Convergence problems in lavaan - measurement invariance categorical Data
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Philipp
Nov 16, 2016, 8:02:29 AM11/16/16
to lavaan
Hey,
I would like to test a modell for measurement invariance. my data is categorical. THe first check (weak invarinace) works well, but in the second check (strict invariance) the model has not converged. Therefore I dont get any fit indices etc. Here you can see syntax and output:
Syntax:
Model_1="Items=~Item_1+Item_2+Item_3+Item_4+Item_5+Item_6+Item_7+Item_8+Item_9"
# #Check weak Invariance
sem.baseline<-sem(model=Model_1,data=data_MI, estimator="WLSMV", std.lv=TRUE, group="Gender",
ordered=c("Item_1","Item_2","Item_3","Item_4","Item_5","Item_6","Item_7","Item_8","Item_9"))
sum=summary(sem.baseline, standardized=TRUE, rsquare=TRUE, fit.measures=TRUE)
sem.loadings<-sem(model=Model_1,data=data_MI, estimator="WLSMV", std.lv=TRUE, group="Gender",
ordered=c("Item_1","Item_2","Item_3","Item_4","Item_5","Item_6","Item_7","Item_8","Item_9"),group.equal=c("loadings"))
sum=summary(sem.loadings, standardized=TRUE, rsquare=TRUE, fit.measures=TRUE)
anova(sem.baseline, sem.loadings)
# #Check strict invariance
sem.baseline_2<-sem(model=Model_1,data=data_MI, estimator="WLSMV", std.lv=TRUE, group="Gender",
ordered=c("Item_1","Item_2","Item_3","Item_4","Item_5","Item_6","Item_7","Item_8","Item_9"))
sum=summary(sem.baseline_2, standardized=TRUE, rsquare=TRUE, fit.measures=TRUE)
sem.load_thres_2<-sem(model=Model_1,data=data_MI, estimator="WLSMV", std.lv=TRUE, group="Gender",
ordered=c("Item_1","Item_2","Item_3","Item_4","Item_5","Item_6","Item_7","Item_8","Item_9"),group.equal=c("loadings","thresholds" ))
sum=summary(sem.load_thres_2, standardized=TRUE, rsquare=TRUE, fit.measures=TRUE)
anova(sem.baseline_2, sem.load_thres_2)
RESULTS
> Model_1="Items=~Item_1+Item_2+Item_3+Item_4+Item_5+Item_6+Item_7+Item_8+Item_9" > #Check weak Invariance > > > sem.baseline<-sem(model=Model_1,data=data_MI, estimator="WLSMV", std.lv=TRUE, group="Gender", + ordered=c("Item_1","Item_2","Item_3","Item_4","Item_5","Item_6","Item_7","Item_8","Item_9")) > sum=summary(sem.baseline, standardized=TRUE, rsquare=TRUE, fit.measures=TRUE) lavaan (0.5-22) converged normally after 42 iterations Number of observations per group 1 315 2 274 Estimator DWLS Robust Minimum Function Test Statistic 45.054 50.907 Degrees of freedom 54 54 P-value (Chi-square) 0.802 0.594 Scaling correction factor 0.951 Shift parameter for each group: 1 1.895 2 1.648 for simple second-order correction (Mplus variant) Chi-square for each group: 1 23.999 27.124 2 21.055 23.783 Model test baseline model: Minimum Function Test Statistic 147.364 140.236 Degrees of freedom 72 72 P-value 0.000 0.000 User model versus baseline model: Comparative Fit Index (CFI) 1.000 1.000 Tucker-Lewis Index (TLI) 1.158 1.060 Robust Comparative Fit Index (CFI) NA Robust Tucker-Lewis Index (TLI) NA Root Mean Square Error of Approximation: RMSEA 0.000 0.000 90 Percent Confidence Interval 0.000 0.025 0.000 0.033 P-value RMSEA <= 0.05 1.000 0.999 Robust RMSEA NA 90 Percent Confidence Interval 0.000 NA Standardized Root Mean Square Residual: SRMR 0.077 0.077 Weighted Root Mean Square Residual: WRMR 1.001 1.001 Parameter Estimates: Information Expected Standard Errors Robust.sem Group 1 [1]: Latent Variables: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Items =~ Item_1 0.262 0.125 2.098 0.036 0.262 0.262 Item_2 0.059 0.116 0.509 0.611 0.059 0.059 Item_3 0.229 0.116 1.966 0.049 0.229 0.229 Item_4 0.152 0.118 1.287 0.198 0.152 0.152 Item_5 0.421 0.109 3.877 0.000 0.421 0.421 Item_6 0.187 0.112 1.667 0.096 0.187 0.187 Item_7 0.410 0.136 3.007 0.003 0.410 0.410 Item_8 -0.351 0.137 -2.568 0.010 -0.351 -0.351 Item_9 0.790 0.171 4.605 0.000 0.790 0.790 Intercepts: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.000 0.000 0.000 .Item_2 0.000 0.000 0.000 .Item_3 0.000 0.000 0.000 .Item_4 0.000 0.000 0.000 .Item_5 0.000 0.000 0.000 .Item_6 0.000 0.000 0.000 .Item_7 0.000 0.000 0.000 .Item_8 0.000 0.000 0.000 .Item_9 0.000 0.000 0.000 Items 0.000 0.000 0.000 Thresholds: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Item_1|t1 -0.853 0.081 -10.540 0.000 -0.853 -0.853 Item_2|t1 0.172 0.071 2.418 0.016 0.172 0.172 Item_3|t1 -0.336 0.072 -4.660 0.000 -0.336 -0.336 Item_4|t1 0.156 0.071 2.193 0.028 0.156 0.156 Item_5|t1 -0.060 0.071 -0.844 0.399 -0.060 -0.060 Item_6|t1 0.328 0.072 4.548 0.000 0.328 0.328 Item_7|t1 -1.054 0.087 -12.106 0.000 -1.054 -1.054 Item_8|t1 1.273 0.096 13.249 0.000 1.273 1.273 Item_9|t1 -1.188 0.092 -12.879 0.000 -1.188 -1.188 Variances: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.932 0.932 0.932 .Item_2 0.997 0.997 0.997 .Item_3 0.948 0.948 0.948 .Item_4 0.977 0.977 0.977 .Item_5 0.823 0.823 0.823 .Item_6 0.965 0.965 0.965 .Item_7 0.832 0.832 0.832 .Item_8 0.877 0.877 0.877 .Item_9 0.377 0.377 0.377 Items 1.000 1.000 1.000 Scales y*: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Item_1 1.000 1.000 1.000 Item_2 1.000 1.000 1.000 Item_3 1.000 1.000 1.000 Item_4 1.000 1.000 1.000 Item_5 1.000 1.000 1.000 Item_6 1.000 1.000 1.000 Item_7 1.000 1.000 1.000 Item_8 1.000 1.000 1.000 Item_9 1.000 1.000 1.000 R-Square: Estimate Item_1 0.068 Item_2 0.003 Item_3 0.052 Item_4 0.023 Item_5 0.177 Item_6 0.035 Item_7 0.168 Item_8 0.123 Item_9 0.623 Group 2 [2]: Latent Variables: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Items =~ Item_1 0.672 0.127 5.285 0.000 0.672 0.672 Item_2 0.352 0.111 3.171 0.002 0.352 0.352 Item_3 0.260 0.108 2.413 0.016 0.260 0.260 Item_4 0.280 0.114 2.446 0.014 0.280 0.280 Item_5 0.124 0.115 1.080 0.280 0.124 0.124 Item_6 0.037 0.127 0.293 0.770 0.037 0.037 Item_7 0.640 0.124 5.149 0.000 0.640 0.640 Item_8 0.100 0.129 0.776 0.438 0.100 0.100 Item_9 0.308 0.116 2.661 0.008 0.308 0.308 Intercepts: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.000 0.000 0.000 .Item_2 0.000 0.000 0.000 .Item_3 0.000 0.000 0.000 .Item_4 0.000 0.000 0.000 .Item_5 0.000 0.000 0.000 .Item_6 0.000 0.000 0.000 .Item_7 0.000 0.000 0.000 .Item_8 0.000 0.000 0.000 .Item_9 0.000 0.000 0.000 Items 0.000 0.000 0.000 Thresholds: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Item_1|t1 -0.580 0.081 -7.188 0.000 -0.580 -0.580 Item_2|t1 -0.297 0.077 -3.854 0.000 -0.297 -0.297 Item_3|t1 0.336 0.077 4.334 0.000 0.336 0.336 Item_4|t1 0.297 0.077 3.854 0.000 0.297 0.297 Item_5|t1 0.355 0.078 4.574 0.000 0.355 0.355 Item_6|t1 0.715 0.083 8.583 0.000 0.715 0.715 Item_7|t1 -0.646 0.082 -7.890 0.000 -0.646 -0.646 Item_8|t1 0.865 0.087 9.932 0.000 0.865 0.865 Item_9|t1 -0.680 0.083 -8.237 0.000 -0.680 -0.680 Variances: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.549 0.549 0.549 .Item_2 0.876 0.876 0.876 .Item_3 0.932 0.932 0.932 .Item_4 0.922 0.922 0.922 .Item_5 0.985 0.985 0.985 .Item_6 0.999 0.999 0.999 .Item_7 0.590 0.590 0.590 .Item_8 0.990 0.990 0.990 .Item_9 0.905 0.905 0.905 Items 1.000 1.000 1.000 Scales y*: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Item_1 1.000 1.000 1.000 Item_2 1.000 1.000 1.000 Item_3 1.000 1.000 1.000 Item_4 1.000 1.000 1.000 Item_5 1.000 1.000 1.000 Item_6 1.000 1.000 1.000 Item_7 1.000 1.000 1.000 Item_8 1.000 1.000 1.000 Item_9 1.000 1.000 1.000 R-Square: Estimate Item_1 0.451 Item_2 0.124 Item_3 0.068 Item_4 0.078 Item_5 0.015 Item_6 0.001 Item_7 0.410 Item_8 0.010 Item_9 0.095 > > sem.loadings<-sem(model=Model_1,data=data_MI, estimator="WLSMV", std.lv=TRUE, group="Gender", + ordered=c("Item_1","Item_2","Item_3","Item_4","Item_5","Item_6","Item_7","Item_8","Item_9"),group.equal=c("loadings")) > sum=summary(sem.loadings, standardized=TRUE, rsquare=TRUE, fit.measures=TRUE) lavaan (0.5-22) converged normally after 32 iterations Number of observations per group 1 315 2 274 Estimator DWLS Robust Minimum Function Test Statistic 65.833 68.692 Degrees of freedom 63 63 P-value (Chi-square) 0.379 0.291 Scaling correction factor 0.989 Shift parameter for each group: 1 1.154 2 1.004 for simple second-order correction (Mplus variant) Chi-square for each group: 1 38.721 40.287 2 27.112 28.404 Model test baseline model: Minimum Function Test Statistic 147.364 140.236 Degrees of freedom 72 72 P-value 0.000 0.000 User model versus baseline model: Comparative Fit Index (CFI) 0.962 0.917 Tucker-Lewis Index (TLI) 0.957 0.905 Robust Comparative Fit Index (CFI) NA Robust Tucker-Lewis Index (TLI) NA Root Mean Square Error of Approximation: RMSEA 0.012 0.018 90 Percent Confidence Interval 0.000 0.038 0.000 0.040 P-value RMSEA <= 0.05 0.997 0.995 Robust RMSEA NA 90 Percent Confidence Interval 0.000 NA Standardized Root Mean Square Residual: SRMR 0.094 0.094 Weighted Root Mean Square Residual: WRMR 1.210 1.210 Parameter Estimates: Information Expected Standard Errors Robust.sem Group 1 [1]: Latent Variables: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Items =~ Item_1 (.p1.) 0.511 0.093 5.479 0.000 0.511 0.511 Item_2 (.p2.) 0.255 0.087 2.948 0.003 0.255 0.255 Item_3 (.p3.) 0.242 0.084 2.884 0.004 0.242 0.242 Item_4 (.p4.) 0.244 0.084 2.891 0.004 0.244 0.244 Item_5 (.p5.) 0.235 0.082 2.849 0.004 0.235 0.235 Item_6 (.p6.) 0.052 0.088 0.589 0.556 0.052 0.052 Item_7 (.p7.) 0.636 0.102 6.245 0.000 0.636 0.636 Item_8 (.p8.) -0.010 0.097 -0.100 0.921 -0.010 -0.010 Item_9 (.p9.) 0.431 0.097 4.461 0.000 0.431 0.431 Intercepts: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.000 0.000 0.000 .Item_2 0.000 0.000 0.000 .Item_3 0.000 0.000 0.000 .Item_4 0.000 0.000 0.000 .Item_5 0.000 0.000 0.000 .Item_6 0.000 0.000 0.000 .Item_7 0.000 0.000 0.000 .Item_8 0.000 0.000 0.000 .Item_9 0.000 0.000 0.000 Items 0.000 0.000 0.000 Thresholds: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Item_1|t1 -0.853 0.081 -10.540 0.000 -0.853 -0.853 Item_2|t1 0.172 0.071 2.418 0.016 0.172 0.172 Item_3|t1 -0.336 0.072 -4.660 0.000 -0.336 -0.336 Item_4|t1 0.156 0.071 2.193 0.028 0.156 0.156 Item_5|t1 -0.060 0.071 -0.844 0.399 -0.060 -0.060 Item_6|t1 0.328 0.072 4.548 0.000 0.328 0.328 Item_7|t1 -1.054 0.087 -12.106 0.000 -1.054 -1.054 Item_8|t1 1.273 0.096 13.249 0.000 1.273 1.273 Item_9|t1 -1.188 0.092 -12.879 0.000 -1.188 -1.188 Variances: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.738 0.738 0.738 .Item_2 0.935 0.935 0.935 .Item_3 0.941 0.941 0.941 .Item_4 0.941 0.941 0.941 .Item_5 0.945 0.945 0.945 .Item_6 0.997 0.997 0.997 .Item_7 0.596 0.596 0.596 .Item_8 1.000 1.000 1.000 .Item_9 0.814 0.814 0.814 Items 1.000 1.000 1.000 Scales y*: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Item_1 1.000 1.000 1.000 Item_2 1.000 1.000 1.000 Item_3 1.000 1.000 1.000 Item_4 1.000 1.000 1.000 Item_5 1.000 1.000 1.000 Item_6 1.000 1.000 1.000 Item_7 1.000 1.000 1.000 Item_8 1.000 1.000 1.000 Item_9 1.000 1.000 1.000 R-Square: Estimate Item_1 0.262 Item_2 0.065 Item_3 0.059 Item_4 0.059 Item_5 0.055 Item_6 0.003 Item_7 0.404 Item_8 0.000 Item_9 0.186 Group 2 [2]: Latent Variables: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Items =~ Item_1 (.p1.) 0.511 0.093 5.479 0.000 0.511 0.511 Item_2 (.p2.) 0.255 0.087 2.948 0.003 0.255 0.255 Item_3 (.p3.) 0.242 0.084 2.884 0.004 0.242 0.242 Item_4 (.p4.) 0.244 0.084 2.891 0.004 0.244 0.244 Item_5 (.p5.) 0.235 0.082 2.849 0.004 0.235 0.235 Item_6 (.p6.) 