분석자의 모형에 CFA 모형에 해당되는 측정모형(measurement model) 과 경로분석과 마찬가지로 변수와 변수의 인과관계를 추정하는 구조모형(structural model) 을 동시에 추정한 모형을 SEM이라 부른다.
### 패키지 불러오기
library(lavaan)## Warning: package 'lavaan' was built under R version 3.4.4## This is lavaan 0.5-23.1097## lavaan is BETA software! Please report any bugs.library(data.table)## Warning: package 'data.table' was built under R version 3.4.2### 파일 불러오기
f4structure <- fread("f4structure.csv")
colnames(f4structure)## [1] "X1" "X2" "X3" "X4" "X5" "X6" "X7" "X8" "X9" "X10" "X11"
## [12] "X12" "X13" "X14" "X15" "X16" "X17" "X18" "X19" "X20"### 구조방정식 추정
mysem1 <- "
X =~ X1+X2+X3+X4+X5
M1 =~ X6+X7+X8+X9+X10
M2 =~ X11+X12+X13+X14+X15
Y =~ X16+X17+X18+X19+X20
X1~~X1; X2~~X2; X3~~X3; X4~~X4; X5~~X5
X6~~X6; X7~~X7; X8~~X8; X9~~X9; X10~~X10
X11~~X11; X12~~X12; X13~~X13; X14~~X14; X15~~X15
X16~~X16; X17~~X17; X18~~X18; X19~~X19; X20~~X20
M1~X; M2~X; Y~X
Y~M1+M2
X~~X
M1~~M1; M2~~M2; Y~~Y; M1~~M2"
obj.mysem1 <- sem(mysem1, data=f4structure)
summary(obj.mysem1, fit.measures=T, standardized=T)## lavaan (0.5-23.1097) converged normally after 31 iterations
##
## Number of observations 254
##
## Estimator ML
## Minimum Function Test Statistic 149.415
## Degrees of freedom 164
## P-value (Chi-square) 0.786
##
## Model test baseline model:
##
## Minimum Function Test Statistic 2158.772
## Degrees of freedom 190
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.009
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -7334.339
## Loglikelihood unrestricted model (H1) -7259.632
##
## Number of free parameters 46
## Akaike (AIC) 14760.678
## Bayesian (BIC) 14923.395
## Sample-size adjusted Bayesian (BIC) 14777.566
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent Confidence Interval 0.000 0.020
## P-value RMSEA <= 0.05 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.039
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X =~
## X1 1.000 0.827 0.673
## X2 1.031 0.113 9.099 0.000 0.853 0.666
## X3 1.173 0.114 10.277 0.000 0.969 0.778
## X4 1.054 0.113 9.288 0.000 0.871 0.683
## X5 1.101 0.113 9.780 0.000 0.910 0.728
## M1 =~
## X6 1.000 0.920 0.721
## X7 0.988 0.096 10.300 0.000 0.909 0.701
## X8 1.000 0.091 10.959 0.000 0.919 0.749
## X9 1.056 0.096 11.050 0.000 0.971 0.756
## X10 1.014 0.091 11.174 0.000 0.933 0.765
## M2 =~
## X11 1.000 0.997 0.757
## X12 0.884 0.084 10.569 0.000 0.881 0.720
## X13 0.800 0.078 10.224 0.000 0.798 0.695
## X14 0.800 0.082 9.789 0.000 0.798 0.664
## X15 0.787 0.082 9.630 0.000 0.785 0.653
## Y =~
## X16 1.000 0.947 0.743
## X17 1.034 0.088 11.725 0.000 0.979 0.782
## X18 0.856 0.088 9.736 0.000 0.810 0.648
## X19 0.975 0.084 11.537 0.000 0.923 0.768
## X20 1.027 0.094 10.924 0.000 0.973 0.726
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## M1 ~
## X 0.549 0.091 6.019 0.000 0.493 0.493
## M2 ~
## X 0.617 0.099 6.204 0.000 0.511 0.511
## Y ~
## X -0.000 0.104 -0.002 0.999 -0.000 -0.000
## M1 0.461 0.090 5.146 0.000 0.448 0.448
## M2 0.171 0.078 2.185 0.029 0.181 0.181
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .M1 ~~
## .M2 0.061 0.057 1.072 0.284 0.089 0.089
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1 0.824 0.086 9.586 0.000 0.824 0.547
## .X2 0.911 0.094 9.651 0.000 0.911 0.556
## .X3 0.615 0.075 8.146 0.000 0.615 0.395
## .X4 0.869 0.092 9.495 0.000 0.869 0.534
## .X5 0.737 0.082 8.973 0.000 0.737 0.471
## .X6 0.783 0.083 9.380 0.000 0.783 0.481
## .X7 0.855 0.089 9.582 0.000 0.855 0.509
## .X8 0.663 0.073 9.031 0.000 0.663 0.439
## .X9 0.709 0.079 8.935 0.000 0.709 0.429
## .X10 0.617 0.070 8.794 0.000 0.617 0.415
## .X11 0.743 0.090 8.299 0.000 0.743 0.428
## .X12 0.723 0.081 8.890 0.000 0.723 0.482
## .X13 0.682 0.074 9.209 0.000 0.682 0.518
## .X14 0.807 0.085 9.531 0.000 0.807 0.559
## .X15 0.829 0.086 9.632 0.000 0.829 0.573
## .X16 0.728 0.080 9.050 0.000 0.728 0.448
## .X17 0.611 0.072 8.431 0.000 0.611 0.389
## .X18 0.909 0.091 9.981 0.000 0.909 0.581
## .X19 0.592 0.068 8.668 0.000 0.592 0.410
## .X20 0.849 0.092 9.264 0.000 0.849 0.473
## X 0.683 0.121 5.658 0.000 1.000 1.000
## .M1 0.640 0.107 6.007 0.000 0.757 0.757
## .M2 0.735 0.119 6.162 0.000 0.739 0.739
## .Y 0.641 0.103 6.213 0.000 0.715 0.715같은 잠재변수의 관칙치의 경우 수정모형이 가능하다. 하지만 모형을 연구자가 목적에 따라 설정해놓고 바꾼다는것이 맞는지 고민 필요…
### 수정지수 확인
### 수정지수 modindices() 함수 이용
modindices(obj.mysem1)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 51 X =~ X6 0.184 -0.042 -0.035 -0.027 -0.027
