Hey there!
I created a cognitive test with 40 true/false and 10 timed performance items, and stumped on the CFA. I am using lavaan with WLSMV estimation and need help!
I used a bi-factorial model where 30 items load on VZ, 10 on GH and 10 timed items on UT. I have nearly perfect fit scores but many items load negatively or insignificantly on sub-factors. Here is my final model and the results. What can I do to improve the model? Are those loadings OK?
# Bi Factor Model on Gv
model3u <- '
General factor
Gv =~ D1 + D4 + D5 + D6 + D7 + D8 + D9 + D10 +
GT1 + GT2 + GT3 + GT5 + GT6 + GT8 + GT9 +
UP1 + UP2 + UP3 + UP4 + UP5 + UP9 + UP10 +
GH1 + GH2 + GH4 + GH5 + GH6 + GH8 + GH9 +
UT1 + UT2 + UT4 + UT5 + UT6 + UT8 + UT9
#group specific factors
VZ =~ D1 + D4 + D5 + D6 + D7 + D8 + D9 + D10 +
GT1 + GT2 + GT3 + GT5 + GT6 + GT8 + GT9 +
UP1 + UP2 + UP3 + UP4 + UP5 + UP9 + UP10
GH =~ GH1 + GH2 + GH4 + GH5 + GH6 + GH8 + GH9
UT =~ UT1 + UT2 + UT4 + UT5 + UT6 + UT8 + UT9
Orthogonal constraints
Gv ~~ 0VZ
Gv ~~ 0GH
Gv ~~ 0UT
VZ ~~ 0GH
VZ ~~ 0UT
GH ~~ 0UT
'
fit3u <- cfa(model3u, data = hcvpt, estimator = "WLSMV", ordered = ordinal_items)
summary(fit3u, fit.measures = TRUE, standardized=TRUE)
lavaan 0.6-18 ended normally after 360 iterations
Estimator DWLS
Optimization method NLMINB
Number of model parameters 115
Number of observations 251
Model Test User Model:
Standard Scaled
Test Statistic 462.108 568.981
Degrees of freedom 558 558
P-value (Chi-square) 0.999 0.364
Scaling correction factor 1.553
Shift parameter 271.351
simple second-order correction
Model Test Baseline Model:
Test statistic 2422.928 1438.410
Degrees of freedom 630 630
P-value 0.000 0.000
Scaling correction factor 2.218
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000 0.986
Tucker-Lewis Index (TLI) 1.060 0.985
Robust Comparative Fit Index (CFI) NA
Robust Tucker-Lewis Index (TLI) NA
Root Mean Square Error of Approximation:
RMSEA 0.000 0.009
90 Percent confidence interval - lower 0.000 0.000
90 Percent confidence interval - upper 0.000 0.023
P-value H_0: RMSEA <= 0.050 1.000 1.000
P-value H_0: RMSEA >= 0.080 0.000 0.000
Robust RMSEA NA
90 Percent confidence interval - lower NA
90 Percent confidence interval - upper NA
P-value H_0: Robust RMSEA <= 0.050 NA
P-value H_0: Robust RMSEA >= 0.080 NA
Standardized Root Mean Square Residual:
SRMR 0.086 0.086
Parameter Estimates:
Parameterization Delta
Standard errors Robust.sem
Information Expected
Information saturated (h1) model Unstructured
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Gv =~
D1 1.000 0.618 0.618
D4 0.502 0.238 2.103 0.035 0.310 0.310
D5 0.570 0.200 2.854 0.004 0.352 0.352
D6 0.287 0.214 1.345 0.179 0.178 0.178
D7 0.647 0.185 3.491 0.000 0.400 0.400
D8 0.323 0.164 1.967 0.049 0.200 0.200
D9 0.245 0.173 1.414 0.157 0.151 0.151
D10 0.256 0.173 1.480 0.139 0.158 0.158
