Dicripancy in reported robust fit indices

[ahmad]

Hi all, I was reading Chapter 18, Categorical Confirmatory Factor Analysis, from Kline’s book Principles and Practice of Structural Equation Modeling. In this chapter, he provides an example of how to analyse a CFA with categorical indicators with results and codes. When reporting the model fit indices, he states: “Values of selected robust fit statistics are listed next χ²WLSMV(5) = 17.895, p = .003 RMSEA = .036, 90% CI [.019, .055] CFI = .994, SRMR = .022” However, in the lavaan output provided in the companion website, the robust model fit values are different. Please see below for the output of his analysis. Am I missing something here, or is there an explanation for this difference? lavaan 0.6-19 ended normally after 18 iterations   Estimator DWLS   Optimization method NLMINB   Number of model parameters 20   Number of observations 2004 Model Test User Model:                                                           Standard Scaled   Test Statistic 8.786 17.895   Degrees of freedom 5 5   P-value (Chi-square) 0.118 0.003   Scaling correction factor 0.494   Shift parameter 0.104     simple second-order correction Model Test Baseline Model:   Test statistic 3117.695 2336.488   Degrees of freedom 10 10   P-value 0.000 0.000   Scaling correction factor 1.336 User Model versus Baseline Model:   Comparative Fit Index (CFI) 0.999 0.994   Tucker-Lewis Index (TLI) 0.998 0.989                             Robust Comparative Fit Index (CFI) 0.988   Robust Tucker-Lewis Index (TLI) 0.976 Root Mean Square Error of Approximation:   RMSEA 0.019 0.036   90 Percent confidence interval - lower 0.000 0.019   90 Percent confidence interval - upper 0.040 0.055   P-value H_0: RMSEA <= 0.050 0.995 0.887   P-value H_0: RMSEA >= 0.080 0.000 0.000                             Robust RMSEA 0.061   90 Percent confidence interval - lower 0.032   90 Percent confidence interval - upper 0.093   P-value H_0: Robust RMSEA <= 0.050 0.236   P-value H_0: Robust RMSEA >= 0.080 0.177 Standardized Root Mean Square Residual:   SRMR 0.022 0.022 Best wishes, Ahmad

[Felipe Vieira]

Hi Ahmad,

I did not look at the chapter nor the code mentioned. But the values reported in the book (as you quoted) are in the output you provided (under scaled column). 

Best, 

Felipe. 

On Tue, Nov 4, 2025 at 3:17 PM ahmad <valik...@gmail.com> wrote:

Hi all, I was reading Chapter 18, Categorical Confirmatory Factor Analysis, from Kline’s book Principles and Practice of Structural Equation Modeling. In this chapter, he provides an example of how to analyse a CFA with categorical indicators with results and codes. When reporting the model fit indices, he states: “Values of selected robust fit statistics are listed next χ²WLSMV(5) = 17.895, p = .003 RMSEA = .036, 90% CI [.019, .055] CFI = .994, SRMR = .022” However, in the lavaan output provided in the companion website, the robust model fit values are different. Please see below for the output of his analysis. Am I missing something here, or is there an explanation for this difference? lavaan 0.6-19 ended normally after 18 iterations   Estimator DWLS   Optimization method NLMINB   Number of model parameters 20   Number of observations 2004 Model Test User Model:                                                           Standard Scaled   Test Statistic 8.786 17.895   Degrees of freedom 5 5   P-value (Chi-square) 0.118 0.003   Scaling correction factor 0.494   Shift parameter 0.104     simple second-order correction Model Test Baseline Model:   Test statistic 3117.695 2336.488   Degrees of freedom 10 10   P-value 0.000 0.000   Scaling correction factor 1.336 User Model versus Baseline Model:   Comparative Fit Index (CFI) 0.999 0.994   Tucker-Lewis Index (TLI) 0.998 0.989                             Robust Comparative Fit Index (CFI) 0.988   Robust Tucker-Lewis Index (TLI) 0.976 Root Mean Square Error of Approximation:   RMSEA 0.019 0.036   90 Percent confidence interval - lower 0.000 0.019   90 Percent confidence interval - upper 0.040 0.055   P-value H_0: RMSEA <= 0.050 0.995 0.887   P-value H_0: RMSEA >= 0.080 0.000 0.000                             Robust RMSEA 0.061   90 Percent confidence interval - lower 0.032   90 Percent confidence interval - upper 0.093   P-value H_0: Robust RMSEA <= 0.050 0.236   P-value H_0: Robust RMSEA >= 0.080 0.177 Standardized Root Mean Square Residual:   SRMR 0.022 0.022 Best wishes, Ahmad

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