## 52 X =~ X7 0.513 -0.073 -0.060 -0.046 -0.046
## 53 X =~ X8 1.439 0.111 0.092 0.075 0.075
## 54 X =~ X9 0.000 0.000 0.000 0.000 0.000
## 55 X =~ X10 0.021 -0.013 -0.011 -0.009 -0.009
## 56 X =~ X11 1.690 0.137 0.114 0.086 0.086
## 57 X =~ X12 1.936 0.139 0.115 0.094 0.094
## 58 X =~ X13 2.634 -0.154 -0.128 -0.111 -0.111
## 59 X =~ X14 0.974 -0.100 -0.083 -0.069 -0.069
## 60 X =~ X15 0.164 -0.041 -0.034 -0.028 -0.028
## 61 X =~ X16 1.991 0.120 0.099 0.078 0.078
## 62 X =~ X17 1.565 -0.101 -0.084 -0.067 -0.067
## 63 X =~ X18 0.010 -0.009 -0.008 -0.006 -0.006
## 64 X =~ X19 0.292 0.042 0.035 0.029 0.029
## 65 X =~ X20 0.314 -0.051 -0.042 -0.031 -0.031
## 66 M1 =~ X1 0.223 0.042 0.039 0.031 0.031
## 67 M1 =~ X2 3.108 0.164 0.151 0.118 0.118
## 68 M1 =~ X3 0.084 -0.025 -0.023 -0.018 -0.018
## 69 M1 =~ X4 0.392 -0.057 -0.053 -0.041 -0.041
## 70 M1 =~ X5 1.182 -0.095 -0.087 -0.070 -0.070
## 71 M1 =~ X11 0.198 -0.036 -0.033 -0.025 -0.025
## 72 M1 =~ X12 2.713 0.126 0.116 0.095 0.095
## 73 M1 =~ X13 0.746 -0.063 -0.058 -0.050 -0.050
## 74 M1 =~ X14 0.518 -0.056 -0.052 -0.043 -0.043
## 75 M1 =~ X15 0.114 0.026 0.024 0.020 0.020
## 76 M1 =~ X16 2.354 -0.133 -0.122 -0.096 -0.096
## 77 M1 =~ X17 0.096 0.026 0.024 0.019 0.019
## 78 M1 =~ X18 0.146 0.035 0.032 0.026 0.026
## 79 M1 =~ X19 0.249 0.040 0.037 0.031 0.031
## 80 M1 =~ X20 0.142 0.035 0.032 0.024 0.024
## 81 M2 =~ X1 0.004 0.005 0.005 0.004 0.004
## 82 M2 =~ X2 2.161 -0.131 -0.131 -0.102 -0.102
## 83 M2 =~ X3 0.382 0.050 0.050 0.040 0.040
## 84 M2 =~ X4 0.522 0.064 0.063 0.050 0.050
## 85 M2 =~ X5 0.009 -0.008 -0.008 -0.006 -0.006
## 86 M2 =~ X6 0.437 -0.048 -0.048 -0.037 -0.037
## 87 M2 =~ X7 0.335 -0.043 -0.043 -0.033 -0.033
## 88 M2 =~ X8 0.607 0.053 0.053 0.043 0.043
## 89 M2 =~ X9 0.010 0.007 0.007 0.005 0.005
## 90 M2 =~ X10 0.064 0.017 0.017 0.014 0.014
## 91 M2 =~ X16 1.469 0.086 0.086 0.067 0.067
## 92 M2 =~ X17 1.507 -0.083 -0.083 -0.066 -0.066
## 93 M2 =~ X18 0.004 -0.005 -0.005 -0.004 -0.004
## 94 M2 =~ X19 1.279 0.074 0.074 0.062 0.062
## 95 M2 =~ X20 1.127 -0.081 -0.080 -0.060 -0.060
## 96 Y =~ X1 4.873 0.168 0.159 0.130 0.130
## 97 Y =~ X2 0.904 -0.076 -0.072 -0.056 -0.056
## 98 Y =~ X3 0.266 -0.037 -0.035 -0.028 -0.028
## 99 Y =~ X4 0.000 -0.001 -0.001 -0.001 -0.001
## 100 Y =~ X5 0.303 -0.041 -0.039 -0.031 -0.031
## 101 Y =~ X6 3.942 -0.170 -0.161 -0.126 -0.126
## 102 Y =~ X7 0.732 0.076 0.072 0.055 0.055
## 103 Y =~ X8 0.009 0.008 0.007 0.006 0.006
## 104 Y =~ X9 0.430 0.055 0.052 0.041 0.041
## 105 Y =~ X10 0.106 0.026 0.024 0.020 0.020
## 106 Y =~ X11 3.007 -0.136 -0.129 -0.098 -0.098
## 107 Y =~ X12 2.116 0.108 0.103 0.084 0.084
## 108 Y =~ X13 1.958 0.099 0.094 0.082 0.082
## 109 Y =~ X14 0.291 -0.041 -0.039 -0.032 -0.032
## 110 Y =~ X15 0.255 -0.039 -0.037 -0.030 -0.030
## 111 X1 ~~ X2 1.219 -0.074 -0.074 -0.047 -0.047
## 112 X1 ~~ X3 0.115 -0.022 -0.022 -0.014 -0.014
## 113 X1 ~~ X4 0.562 0.050 0.050 0.032 0.032
## 114 X1 ~~ X5 0.149 0.025 0.025 0.016 0.016
## 115 X1 ~~ X6 0.091 0.018 0.018 0.011 0.011
## 116 X1 ~~ X7 0.960 -0.059 -0.059 -0.037 -0.037
## 117 X1 ~~ X8 0.390 -0.034 -0.034 -0.023 -0.023
## 118 X1 ~~ X9 0.777 0.050 0.050 0.032 0.032
## 119 X1 ~~ X10 0.063 -0.013 -0.013 -0.009 -0.009
## 120 X1 ~~ X11 0.339 0.035 0.035 0.021 0.021
## 121 X1 ~~ X12 0.033 0.010 0.010 0.007 0.007
## 122 X1 ~~ X13 0.268 -0.028 -0.028 -0.020 -0.020
## 123 X1 ~~ X14 0.165 0.024 0.024 0.016 0.016
## 124 X1 ~~ X15 1.705 -0.077 -0.077 -0.052 -0.052
## 125 X1 ~~ X16 0.547 -0.042 -0.042 -0.027 -0.027
## 126 X1 ~~ X17 0.562 0.040 0.040 0.026 0.026
## 127 X1 ~~ X18 0.506 0.043 0.043 0.028 0.028
## 128 X1 ~~ X19 2.086 0.075 0.075 0.051 0.051
## 129 X1 ~~ X20 0.027 0.010 0.010 0.006 0.006
## 130 X2 ~~ X3 0.037 0.013 0.013 0.008 0.008
## 131 X2 ~~ X4 0.224 0.033 0.033 0.020 0.020
## 132 X2 ~~ X5 0.054 0.016 0.016 0.010 0.010
## 133 X2 ~~ X6 0.155 0.024 0.024 0.015 0.015
## 134 X2 ~~ X7 0.027 -0.010 -0.010 -0.006 -0.006
## 135 X2 ~~ X8 0.373 0.035 0.035 0.022 0.022
## 136 X2 ~~ X9 0.840 0.054 0.054 0.033 0.033
## 137 X2 ~~ X10 0.590 0.043 0.043 0.027 0.027
## 138 X2 ~~ X11 0.169 0.026 0.026 0.015 0.015
## 139 X2 ~~ X12 1.290 0.068 0.068 0.043 0.043
## 140 X2 ~~ X13 0.211 -0.026 -0.026 -0.018 -0.018
## 141 X2 ~~ X14 1.300 -0.070 -0.070 -0.046 -0.046
## 142 X2 ~~ X15 3.137 -0.110 -0.110 -0.071 -0.071
## 143 X2 ~~ X16 0.106 -0.019 -0.019 -0.012 -0.012
## 144 X2 ~~ X17 0.733 -0.048 -0.048 -0.030 -0.030
## 145 X2 ~~ X18 0.036 -0.012 -0.012 -0.008 -0.008
## 146 X2 ~~ X19 0.142 -0.021 -0.021 -0.013 -0.013
## 147 X2 ~~ X20 0.027 0.010 0.010 0.006 0.006
## 148 X3 ~~ X4 0.364 -0.040 -0.040 -0.025 -0.025
## 149 X3 ~~ X5 0.270 0.034 0.034 0.022 0.022
## 150 X3 ~~ X6 0.964 0.053 0.053 0.033 0.033
## 151 X3 ~~ X7 0.007 0.005 0.005 0.003 0.003
## 152 X3 ~~ X8 3.556 0.095 0.095 0.062 0.062
## 153 X3 ~~ X9 0.978 -0.052 -0.052 -0.032 -0.032
## 154 X3 ~~ X10 3.496 -0.092 -0.092 -0.060 -0.060
## 155 X3 ~~ X11 0.259 -0.028 -0.028 -0.017 -0.017
## 156 X3 ~~ X12 3.479 -0.098 -0.098 -0.064 -0.064
## 157 X3 ~~ X13 0.317 0.028 0.028 0.020 0.020
## 158 X3 ~~ X14 0.733 0.046 0.046 0.031 0.031
## 159 X3 ~~ X15 4.814 0.120 0.120 0.080 0.080
## 160 X3 ~~ X16 0.464 0.036 0.036 0.022 0.022
## 161 X3 ~~ X17 0.016 -0.006 -0.006 -0.004 -0.004
## 162 X3 ~~ X18 0.491 -0.039 -0.039 -0.025 -0.025
## 163 X3 ~~ X19 1.400 -0.057 -0.057 -0.038 -0.038
## 164 X3 ~~ X20 0.545 0.041 0.041 0.025 0.025
## 165 X4 ~~ X5 0.273 -0.035 -0.035 -0.022 -0.022
## 166 X4 ~~ X6 0.849 -0.055 -0.055 -0.034 -0.034
## 167 X4 ~~ X7 0.986 0.062 0.062 0.037 0.037
## 168 X4 ~~ X8 0.777 -0.049 -0.049 -0.032 -0.032
## 169 X4 ~~ X9 0.002 -0.002 -0.002 -0.002 -0.002
## 170 X4 ~~ X10 0.028 0.009 0.009 0.006 0.006
## 171 X4 ~~ X11 2.055 0.088 0.088 0.052 0.052
## 172 X4 ~~ X12 0.708 0.050 0.050 0.032 0.032
## 173 X4 ~~ X13 0.168 0.023 0.023 0.016 0.016
## 174 X4 ~~ X14 1.077 -0.063 -0.063 -0.041 -0.041
## 175 X4 ~~ X15 1.606 -0.077 -0.077 -0.050 -0.050
## 176 X4 ~~ X16 