GT1 0.492 0.190 2.589 0.010 0.304 0.304
GT2 0.185 0.180 1.032 0.302 0.114 0.114
GT3 0.292 0.190 1.537 0.124 0.181 0.181
GT5 0.609 0.191 3.190 0.001 0.376 0.376
GT6 0.348 0.176 1.969 0.049 0.215 0.215
GT8 0.498 0.183 2.724 0.006 0.308 0.308
GT9 0.419 0.201 2.088 0.037 0.259 0.259
UP1 0.329 0.173 1.906 0.057 0.203 0.203
UP2 0.674 0.183 3.689 0.000 0.417 0.417
UP3 0.599 0.200 2.997 0.003 0.370 0.370
UP4 0.431 0.172 2.500 0.012 0.266 0.266
UP5 0.510 0.182 2.798 0.005 0.315 0.315
UP9 0.933 0.231 4.038 0.000 0.576 0.576
UP10 0.611 0.195 3.137 0.002 0.378 0.378
GH1 0.624 0.203 3.077 0.002 0.385 0.385
GH2 0.209 0.172 1.219 0.223 0.129 0.129
GH4 0.272 0.161 1.686 0.092 0.168 0.168
GH5 0.308 0.174 1.768 0.077 0.190 0.190
GH6 0.673 0.221 3.039 0.002 0.416 0.416
GH8 0.342 0.180 1.899 0.058 0.211 0.211
GH9 0.851 0.251 3.395 0.001 0.526 0.526
UT1 0.063 0.015 4.074 0.000 0.039 0.412
UT2 0.037 0.011 3.402 0.001 0.023 0.336
UT4 0.034 0.009 3.629 0.000 0.021 0.363
UT5 0.028 0.008 3.566 0.000 0.017 0.381
UT6 0.039 0.010 3.780 0.000 0.024 0.411
UT8 0.037 0.009 3.994 0.000 0.023 0.462
UT9 0.016 0.008 2.039 0.041 0.010 0.182
VZ =~
D1 1.000 0.281 0.281
D4 1.878 0.968 1.941 0.052 0.527 0.527
D5 1.706 0.829 2.058 0.040 0.479 0.479
D6 1.236 0.736 1.679 0.093 0.347 0.347
D7 1.297 0.689 1.882 0.060 0.364 0.364
D8 1.463 0.781 1.873 0.061 0.411 0.411
D9 1.572 0.823 1.910 0.056 0.441 0.441
D10 1.502 0.804 1.869 0.062 0.422 0.422
GT1 -0.162 0.467 -0.346 0.729 -0.045 -0.045
GT2 0.355 0.480 0.739 0.460 0.100 0.100
GT3 -0.009 0.462 -0.020 0.984 -0.003 -0.003
GT5 -0.232 0.432 -0.536 0.592 -0.065 -0.065
GT6 0.753 0.586 1.285 0.199 0.211 0.211
GT8 0.850 0.678 1.254 0.210 0.239 0.239
GT9 0.215 0.501 0.430 0.667 0.060 0.060
UP1 0.342 0.458 0.747 0.455 0.096 0.096
UP2 0.469 0.426 1.102 0.270 0.132 0.132
UP3 0.532 0.474 1.121 0.262 0.149 0.149
UP4 -0.092 0.449 -0.204 0.839 -0.026 -0.026
UP5 -0.288 0.440 -0.655 0.513 -0.081 -0.081
UP9 0.573 0.434 1.321 0.186 0.161 0.161
UP10 -0.152 0.440 -0.346 0.730 -0.043 -0.043
GH =~
GH1 1.000 0.123 0.123
GH2 -0.287 1.089 -0.264 0.792 -0.035 -0.035
GH4 0.118 1.093 0.108 0.914 0.015 0.015
GH5 -4.896 6.222 -0.787 0.431 -0.603 -0.603
GH6 0.372 1.236 0.301 0.764 0.046 0.046
GH8 -3.374 4.220 -0.800 0.424 -0.416 -0.416
GH9 4.041 5.022 0.805 0.421 0.498 0.498
UT =~
UT1 1.000 0.036 0.384
UT2 1.021 0.165 6.173 0.000 0.037 0.539
UT4 1.017 0.159 6.377 0.000 0.037 0.630
UT5 0.624 0.110 5.653 0.000 0.023 0.507
UT6 0.666 0.150 4.432 0.000 0.024 0.416
UT8 0.660 0.109 6.066 0.000 0.024 0.481
UT9 0.734 0.158 4.649 0.000 0.027 0.479
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
Gv ~~
VZ 0.000 0.000 0.000
GH 0.000 0.000 0.000
UT 0.000 0.000 0.000
VZ ~~
GH 0.000 0.000 0.000
UT 0.000 0.000 0.000
GH ~~
UT 0.000 0.000 0.000
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.UT1 0.140 0.007 19.714 0.000 0.140 1.478