0.052 0.088 0.589 0.556 0.052 0.052 Item_7 (.p7.) 0.636 0.102 6.245 0.000 0.636 0.636 Item_8 (.p8.) -0.010 0.097 -0.100 0.921 -0.010 -0.010 Item_9 (.p9.) 0.431 0.097 4.461 0.000 0.431 0.431 Intercepts: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.000 0.000 0.000 .Item_2 0.000 0.000 0.000 .Item_3 0.000 0.000 0.000 .Item_4 0.000 0.000 0.000 .Item_5 0.000 0.000 0.000 .Item_6 0.000 0.000 0.000 .Item_7 0.000 0.000 0.000 .Item_8 0.000 0.000 0.000 .Item_9 0.000 0.000 0.000 Items 0.000 0.000 0.000 Thresholds: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Item_1|t1 -0.580 0.081 -7.188 0.000 -0.580 -0.580 Item_2|t1 -0.297 0.077 -3.854 0.000 -0.297 -0.297 Item_3|t1 0.336 0.077 4.334 0.000 0.336 0.336 Item_4|t1 0.297 0.077 3.854 0.000 0.297 0.297 Item_5|t1 0.355 0.078 4.574 0.000 0.355 0.355 Item_6|t1 0.715 0.083 8.583 0.000 0.715 0.715 Item_7|t1 -0.646 0.082 -7.890 0.000 -0.646 -0.646 Item_8|t1 0.865 0.087 9.932 0.000 0.865 0.865 Item_9|t1 -0.680 0.083 -8.237 0.000 -0.680 -0.680 Variances: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.738 0.738 0.738 .Item_2 0.935 0.935 0.935 .Item_3 0.941 0.941 0.941 .Item_4 0.941 0.941 0.941 .Item_5 0.945 0.945 0.945 .Item_6 0.997 0.997 0.997 .Item_7 0.596 0.596 0.596 .Item_8 1.000 1.000 1.000 .Item_9 0.814 0.814 0.814 Items 1.000 1.000 1.000 Scales y*: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Item_1 1.000 1.000 1.000 Item_2 1.000 1.000 1.000 Item_3 1.000 1.000 1.000 Item_4 1.000 1.000 1.000 Item_5 1.000 1.000 1.000 Item_6 1.000 1.000 1.000 Item_7 1.000 1.000 1.000 Item_8 1.000 1.000 1.000 Item_9 1.000 1.000 1.000 R-Square: Estimate Item_1 0.262 Item_2 0.065 Item_3 0.059 Item_4 0.059 Item_5 0.055 Item_6 0.003 Item_7 0.404 Item_8 0.000 Item_9 0.186 > > > anova(sem.baseline, sem.loadings) Scaled Chi Square Difference Test (method = "satorra.2000") Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq) sem.baseline 54 45.054 sem.loadings 63 65.833 13.89 7.8009 0.07762 . --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > # #Check strict invariance > > > sem.baseline_2<-sem(model=Model_1,data=data_MI, estimator="WLSMV", std.lv=TRUE, group="Gender", + ordered=c("Item_1","Item_2","Item_3","Item_4","Item_5","Item_6","Item_7","Item_8","Item_9")) > sum=summary(sem.baseline_2, standardized=TRUE, rsquare=TRUE, fit.measures=TRUE) lavaan (0.5-22) converged normally after 42 iterations Number of observations per group 1 315 2 274 Estimator DWLS Robust Minimum Function Test Statistic 45.054 50.907 Degrees of freedom 54 54 P-value (Chi-square) 0.802 0.594 Scaling correction factor 0.951 Shift parameter for each group: 1 1.895 2 1.648 for simple second-order correction (Mplus variant) Chi-square for each group: 1 23.999 27.124 2 21.055 23.783 Model test baseline model: Minimum Function Test Statistic 147.364 140.236 Degrees of freedom 72 72 P-value 0.000 0.000 User model versus baseline model: Comparative Fit Index (CFI) 1.000 1.000 Tucker-Lewis Index (TLI) 1.158 1.060 Robust Comparative Fit Index (CFI) NA Robust Tucker-Lewis Index (TLI) NA Root Mean Square Error of Approximation: RMSEA 0.000 0.000 90 Percent Confidence Interval 0.000 0.025 0.000 0.033 P-value RMSEA <= 0.05 1.000 0.999 Robust RMSEA NA 90 Percent Confidence Interval 0.000 NA Standardized Root Mean Square Residual: SRMR 0.077 0.077 Weighted Root Mean Square Residual: WRMR 1.001 1.001 Parameter Estimates: Information Expected Standard Errors Robust.sem Group 1 [1]: Latent Variables: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Items =~ Item_1 0.262 0.125 2.098 0.036 0.262 0.262 Item_2 0.059 0.116 0.509 0.611 0.059 0.059 Item_3 0.229 0.116 1.966 0.049 0.229 0.229 Item_4 0.152 0.118 1.287 0.198 0.152 0.152 Item_5 0.421 0.109 3.877 0.000 0.421 0.421 