1.867 0.080 0.080 0.049 0.049
## 177 X4 ~~ X17 0.120 -0.019 -0.019 -0.012 -0.012
## 178 X4 ~~ X18 0.213 0.029 0.029 0.018 0.018
## 179 X4 ~~ X19 1.273 0.061 0.061 0.040 0.040
## 180 X4 ~~ X20 6.304 -0.158 -0.158 -0.092 -0.092
## 181 X5 ~~ X6 1.099 -0.059 -0.059 -0.037 -0.037
## 182 X5 ~~ X7 0.308 -0.033 -0.033 -0.020 -0.020
## 183 X5 ~~ X8 0.060 -0.013 -0.013 -0.008 -0.008
## 184 X5 ~~ X9 0.230 -0.026 -0.026 -0.016 -0.016
## 185 X5 ~~ X10 1.404 0.061 0.061 0.040 0.040
## 186 X5 ~~ X11 0.025 0.009 0.009 0.006 0.006
## 187 X5 ~~ X12 0.995 0.055 0.055 0.036 0.036
## 188 X5 ~~ X13 2.721 -0.088 -0.088 -0.061 -0.061
## 189 X5 ~~ X14 0.045 -0.012 -0.012 -0.008 -0.008
## 190 X5 ~~ X15 0.494 0.040 0.040 0.027 0.027
## 191 X5 ~~ X16 0.902 0.052 0.052 0.033 0.033
## 192 X5 ~~ X17 0.456 -0.035 -0.035 -0.022 -0.022
## 193 X5 ~~ X18 0.143 -0.022 -0.022 -0.014 -0.014
## 194 X5 ~~ X19 0.523 -0.037 -0.037 -0.024 -0.024
## 195 X5 ~~ X20 0.591 0.045 0.045 0.027 0.027
## 196 X6 ~~ X7 0.019 -0.009 -0.009 -0.005 -0.005
## 197 X6 ~~ X8 7.118 0.161 0.161 0.103 0.103
## 198 X6 ~~ X9 0.236 -0.031 -0.031 -0.019 -0.019
## 199 X6 ~~ X10 0.665 -0.049 -0.049 -0.031 -0.031
## 200 X6 ~~ X11 0.233 0.028 0.028 0.017 0.017
## 201 X6 ~~ X12 0.539 0.041 0.041 0.026 0.026
## 202 X6 ~~ X13 2.641 -0.087 -0.087 -0.060 -0.060
## 203 X6 ~~ X14 0.078 0.016 0.016 0.011 0.011
## 204 X6 ~~ X15 0.045 -0.012 -0.012 -0.008 -0.008
## 205 X6 ~~ X16 0.000 0.001 0.001 0.001 0.001
## 206 X6 ~~ X17 0.598 -0.041 -0.041 -0.026 -0.026
## 207 X6 ~~ X18 0.109 0.020 0.020 0.012 0.012
## 208 X6 ~~ X19 0.257 -0.026 -0.026 -0.017 -0.017
## 209 X6 ~~ X20 0.671 -0.049 -0.049 -0.029 -0.029
## 210 X7 ~~ X8 0.809 -0.055 -0.055 -0.035 -0.035
## 211 X7 ~~ X9 0.260 0.033 0.033 0.020 0.020
## 212 X7 ~~ X10 0.175 0.025 0.025 0.016 0.016
## 213 X7 ~~ X11 1.826 0.082 0.082 0.048 0.048
## 214 X7 ~~ X12 1.191 0.063 0.063 0.040 0.040
## 215 X7 ~~ X13 0.019 -0.008 -0.008 -0.005 -0.005
## 216 X7 ~~ X14 5.118 -0.135 -0.135 -0.087 -0.087
## 217 X7 ~~ X15 1.274 -0.068 -0.068 -0.044 -0.044
## 218 X7 ~~ X16 0.894 0.055 0.055 0.033 0.033
## 219 X7 ~~ X17 1.603 0.069 0.069 0.043 0.043
## 220 X7 ~~ X18 1.215 0.069 0.069 0.042 0.042
## 221 X7 ~~ X19 0.437 -0.035 -0.035 -0.023 -0.023
## 222 X7 ~~ X20 2.482 -0.098 -0.098 -0.056 -0.056
## 223 X8 ~~ X9 2.219 -0.090 -0.090 -0.057 -0.057
## 224 X8 ~~ X10 0.697 -0.048 -0.048 -0.032 -0.032
## 225 X8 ~~ X11 0.293 -0.030 -0.030 -0.018 -0.018
## 226 X8 ~~ X12 0.174 -0.022 -0.022 -0.015 -0.015
## 227 X8 ~~ X13 1.069 -0.052 -0.052 -0.037 -0.037
## 228 X8 ~~ X14 3.629 0.103 0.103 0.070 0.070
## 229 X8 ~~ X15 0.572 0.041 0.041 0.028 0.028
## 230 X8 ~~ X16 1.033 -0.053 -0.053 -0.034 -0.034
## 231 X8 ~~ X17 0.270 -0.026 -0.026 -0.017 -0.017
## 232 X8 ~~ X18 1.922 -0.078 -0.078 -0.051 -0.051
## 233 X8 ~~ X19 0.236 0.023 0.023 0.016 0.016
## 234 X8 ~~ X20 4.830 0.123 0.123 0.075 0.075
## 235 X9 ~~ X10 1.250 0.067 0.067 0.043 0.043
## 236 X9 ~~ X11 0.465 -0.039 -0.039 -0.023 -0.023
## 237 X9 ~~ X12 0.527 -0.040 -0.040 -0.025 -0.025
## 238 X9 ~~ X13 0.682 0.043 0.043 0.029 0.029
## 239 X9 ~~ X14 0.372 -0.034 -0.034 -0.022 -0.022
## 240 X9 ~~ X15 2.009 0.080 0.080 0.052 0.052
## 241 X9 ~~ X16 1.417 -0.065 -0.065 -0.040 -0.040
## 242 X9 ~~ X17 1.030 0.052 0.052 0.032 0.032
## 243 X9 ~~ X18 0.293 0.032 0.032 0.020 0.020
## 244 X9 ~~ X19 0.508 0.036 0.036 0.023 0.023
## 245 X9 ~~ X20 0.237 -0.028 -0.028 -0.016 -0.016
## 246 X10 ~~ X11 0.396 -0.034 -0.034 -0.021 -0.021
## 247 X10 ~~ X12 0.106 0.017 0.017 0.011 0.011
## 248 X10 ~~ X13 0.403 0.031 0.031 0.022 0.022
## 249 X10 ~~ X14 0.040 0.011 0.011 0.007 0.007
## 250 X10 ~~ X15 0.013 -0.006 -0.006 -0.004 -0.004
## 251 X10 ~~ X16 1.116 -0.054 -0.054 -0.035 -0.035
## 252 X10 ~~ X17 0.002 0.002 0.002 0.001 0.001
## 253 X10 ~~ X18 0.002 0.002 0.002 0.001 0.001
## 254 X10 ~~ X19 0.024 0.007 0.007 0.005 0.005
## 255 X10 ~~ X20 1.297 0.062 0.062 0.038 0.038
## 256 X11 ~~ X12 0.293 -0.038 -0.038 -0.024 -0.024
## 257 X11 ~~ X13 0.023 0.010 0.010 0.007 0.007
## 258 X11 ~~ X14 0.003 0.004 0.004 0.002 0.002
## 259 X11 ~~ X15 0.004 0.004 0.004 0.003 0.003
## 260 X11 ~~ X16 0.065 0.015 0.015 0.009 0.009
## 261 X11 ~~ X17 0.613 -0.042 -0.042 -0.026 -0.026
## 262 X11 ~~ X18 4.624 -0.132 -0.132 -0.080 -0.080
## 263 X11 ~~ X19 0.037 -0.010 -0.010 -0.006 -0.006
## 264 X11 ~~ X20 0.657 0.050 0.050 0.028 0.028
## 265 X12 ~~ X13 0.321 -0.035 -0.035 -0.025 -0.025
## 266 X12 ~~ X14 0.235 0.031 0.031 0.021 0.021
## 267 X12 ~~ X15 0.337 -0.037 -0.037 -0.025 -0.025
## 268 X12 ~~ X16 0.414 0.035 0.035 0.023 0.023
## 269 X12 ~~ X17 0.117 0.018 0.018 0.012 0.012
## 270 X12 ~~ X18 0.477 0.041 0.041 0.027 0.027
## 271 X12 ~~ X19 0.522 0.036 0.036 0.025 0.025
## 272 X12 ~~ X20 2.485 -0.093 -0.093 -0.056 -0.056
## 273 X13 ~~ X14 0.025 0.010 0.010 0.007 0.007
## 274 X13 ~~ X15 0.820 0.055 0.055 0.040 0.040
## 275 X13 ~~ X16 0.955 0.051 0.051 0.035 0.035
## 276 X13 ~~ X17 0.939 0.048 0.048 0.033 0.033
## 277 X13 ~~ X18 0.057 0.014 0.014 0.009 0.009
## 278 X13 ~~ X19 0.021 -0.007 -0.007 -0.005 -0.005
## 279 X13 ~~ X20 0.000 -0.001 -0.001 -0.001 -0.001
## 280 X14 ~~ X15 0.000 0.000 0.000 0.000 0.000
## 281 X14 ~~ X16 0.695 -0.047 -0.047 -0.031 -0.031
## 282 X14 ~~ X17 0.071 -0.014 -0.014 -0.009 -0.009
## 283 X14 ~~ X18 0.113 -0.020 -0.020 -0.014 -0.014
## 284 X14 ~~ X19 0.374 0.032 0.032 0.022 0.022
## 285 X14 ~~ X20 0.263 0.031 0.031 0.019 0.019
## 286 X15 ~~ X16 0.214 -0.026 -0.026 -0.017 -0.017
## 287 X15 ~~ X17 1.297 -0.061 -0.061 -0.041 -0.041
## 288 X15 ~~ X18 3.899 0.121 0.121 0.080 0.080
## 289 X15 ~~ X19 0.038 0.010 0.010 0.007 0.007
## 290 X15 ~~ X20 0.752 -0.053 -0.053 -0.033 -0.033
## 291 X16 ~~ X17 0.073 0.017 0.017 0.011 0.011
## 292 X16 ~~ X18 1.277 0.072 0.072 0.045 0.045
## 293 X16 ~~ X19 0.066 -0.015 -0.015 -0.010 -0.010
## 294 X16 ~~ X20 0.221 -0.031 -0.031 -0.018 -0.018
## 295 X17 ~~ X18 0.050 0.014 0.014 0.009 0.009
## 296 X17 ~~ X19 2.053 -0.084 -0.084 -0.056 -0.056
## 297 X17 ~~ X20 1.366 0.076 0.076 0.045 0.045
## 298 X18 ~~ X19 0.129 0.021 0.021 0.014 0.014
## 299 X18 ~~ X20 3.943 -0.135 -0.135 -0.080 -0.080
## 300 X19 ~~ X20 0.857 0.058 0.058 0.036 0.036### CR(개념신뢰도 or 복합신뢰도), AVE(평균분산추출) 계산
### standardizedsolution() 함수 이용
myest <- standardizedsolution(obj.mysem1)
myest## lhs op rhs est.std se z pvalue
## 1 X =~ X1 0.673 0.041 16.468 0.000
## 2 X =~ X2 0.666 0.041 16.083 0.000
## 3 X =~ X3 0.778 0.033 23.648 0.000
## 4 X =~ X4 0.683 0.040 16.999 0.000
## 5 X =~ X5 0.728 0.037 19.821 0.000
## 6 M1 =~ X6 0.721 0.036 19.993 0.000
## 7 M1 =~ X7 0.701 0.038 18.636 0.000
## 8 M1 =~ X8 0.749 0.034 22.195 0.000
## 9 M1 =~ X9 0.756 0.033 22.774 0.000
## 10 M1 =~ X10 0.765 0.032 23.599 0.000
## 11 M2 =~ X11 0.757 0.035 21.396 0.000
## 12 M2 =~ X12 0.720 0.038 18.884 0.000
## 13 M2 =~ X13 0.695 0.040 17.376 0.000
## 14 M2 =~ X14 0.664 0.042 15.721 0.000
## 15 M2 =~ X15 0.653 0.043 15.173 0.000
## 16 Y =~ X16 0.743 0.034 21.583 0.000
## 17 Y =~ X17 0.782 0.031 24.971 0.000
## 18 Y =~ X18 0.648 0.042 15.425 0.000
## 19 Y =~ X19 0.768 0.032 23.725 0.000
## 20 Y =~ X20 0.726 0.036 20.289 0.000
## 21 X1 ~~ X1 0.547 0.055 9.927 0.000
## 22 X2 ~~ X2 0.556 0.055 10.074 0.000
## 23 X3 ~~ X3 0.395 0.051 7.734 0.000
## 24 X4 ~~ X4 0.534 0.055 9.732 0.000
## 25 X5 ~~ X5 0.471 0.053 8.811 0.000
## 26 X6 ~~ X6 0.481 0.052 9.258 0.000
## 27 X7 ~~ X7 0.509 0.053 9.641 0.000
## 28 X8 ~~ X8 0.439 0.051 8.699 0.000
## 29 X9 ~~ X9 0.429 0.050 8.562 0.000
## 30 X10 ~~ X10 0.415 0.050 8.371 0.000
## 31 X11 ~~ X11 0.428 0.054 7.992 0.000
## 32 X12 ~~ X12 0.482 0.055 8.794 0.000
## 33 X13 ~~ X13 0.518 0.056 9.319 0.000
## 34 X14 ~~ X14 0.559 0.056 9.960 0.000
## 35 X15 ~~ X15 0.573 0.056 10.193 0.000
## 36 X16 ~~ X16 0.448 0.051 8.761 0.000
## 37 X17 ~~ X17 0.389 0.049 7.951 0.000
## 38 X18 ~~ X18 0.581 0.054 10.680 0.000
## 39 X19 ~~ X19 0.410 0.050 8.240 0.000
## 40 X20 ~~ X20 0.473 0.052 9.099 0.000
## 41 M1 ~ X 0.493 0.059 8.347 0.000
## 42 M2 ~ X 0.511 0.059 8.617 0.000
## 43 Y ~ X 0.000 0.091 -0.002 0.999
## 44 Y ~ M1 0.448 0.073 6.122 0.000
## 45 Y ~ M2 0.181 0.081 2.241 0.025
## 46 X ~~ X 1.000 0.000 NA NA
## 47 M1 ~~ M1 0.757 0.058 12.989 0.000
## 48 M2 ~~ M2 0.739 0.061 12.184 0.000
## 49 Y ~~ Y 0.715 0.058 12.251 0.000
## 50 M1 ~~ M2 0.089 0.082 1.095 0.274### CR, AVE 계산하기 위한 인자적재치 추출
X.loadings <- myest[1:5,4]
M1.loadings <- myest[6:10,4]
M2.loadings <- myest[11:15,4]
Y.loadings <- myest[16:20,4]
### CR, AVE 계산하기 위한 오차항 분산정보 추출
X.var.theta <- myest[21:25,4]
M1.var.theta <- myest[26:30,4]
M2.var.theta <- myest[31:35,4]
Y.var.theta <- myest[36:40,4]
### CR, AVE 계산하기 위한 함수
CR.AVE.function <- function(myloadings, mythetas){
SS.L2 <- sum(myloadings)^2
SS.Lsq <- sum(myloadings^2)
SS.thetas <- sum(mythetas)
myCR <- SS.L2/(SS.L2+SS.thetas)
myAVE <- SS.Lsq/(SS.Lsq+SS.thetas)
myresult <- cbind(myCR, myAVE)
colnames(myresult) <- c("composite.Reliability", "ave.variance.extracted")
myresult
}
CR.AVE.function(X.loadings, X.var.theta)## composite.Reliability ave.variance.extracted
## [1,] 0.832557 0.4994843CR.AVE.function(M1.loadings, M1.var.theta)## composite.Reliability ave.variance.extracted
## [1,] 0.8569914 0.5454038CR.AVE.function(M2.loadings, M2.var.theta)## composite.Reliability ave.variance.extracted
## [1,] 0.826194 0.4880895CR.AVE.function(Y.loadings, Y.var.theta)## composite.Reliability ave.variance.extracted
## [1,] 0.8538611 0.5398837### k행렬, A행렬을 추가로 추정하는 경우
mysem2 <- paste(mysem1,
"X1~1; X2~1; X3~1; X4~1; X5~1
X6~1; X7~1; X8~1; X9~1; X10~1
X11~1; X12~1; X13~1; X14~1; X15~1
X16~1; X17~1; X18~1; X19~1; X20~1",
sep="\n")
obj.mysem2 <- sem(mysem2, data=f4structure)
summary(obj.mysem2, fit.measures=T, standardized=T)## lavaan (0.5-23.1097) converged normally after 31 iterations
##
## Number of observations 254
##
## Estimator ML
## Minimum Function Test Statistic 149.415
## Degrees of freedom 164
## P-value (Chi-square) 0.786
##
## Model test baseline model:
##
## Minimum Function Test Statistic 2158.772
## Degrees of freedom 190
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.009
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -7334.339
## Loglikelihood unrestricted model (H1) -7259.632
##
## Number of free parameters 66
## Akaike (AIC) 14800.678
## Bayesian (BIC) 15034.142
## Sample-size adjusted Bayesian (BIC) 14824.908
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent Confidence Interval 0.000 0.020
