RMSEA CI lower

[Mike Murray]

Dear lavaan users,

I have difficulty interpreting this output. I run a very simple CFA with 2 factors and 4 items each. The model seems ok but I got suspicious because the lower bound of the the RMSEA CI is 0.000. The X2 is not significant (which is good) so I should not care about the RMSEA (I think?). However, the RMSEA is based on X2 so I still do not get why the upper bound RMSEA is high. Do you see anything in this output that looks bad for model fit? Loadings are good and I've also checked local fit indices - i.e., resid(fit, "cor")$cov -  and they do not exceed +1/-1. I think that N = 300 could be one of the reasons why the CI range is large, I just would like to be sure that when the lower bound of the RMSEA is 0 it is "ok" regardless of the upper bound of the RMSEA.

Thank you very much.
Mike

lavaan 0.6-9 ended normally after 28 iterations

  Estimator                                         ML

  Optimization method                           NLMINB

  Number of model parameters                        17

                                                      

  Number of observations                           300

                                                      

Model Test User Model:

                                               Standard      Robust

  Test Statistic                                 27.466      24.712

  Degrees of freedom                                 19          19

  P-value (Chi-square)                            0.094       0.170

  Scaling correction factor                                   1.111

       Yuan-Bentler correction (Mplus variant)                     

Model Test Baseline Model:

  Test statistic                              2296.914    1879.787

  Degrees of freedom                                28          28

  P-value                                        0.000       0.000

  Scaling correction factor                                  1.222

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.996       0.997

  Tucker-Lewis Index (TLI)                       0.995       0.995

                                                                  

  Robust Comparative Fit Index (CFI)                         0.997

  Robust Tucker-Lewis Index (TLI)                            0.996

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -2524.546   -2524.546

  Scaling correction factor                                  1.465

      for the MLR correction                                      

  Loglikelihood unrestricted model (H1)      -2510.813   -2510.813

  Scaling correction factor                                  1.278

      for the MLR correction                                      

                                                                  

  Akaike (AIC)                                5083.093    5083.093

  Bayesian (BIC)                              5146.057    5146.057

  Sample-size adjusted Bayesian (BIC)         5092.143    5092.143

Root Mean Square Error of Approximation:

  RMSEA                                                              0.039       0.032

  90 Percent confidence interval - lower         0.000       0.000

  90 Percent confidence interval - upper         0.068       0.062

  P-value RMSEA <= 0.05                                    0.704       0.821

                                                                  

  Robust RMSEA                                                             0.033

  90 Percent confidence interval - lower                     0.000

  90 Percent confidence interval - upper                     0.067

Standardized Root Mean Square Residual:

  SRMR                                           0.016       0.016

[Terrence Jorgensen]

the lower bound of the the RMSEA CI is 0.000. The X2 is not significant

There you go.  You cannot reject the H0 of perfect fit with chi-squared, and you also cannot with RMSEA.

 

so I should not care about the RMSEA (I think?)

RMSEA's CI allows you to test other H0 values than 0.  Kline's SEM textbook has an example where chi-squared was not significant, but the RMSEA's upper bound also did not allow the H0 of poor fit to be rejected.  Subsequent inspection of correlation residuals showed a large discrepancy between an observed and model-implied correlation, which was just not a large enough effect size to be captured by chi-squared with that N.

 

I've also checked local fit indices - i.e., resid(fit, "cor")$cov -  and they do not exceed +1/-1.

 Do you mean +/- 0.1?  That is usually the arbitrary rule of thumb I have seen for classifying an discrepancy as "large enough" to consider of practical importance.

I think that N = 300 could be one of the reasons why the CI range is large

Its range is affected by both N and df

https://doi.org/10.1177/0049124114543236

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[Mike Murray]

Thank you Terrence. 

"Do you mean +/- 0.1?"

Yes 

I've just saw the example provided by Kline. After modifications, he retained the model with an upper bound RMSEA of .070. 
 Thank you again for the explanation.