Item_6 0.187 0.112 1.667 0.096 0.187 0.187 Item_7 0.410 0.136 3.007 0.003 0.410 0.410 Item_8 -0.351 0.137 -2.568 0.010 -0.351 -0.351 Item_9 0.790 0.171 4.605 0.000 0.790 0.790 Intercepts: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.000 0.000 0.000 .Item_2 0.000 0.000 0.000 .Item_3 0.000 0.000 0.000 .Item_4 0.000 0.000 0.000 .Item_5 0.000 0.000 0.000 .Item_6 0.000 0.000 0.000 .Item_7 0.000 0.000 0.000 .Item_8 0.000 0.000 0.000 .Item_9 0.000 0.000 0.000 Items 0.000 0.000 0.000 Thresholds: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Item_1|t1 -0.853 0.081 -10.540 0.000 -0.853 -0.853 Item_2|t1 0.172 0.071 2.418 0.016 0.172 0.172 Item_3|t1 -0.336 0.072 -4.660 0.000 -0.336 -0.336 Item_4|t1 0.156 0.071 2.193 0.028 0.156 0.156 Item_5|t1 -0.060 0.071 -0.844 0.399 -0.060 -0.060 Item_6|t1 0.328 0.072 4.548 0.000 0.328 0.328 Item_7|t1 -1.054 0.087 -12.106 0.000 -1.054 -1.054 Item_8|t1 1.273 0.096 13.249 0.000 1.273 1.273 Item_9|t1 -1.188 0.092 -12.879 0.000 -1.188 -1.188 Variances: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.932 0.932 0.932 .Item_2 0.997 0.997 0.997 .Item_3 0.948 0.948 0.948 .Item_4 0.977 0.977 0.977 .Item_5 0.823 0.823 0.823 .Item_6 0.965 0.965 0.965 .Item_7 0.832 0.832 0.832 .Item_8 0.877 0.877 0.877 .Item_9 0.377 0.377 0.377 Items 1.000 1.000 1.000 Scales y*: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Item_1 1.000 1.000 1.000 Item_2 1.000 1.000 1.000 Item_3 1.000 1.000 1.000 Item_4 1.000 1.000 1.000 Item_5 1.000 1.000 1.000 Item_6 1.000 1.000 1.000 Item_7 1.000 1.000 1.000 Item_8 1.000 1.000 1.000 Item_9 1.000 1.000 1.000 R-Square: Estimate Item_1 0.068 Item_2 0.003 Item_3 0.052 Item_4 0.023 Item_5 0.177 Item_6 0.035 Item_7 0.168 Item_8 0.123 Item_9 0.623 Group 2 [2]: Latent Variables: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Items =~ Item_1 0.672 0.127 5.285 0.000 0.672 0.672 Item_2 0.352 0.111 3.171 0.002 0.352 0.352 Item_3 0.260 0.108 2.413 0.016 0.260 0.260 Item_4 0.280 0.114 2.446 0.014 0.280 0.280 Item_5 0.124 0.115 1.080 0.280 0.124 0.124 Item_6 0.037 0.127 0.293 0.770 0.037 0.037 Item_7 0.640 0.124 5.149 0.000 0.640 0.640 Item_8 0.100 0.129 0.776 0.438 0.100 0.100 Item_9 0.308 0.116 2.661 0.008 0.308 0.308 Intercepts: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.000 0.000 0.000 .Item_2 0.000 0.000 0.000 .Item_3 0.000 0.000 0.000 .Item_4 0.000 0.000 0.000 .Item_5 0.000 0.000 0.000 .Item_6 0.000 0.000 0.000 .Item_7 0.000 0.000 0.000 .Item_8 0.000 0.000 0.000 .Item_9 0.000 0.000 0.000 Items 0.000 0.000 0.000 Thresholds: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Item_1|t1 -0.580 0.081 -7.188 0.000 -0.580 -0.580 Item_2|t1 -0.297 0.077 -3.854 0.000 -0.297 -0.297 Item_3|t1 0.336 0.077 4.334 0.000 0.336 0.336 Item_4|t1 0.297 0.077 3.854 0.000 0.297 0.297 Item_5|t1 0.355 0.078 4.574 0.000 0.355 0.355 Item_6|t1 0.715 0.083 8.583 0.000 0.715 0.715 Item_7|t1 -0.646 0.082 -7.890 0.000 -0.646 -0.646 Item_8|t1 0.865 0.087 9.932 0.000 0.865 0.865 Item_9|t1 -0.680 0.083 -8.237 0.000 -0.680 -0.680 Variances: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.549 0.549 0.549 .Item_2 0.876 0.876 0.876 .Item_3 0.932 0.932 0.932 .Item_4 0.922 0.922 0.922 .Item_5 0.985 0.985 0.985 .Item_6 0.999 0.999 0.999 .Item_7 0.590 0.590 0.590 .Item_8 0.990 0.990 0.990 .Item_9 0.905 0.905 0.905 Items 1.000 1.000 1.000 Scales y*: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Item_1 1.000 1.000 1.000 Item_2 1.000 1.000 1.000 Item_3 1.000 1.000 1.000 Item_4 1.000 1.000 1.000 Item_5 1.000 1.000 1.000 Item_6 1.000 1.000 1.000 Item_7 1.000 1.000 1.000 Item_8 1.000 1.000 1.000 Item_9 1.000 1.000 1.000 R-Square: Estimate Item_1 0.451 Item_2 0.124 Item_3 0.068 Item_4 0.078 Item_5 0.015 Item_6 0.001 Item_7 0.410 Item_8 0.010 