## P-value RMSEA <= 0.05 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.037
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X =~
## X1 1.000 0.827 0.673
## X2 1.031 0.113 9.099 0.000 0.853 0.666
## X3 1.173 0.114 10.277 0.000 0.969 0.778
## X4 1.054 0.113 9.288 0.000 0.871 0.683
## X5 1.101 0.113 9.780 0.000 0.910 0.728
## M1 =~
## X6 1.000 0.920 0.721
## X7 0.988 0.096 10.300 0.000 0.909 0.701
## X8 1.000 0.091 10.959 0.000 0.919 0.749
## X9 1.056 0.096 11.050 0.000 0.971 0.756
## X10 1.014 0.091 11.174 0.000 0.933 0.765
## M2 =~
## X11 1.000 0.997 0.757
## X12 0.884 0.084 10.569 0.000 0.881 0.720
## X13 0.800 0.078 10.224 0.000 0.798 0.695
## X14 0.800 0.082 9.789 0.000 0.798 0.664
## X15 0.787 0.082 9.630 0.000 0.785 0.653
## Y =~
## X16 1.000 0.947 0.743
## X17 1.034 0.088 11.725 0.000 0.979 0.782
## X18 0.856 0.088 9.736 0.000 0.810 0.648
## X19 0.975 0.084 11.537 0.000 0.923 0.768
## X20 1.027 0.094 10.924 0.000 0.973 0.726
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## M1 ~
## X 0.549 0.091 6.019 0.000 0.493 0.493
## M2 ~
## X 0.617 0.099 6.204 0.000 0.511 0.511
## Y ~
## X -0.000 0.104 -0.002 0.999 -0.000 -0.000
## M1 0.461 0.090 5.146 0.000 0.448 0.448
## M2 0.171 0.078 2.185 0.029 0.181 0.181
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .M1 ~~
## .M2 0.061 0.057 1.072 0.284 0.089 0.089
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1 4.020 0.077 52.177 0.000 4.020 3.274
## .X2 4.059 0.080 50.542 0.000 4.059 3.171
## .X3 4.028 0.078 51.485 0.000 4.028 3.230
## .X4 4.193 0.080 52.371 0.000 4.193 3.286
## .X5 4.031 0.079 51.345 0.000 4.031 3.222
## .X6 4.094 0.080 51.130 0.000 4.094 3.208
## .X7 4.004 0.081 49.216 0.000 4.004 3.088
## .X8 4.012 0.077 52.071 0.000 4.012 3.267
## .X9 3.933 0.081 48.754 0.000 3.933 3.059
## .X10 4.075 0.077 53.264 0.000 4.075 3.342
## .X11 4.047 0.083 48.928 0.000 4.047 3.070
## .X12 3.988 0.077 51.900 0.000 3.988 3.256
## .X13 3.980 0.072 55.245 0.000 3.980 3.466
## .X14 4.028 0.075 53.414 0.000 4.028 3.352
## .X15 4.122 0.075 54.637 0.000 4.122 3.428
## .X16 3.921 0.080 49.044 0.000 3.921 3.077
## .X17 3.870 0.079 49.229 0.000 3.870 3.089
## .X18 3.925 0.079 50.002 0.000 3.925 3.137
## .X19 3.902 0.075 51.762 0.000 3.902 3.248
## .X20 3.976 0.084 47.305 0.000 3.976 2.968
## X 0.000 0.000 0.000
## .M1 0.000 0.000 0.000
## .M2 0.000 0.000 0.000
## .Y 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1 0.824 0.086 9.586 0.000 0.824 0.547
## .X2 0.911 0.094 9.651 0.000 0.911 0.556
## .X3 0.615 0.075 8.146 0.000 0.615 0.395
## .X4 0.869 0.092 9.495 0.000 0.869 0.534
## .X5 0.737 0.082 8.973 0.000 0.737 0.471
## .X6 0.783 0.083 9.380 0.000 0.783 0.481
## .X7 0.855 0.089 9.582 0.000 0.855 0.509
## .X8 0.663 0.073 9.031 0.000 0.663 0.439
## .X9 0.709 0.079 8.935 0.000 0.709 0.429
## .X10 0.617 0.070 8.794 0.000 0.617 0.415
## .X11 0.743 0.090 8.299 0.000 0.743 0.428
## .X12 0.723 0.081 8.890 0.000 0.723 0.482
## .X13 0.682 0.074 9.209 0.000 0.682 0.518
## .X14 0.807 0.085 9.531 0.000 0.807 0.559
## .X15 0.829 0.086 9.632 0.000 0.829 0.573
## .X16 0.728 0.080 9.050 0.000 0.728 0.448
## .X17 0.611 0.072 8.431 0.000 0.611 0.389
## .X18 0.909 0.091 9.981 0.000 0.909 0.581
## .X19 0.592 0.068 8.668 0.000 0.592 0.410
## .X20 0.849 0.092 9.264 0.000 0.849 0.473
## X 0.683 0.121 5.658 0.000 1.000 1.000
## .M1 0.640 0.107 6.007 0.000 0.757 0.757
## .M2 0.735 0.119 6.162 0.000 0.739 0.739
## .Y 0.641 0.103 6.213 0.000 0.715 0.715### 잠재변수의 k행렬, A행렬을 추정한 경우
mysem3 <- paste(mysem1,
"X1~0; X2~1; X3~1; X4~1; X5~1; X~1
X6~0; X7~1; X8~1; X9~1; X10~1; M1~1
X11~0; X12~1; X13~1; X14~1; X15~1; M2~1
X16~0; X17~1; X18~1; X19~1; X20~1; Y~1",
sep="\n")
obj.mysem3 <- sem(mysem3, data=f4structure)
summary(obj.mysem3, fit.measures=T, standardized=T)## lavaan (0.5-23.1097) converged normally after 116 iterations
##
## Number of observations 254
##
## Estimator ML
## Minimum Function Test Statistic 149.415
## Degrees of freedom 164
## P-value (Chi-square) 0.786
##
## Model test baseline model:
##
## Minimum Function Test Statistic 2158.772
## Degrees of freedom 190
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.009
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -7334.339
## Loglikelihood unrestricted model (H1) -7259.632
##
## Number of free parameters 66
## Akaike (AIC) 14800.678
## Bayesian (BIC) 15034.142
## Sample-size adjusted Bayesian (BIC) 14824.908
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent Confidence Interval 0.000 0.020
## P-value RMSEA <= 0.05 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.037
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X =~
## X1 1.000 0.827 0.673
## X2 1.031 0.113 9.099 0.000 0.853 0.666
## X3 1.173 0.114 10.277 0.000 0.969 0.778
## X4 1.054 0.113 9.288 0.000 0.871 0.683
## X5 1.101 0.113 9.780 0.000 0.910 0.728
## M1 =~
## X6 1.000 0.920 0.721
## X7 0.988 0.096 10.300 0.000 0.909 0.701
## X8 1.000 0.091 10.959 0.000 0.919 0.749
## X9 1.056 0.096 11.050 0.000 0.971 0.756
## X10 1.014 0.091 11.174 0.000 0.933 0.765
## M2 =~
## X11 1.000 0.997 0.757
## X12 0.884 0.084 10.569 0.000 0.881 0.720
## X13 0.800 0.078 10.224 0.000 0.798 0.695
## X14 0.800 0.082 9.789 0.000 0.798 0.664
## X15 0.787 0.082 9.630 0.000 0.785 0.653
## Y =~
## X16 1.000 0.947 0.743
## X17 1.034 0.088 11.725 0.000 0.979 0.782
## X18 0.856 0.088 9.736 0.000 0.810 0.648
## X19 0.975 0.084 11.537 0.000 0.923 0.768
## X20 1.027 0.094 10.924 0.000 0.973 0.726
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## M1 ~
