How to interpret Minimum Function vs. Model Test Staistic in lavaan 0.6-3
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maryam nasseri
Apr 8, 2019, 7:28:51 AM4/8/19
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Hi,
I'm using lavaan 0.6-3 for a CFA/SEM model with the robust MLM estimator; could anyone kindly help me through (as a beginner) how to interpret the two sections that I print below; which is to do with Chi-Square but I don't know which one to report and how to interpret the values. (what are the differences between the Estimator section of chi-square and the Model test baseline model section, and which one to report). Any help will be appreciated, Thanks, Maryam
Estimator ML Robust
Model Fit Test Statistic 4030.704 3398.553
Degrees of freedom 208 208
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.186
for the Satorra-Bentler correction
Model test baseline model:
Minimum Function Test Statistic 8017.055 5398.768
Degrees of freedom 231 231
P-value 0.000 0.000
The full results below just in case you need other values to compare with:
fit<- sem(lex.model, lexdata22.scaled, sample.nobs=210, estimator = "MLM")
summary(fit, ci = TRUE, fit.measures=TRUE, standardized = TRUE)
lavaan 0.6-3 ended normally after 200 iterations
Optimization method NLMINB
Number of free parameters 45
Number of observations 210
Estimator ML Robust
Model Fit Test Statistic 4030.704 3398.553
Degrees of freedom 208 208
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.186
for the Satorra-Bentler correction
Model test baseline model:
Minimum Function Test Statistic 8017.055 5398.768
Degrees of freedom 231 231
P-value 0.000 0.000
User model versus baseline model:
Comparative Fit Index (CFI) 0.509 0.383
Tucker-Lewis Index (TLI) 0.455 0.314
Robust Comparative Fit Index (CFI) 0.507
Robust Tucker-Lewis Index (TLI) 0.452
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -4551.294 -4551.294
Loglikelihood unrestricted model (H1) -2535.942 -2535.942
Number of free parameters 45 45
Akaike (AIC) 9192.589 9192.589
Bayesian (BIC) 9343.208 9343.208
Sample-size adjusted Bayesian (BIC) 9200.622 9200.622
Root Mean Square Error of Approximation:
RMSEA 0.296 0.270
90 Percent Confidence Interval 0.288 0.304 0.263 0.278
P-value RMSEA <= 0.05 0.000 0.000
Robust RMSEA 0.294
90 Percent Confidence Interval 0.286 0.303
Standardized Root Mean Square Residual:
SRMR 0.196 0.196
Parameter Estimates:
Information Expected
Information saturated (h1) model Structured
Standard Errors Robust.sem
Latent Variables:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
group1 =~
mattr 1.000 1.000 1.000 0.997 0.999
mtld 0.958 0.063 15.121 0.000 0.834 1.083 0.955 0.958
vocd 0.770 0.085 9.098 0.000 0.604 0.936 0.768 0.769
ndwerz 0.714 0.045 15.721 0.000 0.625 0.802 0.711 0.713
ndwesz 0.897 0.031 29.041 0.000 0.836 0.957 0.894 0.896
msttr 0.999 0.005 211.618 0.000 0.990 1.009 0.996 0.999
hdd 0.859 0.041 20.820 0.000 0.778 0.940 0.856 0.858
logttr 0.586 0.048 12.210 0.000 0.492 0.680 0.584 0.585
rttr 0.661 0.060 11.039 0.000 0.544 0.778 0.659 0.660
uber 0.710 0.061 11.720 0.000 0.591 0.829 0.707 0.709
maas -0.796 0.040 -19.860 0.000 -0.874 -0.717 -0.793 -0.795
lv 0.272 0.063 4.323 0.000 0.149 0.396 0.271 0.272
