 0.650
.x4 0.445 0.073 6.113 0.000 0.445 0.336
.x5 0.502 0.081 6.197 0.000 0.502 0.313
.x6 0.263 0.058 4.525 0.000 0.263 0.256
.x7 0.888 0.128 6.952 0.000 0.888 0.734
.x8 0.541 0.089 6.072 0.000 0.541 0.568
.x9 0.654 0.115 5.685 0.000 0.654 0.666
visual 0.796 0.239 3.336 0.001 1.000 1.000
textual 0.879 0.135 6.513 0.000 1.000 1.000
speed 0.322 0.092 3.499 0.000 1.000 1.000
Group 2 [Grant-White]:
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
visual =~
x1 1.000 0.841 0.721
x2 (.p2.) 0.576 0.131 4.395 0.000 0.484 0.442
x3 (.p3.) 0.798 0.173 4.627 0.000 0.672 0.643
textual =~
x4 1.000 0.933 0.847
x5 (.p5.) 1.120 0.067 16.623 0.000 1.045 0.862
x6 (.p6.) 0.932 0.064 14.652 0.000 0.869 0.796
speed =~
x7 1.000 0.711 0.668
x8 (.p8.) 1.130 0.133 8.488 0.000 0.803 0.773
x9 (.p9.) 1.009 0.207 4.864 0.000 0.717 0.704
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
visual ~~
textual 0.427 0.107 4.003 0.000 0.544 0.544
speed 0.329 0.101 3.268 0.001 0.550 0.550
textual ~~
speed 0.236 0.097 2.423 0.015 0.356 0.356
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.x1 (.25.) 5.001 0.094 53.050 0.000 5.001 4.286
.x2 (.26.) 6.151 0.087 70.867 0.000 6.151 5.618
.x3 (.27.) 2.271 0.095 24.016 0.000 2.271 2.174
.x4 (.28.) 2.778 0.086 32.173 0.000 2.778 2.522
.x5 (.29.) 4.035 0.103 39.095 0.000 4.035 3.330
.x6 (.30.) 1.926 0.075 25.751 0.000 1.926 1.763
.x7 (.31.) 4.242 0.079 53.702 0.000 4.242 3.991
.x8 (.32.) 5.630 0.075 75.002 0.000 5.630 5.422
.x9 (.33.) 5.465 0.072 76.114 0.000 5.465 5.369
visual -0.148 0.140 -1.053 0.292 -0.176 -0.176
textual 0.576 0.119 4.841 0.000 0.618 0.618
speed -0.177 0.104 -1.712 0.087 -0.250 -0.250
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.x1 0.654 0.177 3.691 0.000 0.654 0.480
.x2 0.964 0.152 6.351 0.000 0.964 0.804
.x3 0.641 0.129 4.950 0.000 0.641 0.587
.x4 0.343 0.065 5.275 0.000 0.343 0.283
.x5 0.376 0.073 5.164 0.000 0.376 0.256
.x6 0.437 0.074 5.922 0.000 0.437 0.366
.x7 0.625 0.106 5.901 0.000 0.625 0.553
.x8 0.434 0.147 2.948 0.003 0.434 0.403
.x9 0.522 0.125 4.163 0.000 0.522 0.504
visual 0.708 0.186 3.804 0.000 1.000 1.000
textual 0.870 0.143 6.069 0.000 1.000 1.000
speed 0.505 0.125 4.053 0.000 1.000 1.000
パス図
library(semPlot)
semPaths(fit,
what = "std",
layout = "tree2",
curvePivot = TRUE,
residuals = FALSE,
intercepts = FALSE,
edge.label.cex = 1.0,
edge.color = "black",
edge.label.position = 0.6,
title = FALSE
)