## X 0.549 0.091 6.019 0.000 0.493 0.493
## M2 ~
## X 0.617 0.099 6.204 0.000 0.511 0.511
## Y ~
## X -0.000 0.104 -0.002 0.999 -0.000 -0.000
## M1 0.461 0.090 5.146 0.000 0.448 0.448
## M2 0.171 0.078 2.185 0.029 0.181 0.181
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .M1 ~~
## .M2 0.061 0.057 1.072 0.284 0.089 0.089
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1 0.000 0.000 0.000
## .X2 -0.087 0.463 -0.188 0.851 -0.087 -0.068
## .X3 -0.686 0.466 -1.471 0.141 -0.686 -0.550
## .X4 -0.043 0.464 -0.093 0.926 -0.043 -0.034
## .X5 -0.395 0.460 -0.859 0.390 -0.395 -0.316
## X 4.020 0.077 52.177 0.000 4.862 4.862
## .X6 0.000 0.000 0.000
## .X7 -0.043 0.401 -0.108 0.914 -0.043 -0.033
## .X8 -0.081 0.381 -0.214 0.831 -0.081 -0.066
## .X9 -0.392 0.399 -0.981 0.326 -0.392 -0.305
## .X10 -0.077 0.379 -0.204 0.839 -0.077 -0.063
## .M1 1.890 0.375 5.036 0.000 2.055 2.055
## .X11 0.000 0.000 0.000
## .X12 0.412 0.346 1.192 0.233 0.412 0.337
## .X13 0.744 0.324 2.298 0.022 0.744 0.648
## .X14 0.789 0.338 2.331 0.020 0.789 0.657
## .X15 0.935 0.339 2.762 0.006 0.935 0.778
## .M2 1.569 0.408 3.842 0.000 1.573 1.573
## .X16 0.000 0.000 0.000
## .X17 -0.186 0.354 -0.527 0.598 -0.186 -0.149
## .X18 0.569 0.353 1.614 0.107 0.569 0.455
## .X19 0.079 0.339 0.234 0.815 0.079 0.066
## .X20 -0.053 0.377 -0.140 0.889 -0.053 -0.039
## .Y 1.341 0.395 3.395 0.001 1.416 1.416
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1 0.824 0.086 9.586 0.000 0.824 0.547
## .X2 0.911 0.094 9.651 0.000 0.911 0.556
## .X3 0.615 0.075 8.146 0.000 0.615 0.395
## .X4 0.869 0.092 9.495 0.000 0.869 0.534
## .X5 0.737 0.082 8.973 0.000 0.737 0.471
## .X6 0.783 0.083 9.380 0.000 0.783 0.481
## .X7 0.855 0.089 9.582 0.000 0.855 0.509
## .X8 0.663 0.073 9.032 0.000 0.663 0.439
## .X9 0.709 0.079 8.935 0.000 0.709 0.429
## .X10 0.617 0.070 8.794 0.000 0.617 0.415
## .X11 0.743 0.090 8.300 0.000 0.743 0.428
## .X12 0.723 0.081 8.890 0.000 0.723 0.482
## .X13 0.682 0.074 9.209 0.000 0.682 0.518
## .X14 0.807 0.085 9.531 0.000 0.807 0.559
## .X15 0.829 0.086 9.632 0.000 0.829 0.573
## .X16 0.728 0.080 9.050 0.000 0.728 0.448
## .X17 0.611 0.072 8.431 0.000 0.611 0.389
## .X18 0.909 0.091 9.981 0.000 0.909 0.581
## .X19 0.592 0.068 8.668 0.000 0.592 0.410
## .X20 0.849 0.092 9.264 0.000 0.849 0.473
## X 0.683 0.121 5.659 0.000 1.000 1.000
## .M1 0.640 0.107 6.007 0.000 0.757 0.757
## .M2 0.735 0.119 6.162 0.000 0.739 0.739
## .Y 0.641 0.103 6.213 0.000 0.715 0.715### 동등성 제약을 이용하여 M2 인자적재치들이 동등한지 여부 테스트
mysem1a <- "
X =~ X1+X2+X3+X4+X5
M1 =~ X6+X7+X8+X9+X10
M2 =~ g3_*X11+g3_*X12+g3_*X13+g3_*X14+g3_*X15
Y =~ X16+X17+X18+X19+X20
X1~~X1; X2~~X2; X3~~X3; X4~~X4; X5~~X5
X6~~X6; X7~~X7; X8~~X8; X9~~X9; X10~~X10
X11~~X11; X12~~X12; X13~~X13; X14~~X14; X15~~X15
X16~~X16; X17~~X17; X18~~X18; X19~~X19; X20~~X20
M1~X; M2~X; Y~X
Y~M1+M2
X~~X
M1~~M1; M2~~M2; Y~~Y; M1~~M2"
obj.mysem1a <- sem(mysem1a, data=f4structure)
anova(obj.mysem1, obj.mysem1a)## Chi Square Difference Test
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## obj.mysem1 164 14761 14923 149.41
## obj.mysem1a 168 14760 14909 157.18 7.7685 4 0.1004### 동등성 제약을 이용하여 A행렬의 모수들의 동등성을 테스트
mysem2a <- paste(mysem1,
"X1~1; X2~1; X3~1; X4~1; X5~1
X6~1; X7~1; X8~1; X9~1; X10~1
X11~a2*1; X12~a2*1; X13~a2*1; X14~a2*1; X15~a2*1
X16~1; X17~1; X18~1; X19~1; X20~1",
sep="\n")
obj.mysem2a <- sem(mysem2a, data=f4structure)
anova(obj.mysem2, obj.mysem2a)## Chi Square Difference Test
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## obj.mysem2 164 14801 15034 149.41
## obj.mysem2a 168 14797 15016 153.63 4.2113 4 0.3782### 동등성 제약을 이용하여 세 내생변수의 절편값들이 서로 동등한지를 테스트
mysem3a <- paste(mysem1,
"X1~0; X2~1; X3~1; X4~1; X5~1; X~1
X6~0; X7~1; X8~1; X9~1; X10~1; M1~a234*1
X11~0; X12~1; X13~1; X14~1; X15~1; M2~a234*1
X16~0; X17~1; X18~1; X19~1; X20~1; Y~a234*1",
sep="\n")
obj.mysem3a <- sem(mysem3a, data=f4structure)
anova(obj.mysem3, obj.mysem3a)## Chi Square Difference Test
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## obj.mysem3 164 14801 15034 149.41
## obj.mysem3a 166 14798 15024 150.36 0.94237 2 0.6243### X가 Y에 미치는 직접효과, 간접효과, 총효과의 추정 및 통계적 유의도 검증
mysem4 <- "
X =~ X1+X2+X3+X4+X5
M1 =~ X6+X7+X8+X9+X10
M2 =~ X11+X12+X13+X14+X15
Y =~ X16+X17+X18+X19+X20
X1~~X1; X2~~X2; X3~~X3; X4~~X4; X5~~X5
X6~~X6; X7~~X7; X8~~X8; X9~~X9; X10~~X10
X11~~X11; X12~~X12; X13~~X13; X14~~X14; X15~~X15
X16~~X16; X17~~X17; X18~~X18; X19~~X19; X20~~X20
M1~g1*X; M2~g2*X; Y~g3*X
Y~b1*M1+b2*M2
X~~X
M1~~M1; M2~~M2; Y~~Y; M1~~M2
X1~0; X2~1; X3~1; X4~1; X5~1; X~1
X6~0; X7~1; X8~1; X9~1; X10~1; M1~1
X11~0; X12~1; X13~1; X14~1; X15~1; M2~1
X16~0; X17~1; X18~1; X19~1; X20~1; Y~1
DE:= g3
IE1 := g1*b1
IE2 := g2*b2
IE := IE1+IE2
TE := DE+IE
diff.IE := IE1-IE2"
obj.mysem4 <- sem(mysem4, data=f4structure)
summary(obj.mysem4, standardized=T)## lavaan (0.5-23.1097) converged normally after 116 iterations
