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Hi: I am trying to compare the following two models. Model A is a simple regression where the main endogenous latent variable is perfectly measured by a vocabulary test score. Model B is akin to a MIMIC model where the endougenous latent variable predicts the 10 individual items on the test, presumably extracting the shared variance. What is the best way to show that Model B is better than Model A? The rsquared of the latent variable in Model B is better than Model B, but is there some formal test (the models are nonnested). The likelihood functions appear to be different, since they are very off from each other. Thanks! I can email the code for the models. 


I don't know of any way to compare nonnested models. Rsquare is not a test of model fit. 


Hi: Thanks so much for your response! What is the best way, then, to interpret the rsquare statistics of the latent variables? 


It is the variance explained by the set of predictors. 

deana desa posted on Tuesday, October 29, 2013  8:27 am



Hi, If I wanted to compare CFA modeling using continuous and categorical approaches, are the fit indices (CFI, TLI, RMSEA, SRMR/WRMR) can be directly compared to show which approach has performed better? Do you have examples of literature where I can cite this? 


I don't think you should compare continuous and categorical approaches wrt fit. The variables in your data are either cont's or cat'l. There is also the issue of power differences where categorical variables gives less power to reject a model. You may also want to study the MuthenKaplan (1985) article in BJMSP. 

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