Item_9 0.095 > > sem.load_thres_2<-sem(model=Model_1,data=data_MI, estimator="WLSMV", std.lv=TRUE, group="Gender", + ordered=c("Item_1","Item_2","Item_3","Item_4","Item_5","Item_6","Item_7","Item_8","Item_9"),group.equal=c("loadings","thresholds" )) Warning message: In lavaan::lavaan(model = Model_1, data = data_MI, std.lv = TRUE, : lavaan WARNING: model has NOT converged! > sum=summary(sem.load_thres_2, standardized=TRUE, rsquare=TRUE, fit.measures=TRUE) ** WARNING ** lavaan (0.5-22) did NOT converge after 644 iterations ** WARNING ** Estimates below are most likely unreliable Number of observations per group 1 315 2 274 Estimator DWLS Minimum Function Test Statistic NA Degrees of freedom NA P-value NA Chi-square for each group: 1 NA 2 NA Parameter Estimates: Information Expected Standard Errors Robust.sem Group 1 [1]: Latent Variables: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Items =~ Item_1 (.p1.) 0.302 NA 0.302 0.302 Item_2 (.p2.) 0.000 NA 0.000 0.000 Item_3 (.p3.) 0.321 NA 0.321 0.321 Item_4 (.p4.) 0.000 NA 0.000 0.000 Item_5 (.p5.) 0.534 NA 0.534 0.534 Item_6 (.p6.) 0.040 NA 0.040 0.040 Item_7 (.p7.) 0.366 NA 0.366 0.366 Item_8 (.p8.) -0.053 NA -0.053 -0.053 Item_9 (.p9.) 0.335 NA 0.335 0.335 Intercepts: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.000 0.000 0.000 .Item_2 0.000 0.000 0.000 .Item_3 0.000 0.000 0.000 .Item_4 0.000 0.000 0.000 .Item_5 0.000 0.000 0.000 .Item_6 0.000 0.000 0.000 .Item_7 0.000 0.000 0.000 .Item_8 0.000 0.000 0.000 .Item_9 0.000 0.000 0.000 Items 0.000 0.000 0.000 Thresholds: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Itm_1|1 (.10.) -0.858 NA -0.858 -0.858 Itm_2|1 (.11.) -0.000 NA -0.000 -0.000 Itm_3|1 (.12.) -0.304 NA -0.304 -0.304 Itm_4|1 (.13.) -0.000 NA -0.000 -0.000 Itm_5|1 (.14.) -0.054 NA -0.054 -0.054 Itm_6|1 (.15.) 0.333 NA 0.333 0.333 Itm_7|1 (.16.) -1.072 NA -1.072 -1.072 Itm_8|1 (.17.) 1.277 NA 1.277 1.277 Itm_9|1 (.18.) -1.227 NA -1.227 -1.227 Variances: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.909 0.909 0.909 .Item_2 1.000 1.000 1.000 .Item_3 0.897 0.897 0.897 .Item_4 1.000 1.000 1.000 .Item_5 0.715 0.715 0.715 .Item_6 0.998 0.998 0.998 .Item_7 0.866 0.866 0.866 .Item_8 0.997 0.997 0.997 .Item_9 0.888 0.888 0.888 Items 1.000 1.000 1.000 Scales y*: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Item_1 1.000 1.000 1.000 Item_2 1.000 1.000 1.000 Item_3 1.000 1.000 1.000 Item_4 1.000 1.000 1.000 Item_5 1.000 1.000 1.000 Item_6 1.000 1.000 1.000 Item_7 1.000 1.000 1.000 Item_8 1.000 1.000 1.000 Item_9 1.000 1.000 1.000 R-Square: Estimate Item_1 0.091 Item_2 0.000 Item_3 0.103 Item_4 0.000 Item_5 0.285 Item_6 0.002 Item_7 0.134 Item_8 0.003 Item_9 0.112 Group 2 [2]: Latent Variables: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Items =~ Item_1 (.p1.) 0.302 NA 0.302 0.639 Item_2 (.p2.) 0.000 NA 0.000 0.342 Item_3 (.p3.) 0.321 NA 0.321 0.298 Item_4 (.p4.) 0.000 NA 0.000 0.283 Item_5 (.p5.) 0.534 NA 0.534 0.183 Item_6 (.p6.) 0.040 NA 0.040 0.070 Item_7 (.p7.) 0.366 NA 0.366 0.641 Item_8 (.p8.) -0.053 NA -0.053 -0.039 Item_9 (.p9.) 0.335 NA 0.335 0.377 Intercepts: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.000 0.000 0.000 .Item_2 0.000 0.000 0.000 .Item_3 0.000 0.000 0.000 .Item_4 0.000 0.000 0.000 .Item_5 0.000 0.000 0.000 .Item_6 0.000 0.000 0.000 .Item_7 0.000 0.000 0.000 .Item_8 0.000 0.000 0.000 .Item_9 0.000 0.000 0.000 Items -1.933 NA -1.933 -1.933 Thresholds: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Itm_1|1 (.10.) -0.858 NA -0.858 -1.812 Itm_2|1 (.11.) -0.000 NA -0.000 -0.958 Itm_3|1 (.12.) -0.304 NA -0.304 -0.282 Itm_4|1 (.13.) -0.000 NA -0.000 -0.249 Itm_5|1 (.14.) -0.054 NA -0.054 -0.018 Itm_6|1 (.15.) 0.333 NA 0.333 0.576 Itm_7|1 (.16.) -1.072 NA -1.072 -1.875 Itm_8|1 (.17.) 