##
## Number of observations 254
##
## Estimator ML
## Minimum Function Test Statistic 149.415
## Degrees of freedom 164
## P-value (Chi-square) 0.786
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X =~
## X1 1.000 0.827 0.673
## X2 1.031 0.113 9.099 0.000 0.853 0.666
## X3 1.173 0.114 10.277 0.000 0.969 0.778
## X4 1.054 0.113 9.288 0.000 0.871 0.683
## X5 1.101 0.113 9.780 0.000 0.910 0.728
## M1 =~
## X6 1.000 0.920 0.721
## X7 0.988 0.096 10.300 0.000 0.909 0.701
## X8 1.000 0.091 10.959 0.000 0.919 0.749
## X9 1.056 0.096 11.050 0.000 0.971 0.756
## X10 1.014 0.091 11.174 0.000 0.933 0.765
## M2 =~
## X11 1.000 0.997 0.757
## X12 0.884 0.084 10.569 0.000 0.881 0.720
## X13 0.800 0.078 10.224 0.000 0.798 0.695
## X14 0.800 0.082 9.789 0.000 0.798 0.664
## X15 0.787 0.082 9.630 0.000 0.785 0.653
## Y =~
## X16 1.000 0.947 0.743
## X17 1.034 0.088 11.725 0.000 0.979 0.782
## X18 0.856 0.088 9.736 0.000 0.810 0.648
## X19 0.975 0.084 11.537 0.000 0.923 0.768
## X20 1.027 0.094 10.924 0.000 0.973 0.726
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## M1 ~
## X (g1) 0.549 0.091 6.019 0.000 0.493 0.493
## M2 ~
## X (g2) 0.617 0.099 6.204 0.000 0.511 0.511
## Y ~
## X (g3) -0.000 0.104 -0.002 0.999 -0.000 -0.000
## M1 (b1) 0.461 0.090 5.146 0.000 0.448 0.448
## M2 (b2) 0.171 0.078 2.185 0.029 0.181 0.181
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .M1 ~~
## .M2 0.061 0.057 1.072 0.284 0.089 0.089
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1 0.000 0.000 0.000
## .X2 -0.087 0.463 -0.188 0.851 -0.087 -0.068
## .X3 -0.686 0.466 -1.471 0.141 -0.686 -0.550
## .X4 -0.043 0.464 -0.093 0.926 -0.043 -0.034
## .X5 -0.395 0.460 -0.859 0.390 -0.395 -0.316
## X 4.020 0.077 52.177 0.000 4.862 4.862
## .X6 0.000 0.000 0.000
## .X7 -0.043 0.401 -0.108 0.914 -0.043 -0.033
## .X8 -0.081 0.381 -0.214 0.831 -0.081 -0.066
## .X9 -0.392 0.399 -0.981 0.326 -0.392 -0.305
## .X10 -0.077 0.379 -0.204 0.839 -0.077 -0.063
## .M1 1.890 0.375 5.036 0.000 2.055 2.055
## .X11 0.000 0.000 0.000
## .X12 0.412 0.346 1.192 0.233 0.412 0.337
## .X13 0.744 0.324 2.298 0.022 0.744 0.648
## .X14 0.789 0.338 2.331 0.020 0.789 0.657
## .X15 0.935 0.339 2.762 0.006 0.935 0.778
## .M2 1.569 0.408 3.842 0.000 1.573 1.573
## .X16 0.000 0.000 0.000
## .X17 -0.186 0.354 -0.527 0.598 -0.186 -0.149
## .X18 0.569 0.353 1.614 0.107 0.569 0.455
## .X19 0.079 0.339 0.234 0.815 0.079 0.066
## .X20 -0.053 0.377 -0.140 0.889 -0.053 -0.039
## .Y 1.341 0.395 3.395 0.001 1.416 1.416
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1 0.824 0.086 9.586 0.000 0.824 0.547
## .X2 0.911 0.094 9.651 0.000 0.911 0.556
## .X3 0.615 0.075 8.146 0.000 0.615 0.395
## .X4 0.869 0.092 9.495 0.000 0.869 0.534
## .X5 0.737 0.082 8.973 0.000 0.737 0.471
## .X6 0.783 0.083 9.380 0.000 0.783 0.481
## .X7 0.855 0.089 9.582 0.000 0.855 0.509
## .X8 0.663 0.073 9.032 0.000 0.663 0.439
## .X9 0.709 0.079 8.935 0.000 0.709 0.429
## .X10 0.617 0.070 8.794 0.000 0.617 0.415
## .X11 0.743 0.090 8.300 0.000 0.743 0.428
## .X12 0.723 0.081 8.890 0.000 0.723 0.482
## .X13 0.682 0.074 9.209 0.000 0.682 0.518
## .X14 0.807 0.085 9.531 0.000 0.807 0.559
## .X15 0.829 0.086 9.632 0.000 0.829 0.573
## .X16 0.728 0.080 9.050 0.000 0.728 0.448
## .X17 0.611 0.072 8.431 0.000 0.611 0.389
## .X18 0.909 0.091 9.981 0.000 0.909 0.581
## .X19 0.592 0.068 8.668 0.000 0.592 0.410
## .X20 0.849 0.092 9.264 0.000 0.849 0.473
## X 0.683 0.121 5.659 0.000 1.000 1.000
## .M1 0.640 0.107 6.007 0.000 0.757 0.757
## .M2 0.735 0.119 6.162 0.000 0.739 0.739
## .Y 0.641 0.103 6.213 0.000 0.715 0.715
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DE -0.000 0.104 -0.002 0.999 -0.000 -0.000
## IE1 0.253 0.061 4.141 0.000 0.221 0.221
## IE2 0.106 0.051 2.086 0.037 0.092 0.092
## IE 0.359 0.081 4.401 0.000 0.313 0.313
## TE 0.358 0.088 4.067 0.000 0.313 0.313
## diff.IE 0.147 0.077 1.906 0.057 0.128 0.128### 동등성 제약을 부여한 후 새로운 모수를 생성 및 추정
mysem3b <- "
X = ~l1_*X1+l1_*X2+l1_*X3+l1_*X4+l1_*X5
M1 =~ l2_*X6+l2_*X7+l2_*X8+l2_*X9+l2_*X10
M2 =~ l3_*X11+l3_*X12+l3_*X13+l3_*X14+l3_*X15
Y =~ l4_*X16+l4_*X17+l4_*X18+l4_*X19+l4_*X20
X1~~X1; X2~~X2; X3~~X3; X4~~X4; X5~~X5
X6~~X6; X7~~X7; X8~~X8; X9~~X9; X10~~X10
X11~~X11; X12~~X12; X13~~X13; X14~~X14; X15~~X15
X16~~X16; X17~~X17; X18~~X18; X19~~X19; X20~~X20
M1~g1*X; M2~g2*X; Y~g3*X
Y~b1*M1+b2*M2
X~~X
M1~~M1; M2~~M2; Y~~Y; M1~~M2
X1~0; X2~1; X3~1; X4~1; X5~1; X~1
X6~0; X7~1; X8~1; X9~1; X10~1; M1~1
X11~0; X12~1; X13~1; X14~1; X15~1; M2~1
X16~0; X17~1; X18~1; X19~1; X20~1; Y~1
DE := g3
IE1 := g1*b1
IE2 := g2*b2
IE := IE1+IE2
TE := DE+IE
diff.IE := IE1-IE2"
obj.mysem3b <- sem(mysem3b, data=f4structure)
anova(obj.mysem3, obj.mysem3b)## Chi Square Difference Test
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## obj.mysem3 164 14801 15034 149.41
## obj.mysem3b 180 14785 14962 165.82 16.408 16 0.4248summary(obj.mysem3b, standardized=T)## lavaan (0.5-23.1097) converged normally after 81 iterations
##
## Number of observations 254
##
## Estimator ML
## Minimum Function Test Statistic 165.823
## Degrees of freedom 180
## P-value (Chi-square) 0.768
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X =~
