understanding robust CFI and TLI statistics when using WLSMV
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anhh...@gmail.com
Sep 17, 2020, 4:41:46 AM9/17/20
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Hello lavaan community,
I recently ran a one factor model using WLSMV as my estimator since the data are ordinal. What's a little puzzling to me is that when I requested for the output using the following command, summary(fit.paras.one.factor.ordered, fit.measures=TRUE), the CFI and TLI had .861 and .848 as values, respectively, in the second column of the output, which I interpret these to mean that they are robust values and that they should be reported rather than the standard ones.
However, when I followed up with fitMeasures(fit.paras.one.factor.ordered) to see a more comprehensive list of fit indices, I saw that these values were labeled under "cfi.scaled" and "tli.scaled" whereas "cfi.robust" and "tli.robust" had "NAs" as values.
I thought that any values labeled under Robust in the second column of output are robust statistics, but what I just encountered challenged my assumption and understanding. Would someone be able to help me understand through this?
I've included the relevant portion of output in case this is helpful. Thank you for your time!
Estimator DWLS
Optimization method NLMINB
Number of free parameters 109
Used Total
Number of observations 180 187
Number of missing patterns 23
Model Test User Model:
Standard Robust
Test Statistic 1165.409 768.990
Degrees of freedom 252 252
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.909
Shift parameter 158.376
simple second-order correction
Model Test Baseline Model:
Test statistic 11346.564 4002.758
Degrees of freedom 276 276
P-value 0.000 0.000
Scaling correction factor 2.971
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.917 0.861
Tucker-Lewis Index (TLI) 0.910 0.848
Robust Comparative Fit Index (CFI) NA
Robust Tucker-Lewis Index (TLI) NA
Root Mean Square Error of Approximation:
RMSEA 0.142 0.107
90 Percent confidence interval - lower 0.134 0.098
90 Percent confidence interval - upper 0.151 0.116
P-value RMSEA <= 0.05 0.000 0.000
Robust RMSEA NA
90 Percent confidence interval - lower NA
90 Percent confidence interval - upper NA
Standardized Root Mean Square Residual:
SRMR 0.195 0.195
> fitMeasures(fit.paras.one.factor.ordered)
npar fmin chisq df
109.000 3.237 1165.409 252.000
pvalue chisq.scaled df.scaled pvalue.scaled
0.000 768.990 252.000 0.000
chisq.scaling.factor baseline.chisq baseline.df baseline.pvalue
1.909 11346.564 276.000 0.000
baseline.chisq.scaled baseline.df.scaled baseline.pvalue.scaled baseline.chisq.scaling.factor
4002.758 276.000 0.000 2.971
cfi tli nnfi rfi
0.917 0.910 0.910 0.888
nfi pnfi ifi rni
0.897 0.819 0.918 0.917
cfi.scaled tli.scaled cfi.robust tli.robust
0.861 0.848 NA NA
nnfi.scaled nnfi.robust rfi.scaled nfi.scaled
0.848 NA 0.790 0.808
ifi.scaled rni.scaled rni.robust rmsea
0.862 0.861 NA 0.142
rmsea.ci.lower rmsea.ci.upper rmsea.pvalue rmsea.scaled
0.134 0.151 0.000 0.107
rmsea.ci.lower.scaled rmsea.ci.upper.scaled rmsea.pvalue.scaled rmsea.robust
0.098 0.116 0.000 NA
rmsea.ci.lower.robust rmsea.ci.upper.robust rmsea.pvalue.robust rmr
NA NA NA 0.188
rmr_nomean srmr srmr_bentler srmr_bentler_nomean
0.195 0.195 0.188 0.195
crmr crmr_nomean srmr_mplus srmr_mplus_nomean
0.195 0.203 NA NA
cn_05 cn_01 gfi agfi
45.547 48.176 0.937 0.910
pgfi mfi
0.654 0.078
Terrence Jorgensen
Sep 17, 2020, 5:29:00 AM9/17/20
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the CFI and TLI had .861 and .848 as values, respectively, in the second column of the output, which I interpret these to mean that they are robust values
They are calculated using the scaled (robust) chi-squared values in that column, but they only use the original formulas for CFI/TLI/RMSEA that were not designed for robust statistics.
The ones explicitly labeled "robust CFI" etc. have modified formulas for robust statistics. This article illuminates differences, and cites their origins.
with fitMeasures(), I saw that these values were labeled under "cfi.scaled" and "tli.scaled" whereas "cfi.robust" and "tli.robust" had "NAs" as values.
The ones labeled scaled simply use the scaled chi-squared in original formulas. The ones explicitly labeled robust use the modified formulas for robust statistics.
Searching for this topic in the group's search bar should have returned several past threads on the same topic.
Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
anhh...@gmail.com
Sep 17, 2020, 1:07:13 PM9/17/20
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Dear Terrence,
Thank you so much for the article, your helpful response, and patience. And I am sorry (and very embarrassed) for not having searched before asking the same question.
Thank you again and have a wonderful day!
Anh
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