nv 0.187 0.065 2.898 0.004 0.061 0.314 0.187 0.187
vv1 0.154 0.073 2.094 0.036 0.010 0.297 0.153 0.154
vv2 0.114 0.069 1.660 0.097 -0.021 0.249 0.114 0.114
cvv1 0.351 0.063 5.591 0.000 0.228 0.474 0.350 0.351
adjv 0.227 0.065 3.487 0.000 0.099 0.354 0.226 0.227
ld -0.009 0.075 -0.125 0.900 -0.157 0.138 -0.009 -0.009
group2 =~
ls1 1.000 1.000 1.000 0.061 0.061
ls2 9.241 10.569 0.874 0.382 -11.474 29.955 0.565 0.567
vs2 15.831 18.684 0.847 0.397 -20.789 52.451 0.969 0.971
cvs1 16.406 19.213 0.854 0.393 -21.251 54.063 1.004 1.006
Covariances:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
group1 ~~
group2 0.017 0.020 0.848 0.397 -0.023 0.057 0.284 0.284
Variances:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
.mattr 0.002 0.001 1.328 0.184 -0.001 0.004 0.002 0.002
.mtld 0.083 0.031 2.663 0.008 0.022 0.143 0.083 0.083
.vocd 0.406 0.085 4.761 0.000 0.239 0.573 0.406 0.408
.ndwerz 0.489 0.042 11.609 0.000 0.407 0.572 0.489 0.492
.ndwesz 0.196 0.019 10.152 0.000 0.158 0.234 0.196 0.197
.msttr 0.003 0.002 1.917 0.055 -0.000 0.006 0.003 0.003
.hdd 0.262 0.027 9.660 0.000 0.209 0.315 0.262 0.263
.logttr 0.654 0.066 9.876 0.000 0.525 0.784 0.654 0.658
.rttr 0.561 0.060 9.354 0.000 0.444 0.679 0.561 0.564
.uber 0.495 0.047 10.482 0.000 0.402 0.587 0.495 0.497
.maas 0.366 0.034 10.734 0.000 0.299 0.433 0.366 0.368
.lv 0.922 0.084 10.909 0.000 0.756 1.087 0.922 0.926
.nv 0.960 0.100 9.587 0.000 0.764 1.157 0.960 0.965
.vv1 0.972 0.086 11.350 0.000 0.804 1.140 0.972 0.976
.vv2 0.982 0.092 10.734 0.000 0.803 1.162 0.982 0.987
.cvv1 0.873 0.085 10.211 0.000 0.705 1.040 0.873 0.877
.adjv 0.944 0.147 6.419 0.000 0.656 1.232 0.944 0.949
.ld 0.995 0.119 8.387 0.000 0.763 1.228 0.995 1.000
.ls1 0.991 0.084 11.769 0.000 0.826 1.157 0.991 0.996
.ls2 0.676 0.065 10.401 0.000 0.548 0.803 0.676 0.679
.vs2 0.057 0.022 2.630 0.009 0.015 0.100 0.057 0.057
.cvs1 -0.012 0.021 -0.591 0.555 -0.053 0.029 -0.012 -0.012
group1 0.993 0.129 7.677 0.000 0.740 1.247 1.000 1.000
group2 0.004 0.009 0.426 0.670 -0.013 0.021 1.000 1.000
Terrence Jorgensen
Apr 8, 2019, 7:43:36 AM4/8/19
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model with the robust MLM estimator... I don't know which one to report
You requested a robust test, so report that one.
how to interpret the values
Compare your p value to a predetermined alpha level. I'm sure you'll notice severe model misfit.
what are the differences between the Estimator section of chi-square and the Model test baseline model section
The top one is for your hypothesized model. The baseline model is the one used for calculating incremental fit indices like CFI and TLI.
Widaman, K. F., & Thompson, J. S. (2003). On specifying the null model for incremental fit indices in structural equation modeling. Psychological Methods, 8(1), 16.
Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
PD
Apr 8, 2019, 8:01:49 AM4/8/19
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You would interpret the robust in this output:
maryam nasseri
Apr 8, 2019, 2:15:37 PM4/8/19
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Thanks a lot Terrence and PD for your prompt responses.
Best
Maryam
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