Scaled or robust statistics/fit indices in ordinal CFA

[Stef Meliss]

Hello,

I am very new to lavaan and CFA, so please accept my apologies if the answer to this question is very obvious.

I am estimating the following CFA model: 

model <- "SELFCON_baseline =~ SQA06A + SQA06B + SQA06C + SQA06D + SQA06E + SQA06F"

using in lavaan, treating all items as ordinal.

base <-lavaan::cfa(model, ordered = T, missing = "pairwise", warn = FALSE, data = stud)

When I look at the fit using

summary(base, fit.measures = TRUE)

I get the following output

lavaan 0.6.17 ended normally after 18 iterations Estimator DWLS Optimization method NLMINB Number of model parameters 24 Used Total Number of observations 12744 13530 Number of missing patterns 32 Model Test User Model: Standard Scaled Test Statistic 439.109 1080.548 Degrees of freedom 9 9 P-value (Chi-square) 0.000 0.000 Scaling correction factor 0.406 Shift parameter 0.282 simple second-order correction Model Test Baseline Model: Test statistic 248402.831 137599.841 Degrees of freedom 15 15 P-value 0.000 0.000 Scaling correction factor 1.805 User Model versus Baseline Model: Comparative Fit Index (CFI) 0.998 0.992 Tucker-Lewis Index (TLI) 0.997 0.987 Robust Comparative Fit Index (CFI) 0.972 Robust Tucker-Lewis Index (TLI) 0.954 Root Mean Square Error of Approximation: RMSEA 0.061 0.097 90 Percent confidence interval - lower 0.056 0.092 90 Percent confidence interval - upper 0.066 0.102 P-value H_0: RMSEA <= 0.050 0.000 0.000 P-value H_0: RMSEA >= 0.080 0.000 1.000 Robust RMSEA 0.115 90 Percent confidence interval - lower 0.109 90 Percent confidence interval - upper 0.121 P-value H_0: Robust RMSEA <= 0.050 0.000 P-value H_0: Robust RMSEA >= 0.080 1.000 Standardized Root Mean Square Residual: SRMR 0.027 0.027 Parameter Estimates: Parameterization Delta Standard errors Robust.sem Information Expected Information saturated (h1) model Unstructured Latent Variables: Estimate Std.Err z-value P(>|z|) SELFCON_baseline =~ SQA06A 1.000 SQA06B 0.986 0.007 148.832 0.000 SQA06C 1.110 0.006 184.106 0.000 SQA06D 1.134 0.007 174.134 0.000 SQA06E 0.916 0.007 128.925 0.000 SQA06F 1.063 0.006 174.286 0.000 Thresholds: Estimate Std.Err z-value P(>|z|) SQA06A|t1 -1.300 0.015 -84.836 0.000 SQA06A|t2 -0.059 0.011 -5.283 0.000 SQA06A|t3 1.418 0.016 86.865 0.000 SQA06B|t1 -1.657 0.019 -87.529 0.000 SQA06B|t2 -0.363 0.011 -31.833 0.000 SQA06B|t3 1.229 0.015 83.030 0.000 SQA06C|t1 -1.558 0.018 -87.726 0.000 SQA06C|t2 -0.232 0.011 -20.633 0.000 SQA06C|t3 1.082 0.014 78.009 0.000 SQA06D|t1 -1.393 0.016 -86.394 0.000 SQA06D|t2 0.025 0.011 2.242 0.025 SQA06D|t3 1.300 0.015 84.700 0.000 SQA06E|t1 -1.779 0.021 -86.222 0.000 SQA06E|t2 -0.517 0.012 -44.212 0.000 SQA06E|t3 0.986 0.013 73.864 0.000 SQA06F|t1 -1.589 0.018 -87.764 0.000 SQA06F|t2 -0.237 0.011 -21.103 0.000 SQA06F|t3 1.152 0.014 80.635 0.000 Variances: Estimate Std.Err z-value P(>|z|) .SQA06A 0.377 .SQA06B 0.395 .SQA06C 0.233 .SQA06D 0.199 .SQA06E 0.477 .SQA06F 0.296 SELFCON_baseln 0.623 0.007 95.206 0.000

My understanding is that because all my items are ordered categorical, diagonally weighted least squares (DWLS) estimation in its robust mean and variance-adjusted weighted least squares (WLSMV) variant is used. Following the suggestions by Wirth & Edwards (2007), the test statistics and fit indices have to hence be adjusted. I have further read that the adjustment is possible via scaled tests or robust estimation. My interpretation of the output is that for the fit indices (CFI, TLI and RMSEA), the output includes "raw" values, scaled values and "scaled robust" values. Is this correct? However, what I am unclear about is which one is most appropriate to use to evaluate model fit and report in the paper. Is it sufficient to consider the scaled indices?

Thanks very much in advance, any pointers will be very appreciated.

Kind regards,

Stef

[Serena]

Hi Stef,

My understanding is that when there are robust results, then report robust ones.

Hope this is helpful.

Best,

Serena