1.277 NA 1.277 0.936 Itm_9|1 (.18.) -1.227 NA -1.227 -1.381 Variances: Estimate Std.Err z-value P(>|z|) Std.lv Std.all .Item_1 0.133 0.133 0.592 .Item_2 0.000 0.000 0.883 .Item_3 1.057 1.057 0.911 .Item_4 0.000 0.000 0.920 .Item_5 8.283 8.283 0.967 .Item_6 0.332 0.332 0.995 .Item_7 0.193 0.193 0.589 .Item_8 1.857 1.857 0.998 .Item_9 0.676 0.676 0.858 Items 1.000 1.000 1.000 Scales y*: Estimate Std.Err z-value P(>|z|) Std.lv Std.all Item_1 2.112 NA 2.112 1.000 Item_2 493202.494 NA 493202.494 1.000 Item_3 0.928 NA 0.928 1.000 Item_4 31677.581 NA 31677.581 1.000 Item_5 0.342 NA 0.342 1.000 Item_6 1.731 NA 1.731 1.000 Item_7 1.749 NA 1.749 1.000 Item_8 0.733 NA 0.733 1.000 Item_9 1.126 NA 1.126 1.000 R-Square: Estimate Item_1 0.408 Item_2 0.117 Item_3 0.089 Item_4 0.080 Item_5 0.033 Item_6 0.005 Item_7 0.411 Item_8 0.002 Item_9 0.142 Warning message: In .local(object, ...) : lavaan WARNING: fit measures not available if model did not converge > > > > anova(sem.baseline_2, sem.load_thres_2) Chi Square Difference Test Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq) sem.baseline_2 54 45.054 sem.load_thres_2
All your comments, hints and suggestions are welcome. Thank you so much!!
Best,
Philipp
Terrence Jorgensen
Nov 17, 2016, 7:38:32 AM11/17/16
to lavaan
my data are categorical
Specifically, they are binary. This has practical implications, namely that you cannot have separate tests of weak and strong invariance because any differences in factor loadings can be re-expressed as differences in thresholds when you constrain loadings. Check out the information on this web page, including a link to a great article on the subject, as well as many lavaan examples.
THe first check (weak invarinace) works well
You cannot draw that conclusion when you have binary indicators. You have to constrain loadings and thresholds in a single step and compare that model to the configural model (which is what you did next).
but in the second check (strict invariance) the model has not converged.
You tested strong invariance (constraining loadings and thresholds). Strict invariance is when the residual variances are also constrained to equality across groups. That constraint is not required for comparing common-factor parameters across groups, so you do not need to test strict invariance.
Actually, you need to refine your tests anyway. When you constrain loadings and thresholds across groups, you need to free the factor variance and mean in all but the first group. Otherwise, you are simultaneously testing two hypotheses instead of one: is there invariance AND are the distributions of common factors identical across groups. You need to test the first hypothesis (invariance) separately. The easiest way to do this correctly would be to set std.lv = FALSE. Even easier, you could use the measurementInvarianceCat() function in the semTools package, which is written by the person who wrote the web page I linked to above, so it implements the steps automatically and correctly.
The overly restrictive strong-invariance model may be the reason for nonconvergence, but I think it is more likely that your configural model is incorrect. Look at the configural model results. In group 1, your factor does not appear related to items 2 or 4, whereas in group 2, your factor does not appear to be related to items 5, 6, or 8. It looks like you are measuring different things in the two groups, or at least that the indicators do not all function equivalently. So the strong invariance model is a gross model misspecification, in which case you should expect convergence problems (how can you converge on a single estimate across groups of a parameter that may not exist in all groups?).