## X1 (l1_) 1.000 0.890 0.705
## X2 (l1_) 1.000 0.890 0.684
## X3 (l1_) 1.000 0.890 0.740
## X4 (l1_) 1.000 0.890 0.693
## X5 (l1_) 1.000 0.890 0.718
## M1 =~
## X6 (l2_) 1.000 0.931 0.726
## X7 (l2_) 1.000 0.931 0.711
## X8 (l2_) 1.000 0.931 0.754
## X9 (l2_) 1.000 0.931 0.738
## X10 (l2_) 1.000 0.931 0.764
## M2 =~
## X11 (l3_) 1.000 0.849 0.682
## X12 (l3_) 1.000 0.849 0.704
## X13 (l3_) 1.000 0.849 0.722
## X14 (l3_) 1.000 0.849 0.691
## X15 (l3_) 1.000 0.849 0.687
## Y =~
## X16 (l4_) 1.000 0.930 0.736
## X17 (l4_) 1.000 0.930 0.759
## X18 (l4_) 1.000 0.930 0.703
## X19 (l4_) 1.000 0.930 0.772
## X20 (l4_) 1.000 0.930 0.706
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## M1 ~
## X (g1) 0.518 0.071 7.286 0.000 0.495 0.495
## M2 ~
## X (g2) 0.479 0.066 7.233 0.000 0.502 0.502
## Y ~
## X (g3) 0.004 0.094 0.037 0.970 0.003 0.003
## M1 (b1) 0.443 0.079 5.626 0.000 0.444 0.444
## M2 (b2) 0.206 0.089 2.324 0.020 0.188 0.188
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .M1 ~~
## .M2 0.055 0.049 1.106 0.269 0.092 0.092
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1 0.000 0.000 0.000
## .X2 0.039 0.082 0.481 0.631 0.039 0.030
## .X3 0.008 0.076 0.104 0.917 0.008 0.007
## .X4 0.173 0.081 2.141 0.032 0.173 0.135
## .X5 0.012 0.078 0.151 0.880 0.012 0.010
## X 4.020 0.079 50.702 0.000 4.515 4.515
## .X6 0.000 0.000 0.000
## .X7 -0.091 0.080 -1.131 0.258 -0.091 -0.069
## .X8 -0.083 0.075 -1.100 0.271 -0.083 -0.067
## .X9 -0.161 0.077 -2.098 0.036 -0.161 -0.128
## .X10 -0.020 0.074 -0.266 0.791 -0.020 -0.016
## .M1 2.012 0.297 6.776 0.000 2.161 2.161
## .X11 0.000 0.000 0.000
## .X12 -0.059 0.079 -0.752 0.452 -0.059 -0.049
## .X13 -0.067 0.077 -0.873 0.382 -0.067 -0.057
## .X14 -0.020 0.080 -0.246 0.805 -0.020 -0.016
## .X15 0.075 0.080 0.932 0.352 0.075 0.061
## .M2 2.123 0.277 7.656 0.000 2.500 2.500
## .X16 0.000 0.000 0.000
## .X17 -0.051 0.073 -0.698 0.485 -0.051 -0.042
## .X18 0.004 0.080 0.049 0.961 0.004 0.003
## .X19 -0.020 0.072 -0.274 0.784 -0.020 -0.016
## .X20 0.055 0.079 0.694 0.488 0.055 0.042
## .Y 1.258 0.351 3.580 0.000 1.353 1.353
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1 0.804 0.084 9.546 0.000 0.804 0.504
## .X2 0.900 0.093 9.733 0.000 0.900 0.532
## .X3 0.657 0.072 9.153 0.000 0.657 0.453
## .X4 0.859 0.089 9.657 0.000 0.859 0.520
## .X5 0.745 0.079 9.408 0.000 0.745 0.485
## .X6 0.778 0.081 9.580 0.000 0.778 0.473
## .X7 0.849 0.087 9.724 0.000 0.849 0.495
## .X8 0.657 0.071 9.265 0.000 0.657 0.431
## .X9 0.726 0.077 9.458 0.000 0.726 0.456
## .X10 0.618 0.068 9.138 0.000 0.618 0.416
## .X11 0.830 0.086 9.633 0.000 0.830 0.535
## .X12 0.735 0.078 9.418 0.000 0.735 0.505
## .X13 0.661 0.072 9.206 0.000 0.661 0.478
## .X14 0.790 0.083 9.548 0.000 0.790 0.523
## .X15 0.807 0.084 9.586 0.000 0.807 0.528
## .X16 0.730 0.078 9.418 0.000 0.730 0.458
## .X17 0.635 0.070 9.136 0.000 0.635 0.424
## .X18 0.884 0.091 9.744 0.000 0.884 0.506
## .X19 0.585 0.065 8.953 0.000 0.585 0.404
## .X20 0.872 0.090 9.723 0.000 0.872 0.502
## X 0.793 0.085 9.377 0.000 1.000 1.000
## .M1 0.654 0.075 8.746 0.000 0.755 0.755
## .M2 0.540 0.065 8.311 0.000 0.748 0.748
## .Y 0.616 0.071 8.692 0.000 0.712 0.712
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DE 0.004 0.094 0.037 0.970 0.003 0.003
## IE1 0.230 0.052 4.441 0.000 0.220 0.220
## IE2 0.099 0.045 2.211 0.027 0.094 0.094
## IE 0.328 0.068 4.849 0.000 0.314 0.314
## TE 0.332 0.075 4.431 0.000 0.318 0.318
## diff.IE 0.131 0.069 1.902 0.057 0.126 0.126### 측정오차가 인과관계 추정에 미치는 영향 <p.169>
pm <- fread("sem_with_reliability.csv")
#### s행렬
cov(pm)## x y
## x 1.0000000 0.1262732
## y 0.1262732 1.0000000#### 관측변수의 고유분산이 전혀 존재하지 않는 경우
merror1 <- "
X=~x
Y=~y
x~~0*x
y~~0*y
Y~X
X~~X
Y~~Y"
obj.morror1<- sem(merror1, data=pm)
summary(obj.morror1, fit.measures=F, standardized=T)## lavaan (0.5-23.1097) converged normally after 14 iterations
##
## Number of observations 250
##
## Estimator ML
## Minimum Function Test Statistic 0.000
## Degrees of freedom 0
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X =~
## x 1.000 0.998 1.000
## Y =~
## y 1.000 0.998 1.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Y ~
## X 0.126 0.063 2.013 0.044 0.126 0.126
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .x 0.000 0.000 0.000
## .y 0.000 0.000 0.000
## X 0.996 0.089 11.180 0.000 1.000 1.000
## .Y 0.980 0.088 11.180 0.000 0.984 0.984### 관측변수의 고유분산이 관측변수 분산의 절반인 경우
merror2 <- "
X=~x
Y=~y
x~~0.5*x
y~~0.5*y
Y~X
X~~X
Y~~Y"
obj.morror2<- sem(merror2, data=pm)
summary(obj.morror2, fit.measures=F, standardized=T)## lavaan (0.5-23.1097) converged normally after 14 iterations
##
## Number of observations 250
##
## Estimator ML
## Minimum Function Test Statistic 0.000
## Degrees of freedom 0
## Minimum Function Value 0.0000000000000
##
## Parameter Estimates:
##
## Information Expected
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X =~
## x 1.000 0.704 0.706
## Y =~
## y 1.000 0.704 0.706
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Y ~
## X 0.254 0.128 1.980 0.048 0.254 0.254
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .x 0.500 0.500 0.502
## .y 0.500 0.500 0.502
## X 0.496 0.089 5.568 0.000 1.000 1.000
## .Y 0.464 0.089 5.208 0.000 0.936 0.936