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 Dorothee Durpoix posted on Thursday, April 16, 2009 - 12:37 am
Hello,

Two ESEM models fit well my data (Chi-square p > 0.05, CFI/TLI > 0.96, RMSEA < 0.06, WRMR < 1.0) and I'd like to assess if one fits better than the other.
The second model uses the same variables as model 1 minus one variable. Therefore, I believe I could run the chi-square test difference between the two models, if I was able to specify model 2 from model 1 by constraining to zero (in model 1) the loadings of the variable not present in model 2.
However, factor loadings cannot be constrained in the EFA part of ESEM.

Q. Is it possible to use chi-square difference test in ESEM (WLSMV estimator), when one model has the same number of variables used in the other model minus one? If yes, could you please explain how?

Any input would be greatly appreciated.
 Linda K. Muthen posted on Friday, April 17, 2009 - 4:40 pm
Nested models must have the same set of observed variables.
 Dorothee Durpoix posted on Sunday, April 19, 2009 - 11:10 pm
Hi Linda,

Thanks for your answer. I realized after sending it that because the loading I wanted to constrain to 0 was not a real 0 loading, the models were not nested.
My core question is how can you decide which model fits the best the data in ESEM with ordinal data, when the models are not nested, and with some models involving correlated residuals?
 Linda K. Muthen posted on Monday, April 20, 2009 - 4:06 pm
You can asssess statistically significant differences in model fit only for nested models. For non-nested models, you can look at p-values or BIC if it is available.
 Dorothee Durpoix posted on Monday, April 20, 2009 - 8:29 pm
Hello Linda,

Thanks for your answer.

1. When you mention 'p values', do you mean the estimates' p value or the chi-square's p value?

2. Could you please confirm, or infirm, that in ESEM analysis of ordinal data I cannot obtain BIC (as MLR estimator is not available in this case)?

Thank you.
 Linda K. Muthen posted on Monday, April 20, 2009 - 8:58 pm
1. The p-value of the test statistic.
2. No you cannot obtain BIC. It is only for maximum likelihood estimation.
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