.UT2 0.152 0.004 34.706 0.000 0.152 2.207
.UT4 0.096 0.004 24.509 0.000 0.096 1.634
.UT5 0.069 0.003 23.861 0.000 0.069 1.545
.UT6 0.092 0.004 24.624 0.000 0.092 1.579
.UT8 0.075 0.003 23.116 0.000 0.075 1.508
.UT9 0.089 0.004 24.960 0.000 0.089 1.599
Thresholds:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
D1|t1 -1.240 0.106 -11.705 0.000 -1.240 -1.240
D4|t1 -1.198 0.104 -11.536 0.000 -1.198 -1.198
D5|t1 -0.748 0.088 -8.516 0.000 -0.748 -0.748
D6|t1 -0.933 0.093 -10.017 0.000 -0.933 -0.933
D7|t1 0.015 0.079 0.189 0.850 0.015 0.015
D8|t1 -0.278 0.080 -3.460 0.001 -0.278 -0.278
D9|t1 0.005 0.079 0.063 0.950 0.005 0.005
D10|t1 -0.206 0.080 -2.581 0.010 -0.206 -0.206
GT1|t1 0.299 0.081 3.711 0.000 0.299 0.299
GT2|t1 0.563 0.084 6.698 0.000 0.563 0.563
GT3|t1 0.438 0.082 5.336 0.000 0.438 0.438
GT5|t1 0.362 0.081 4.463 0.000 0.362 0.362
GT6|t1 0.610 0.085 7.188 0.000 0.610 0.610
GT8|t1 1.101 0.099 11.070 0.000 1.101 1.101
GT9|t1 0.888 0.092 9.680 0.000 0.888 0.888
UP1|t1 -0.516 0.083 -6.204 0.000 -0.516 -0.516
UP2|t1 0.065 0.079 0.819 0.413 0.065 0.065
UP3|t1 -0.035 0.079 -0.441 0.659 -0.035 -0.035
UP4|t1 0.145 0.080 1.826 0.068 0.145 0.145
UP5|t1 0.166 0.080 2.078 0.038 0.166 0.166
UP9|t1 0.166 0.080 2.078 0.038 0.166 0.166
UP10|t1 0.247 0.080 3.084 0.002 0.247 0.247
GH1|t1 0.341 0.081 4.212 0.000 0.341 0.341
GH2|t1 -0.085 0.079 -1.071 0.284 -0.085 -0.085
GH4|t1 -0.352 0.081 -4.337 0.000 -0.352 -0.352
GH5|t1 -0.309 0.081 -3.837 0.000 -0.309 -0.309
GH6|t1 -0.671 0.086 -7.796 0.000 -0.671 -0.671
GH8|t1 -0.125 0.079 -1.574 0.115 -0.125 -0.125
GH9|t1 -1.240 0.106 -11.705 0.000 -1.240 -1.240
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.D1 0.540 0.540 0.540
.D4 0.626 0.626 0.626
.D5 0.647 0.647 0.647
.D6 0.848 0.848 0.848
.D7 0.708 0.708 0.708
.D8 0.792 0.792 0.792
.D9 0.783 0.783 0.783
.D10 0.797 0.797 0.797
.GT1 0.906 0.906 0.906
.GT2 0.977 0.977 0.977
.GT3 0.967 0.967 0.967
.GT5 0.854 0.854 0.854
.GT6 0.909 0.909 0.909
.GT8 0.848 0.848 0.848
.GT9 0.929 0.929 0.929
.UP1 0.949 0.949 0.949
.UP2 0.809 0.809 0.809
.UP3 0.841 0.841 0.841
.UP4 0.928 0.928 0.928
.UP5 0.894 0.894 0.894
.UP9 0.642 0.642 0.642
.UP10 0.855 0.855 0.855
.GH1 0.836 0.836 0.836
.GH2 0.982 0.982 0.982
.GH4 0.972 0.972 0.972
.GH5 0.600 0.600 0.600
.GH6 0.825 0.825 0.825
.GH8 0.782 0.782 0.782
.GH9 0.475 0.475 0.475
.UT1 0.006 0.000 17.955 0.000 0.006 0.683
.UT2 0.003 0.000 11.267 0.000 0.003 0.597
.UT4 0.002 0.000 9.526 0.000 0.002 0.472
.UT5 0.001 0.000 12.123 0.000 0.001 0.597
.UT6 0.002 0.000 10.679 0.000 0.002 0.658
.UT8 0.001 0.000 12.588 0.000 0.001 0.555
.UT9 0.002 0.000 10.268 0.000 0.002 0.737
Gv 0.382 0.148 2.571 0.010 1.000 1.000
VZ 0.079 0.074 1.069 0.285 1.000 1.000
GH 0.015 0.036 0.425 0.671 1.000 1.000
UT 0.001 0.000 3.270 0.001 1.000 1.000