Terrence D. Jorgensen
Postdoctoral Researcher, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
UvA web page: http://www.uva.nl/profile/t.d.jorgensen
Philipp Schäpers
Nov 17, 2016, 12:24:36 PM11/17/16
to lav...@googlegroups.com
Dear Terrence,
thank you so much!!! Your response was very very helpful! On the basis of your comments and the recommendations of Millsap and Yun-Tein's (2004) I refined my baseline/configural model. But I did not get even a fitted model for the configurale invariance, holy cow...are there so huge diffrences between groups... I mean configural invariance... or is it a really strict approach? Or is there a mystake in my syntax? Here you can see syntax and output:library(foreign)
library(lavaan)
data_MI<-read.spss("Messinvarianz.sav", use.value.labels = FALSE, to.data.frame = TRUE)
Modell<- "Items=~c(1,1)*Item_1+Item_2+Item_3+Item_4+Item_5+
Item_6+Item_7+Item_8+Item_9
Item_1 | c(t11, t11)*t1
Item_2 | c(t21, t21)*t1
Item_3 | c(t31, t31)*t1
Item_4 | c(t41, t41)*t1
Item_5 | c(t51, t51)*t1
Item_6 | c(t61, t61)*t1
Item_7 | c(t71, t71)*t1
Item_8 | c(t81, t81)*t1
Item_9 | c(t91, t91)*t1
Items ~~ NA*Items
Item_1 ~~ c(1, 1)*Item_1
Item_2 ~~ c(1, NA)*Item_2
Item_3 ~~ c(1, NA)*Item_3
Item_4 ~~ c(1, NA)*Item_4
Item_5 ~~ c(1, NA)*Item_5
Item_6 ~~ c(1, NA)*Item_6
Item_7 ~~ c(1, NA)*Item_7
Item_8 ~~ c(1, NA)*Item_8
Item_9 ~~ c(1, NA)*Item_9
Items ~ c(0, NA)*1"
sem.baseline <- sem(Modell,data=data_MI, group ="Gender", parameterization="theta", estimator="wlsmv",
ordered=c("Item_1","Item_2","Item_3","Item_4","Item_5","Item_6","Item_7","Item_8","Item_9"))
sum=summary(sem.baseline, standardized=TRUE, rsquare=TRUE, fit.measures=TRUE)
Warning message: In lavaan::lavaan(model = Modell, data = data_MI, parameterization = "theta", :
lavaan WARNING: model has NOT converged!
All your comments, hints and suggestions are welcome. Thank you so much!!
Best,
Philipp
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Terrence Jorgensen
Nov 18, 2016, 5:33:42 AM11/18/16
to lavaan
The model syntax you posted constrains thresholds across groups, so it is not the configural model. The configural model has free loadings and thresholds across groups. The scalar equivalence / strong invariance model has equality-constrained loadings and thresholds across groups. Then you compare the configural and scalar/strong models. The cfa() and sem() functions will automatically free the residual variances in the subsequent group when the loadings are constrained, so you don't have to add that to your syntax. Likewise, using the default std.lv = FALSE will automatically fix the first loading to 1, so you don't need that in your syntax. Actually, your syntax can quite simply be the factor loadings.
Modell <- 'Factor =~ Item_1 + Item_2 + Item_3 + Item_4 + Item_5 +Item_6 + Item_7 + Item_8 + Item_9'fit.configural <- cfa(Modell, data = data_MI, group = "Gender",
parameterization = "theta", estimator = "wlsmv",
ordered = paste0("Item_", 1:9))
fit.scalar <- cfa(Modell, data = data_MI, group = "Gender",
parameterization = "theta", estimator = "wlsmv",
ordered = paste0("Item_", 1:9),
group.equal = c("loadings","thresholds"))
anova(fit.configural, fit.scalar)
The reason for non-convergence is probably that you tried to freely estimate residual variances in Group 2 without constraining factor loadings to equality.
Philipp
Nov 21, 2016, 11:40:38 AM11/21/16
to lavaan
Hi,
thanks a lot for your response. Now, I am little bit confused. On your recommended website Sunthud Pornprasertmanit posted:
So have Thresholds to be equally for configural Invariance or not? In your syntax thresholds are not equally in the configural model....
thanks a lot for your response. Now, I am little bit confused. On your recommended website Sunthud Pornprasertmanit posted:
Dichotomous Items
For dichotomous items, the following specification is needed to set the scale identification:
- For each factor, the factor loading of one marker variable is fixed (usually as 1). Other factor loadings are freely estimated across groups.
- All thresholds are equally constrained across groups.
- The unique variances of the first group are fixed as 1. The unique variances of other groups are freely estimated except that the unique variances of the marker variables are fixed as 1.
- The factor covariance matrices (variances and covariances) of all groups are free.
- The factor means of the first group are fixed as 0. The factor means of the other groups are freely estimated.
From here, we have configural invariance model. The weak invariance can be estiblished by constraining all free loadings to be equal across groups. The strong invariance cannot be established because the thresholds in the configural invariance model are all equally constrained to set the scale. The strict invariance can be established by fixing all unique variances of all groups to be 1.
So have Thresholds to be equally for configural Invariance or not? In your syntax thresholds are not equally in the configural model....
Terrence Jorgensen
Nov 22, 2016, 4:05:19 AM11/22/16
to lavaan
So have Thresholds to be equally for configural Invariance or not?
The answer is in the article linked on the same web page. I hadn't read it over in a while, so I forgot about starting with equality constrained thresholds for binary items in the configural model.
Philipp
Nov 22, 2016, 10:05:34 AM11/22/16
to lavaan
Terrence! Thank you so much! You helped me a lot!!
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