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Hello, Two ESEM models fit well my data (Chisquare 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 chisquare 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 chisquare 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. 


Nested models must have the same set of observed variables. 


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? 


You can asssess statistically significant differences in model fit only for nested models. For nonnested models, you can look at pvalues or BIC if it is available. 


Hello Linda, Thanks for your answer. 1. When you mention 'p values', do you mean the estimates' p value or the chisquare'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. 


1. The pvalue of the test statistic. 2. No you cannot obtain BIC. It is only for maximum likelihood estimation. 

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