

Latent var. makes model fit Chisqrd ... 

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Suyin Chang posted on Friday, February 14, 2014  6:37 pm



Hi, I am testing a two equation nonrecursive model, where one of the shared explanatory variables is a latent variable measured by 5 indicators. If I run the same model five times, each using one of the indicators instead of the latente variable itself, I get a nonsignifican ChiSqr of the mode fit and good CFI, TLI and RMSEA as well. However, if I use the latent variable itself measured by the 5 indicators, CFI, TLI and RMSEA get a bit worse, but ChiSqr even becomes highly significant. Is there na usual reason for such an odd thing? I would expect better fit as with latent variable we are modeling the measurement error out of the main model distrurbance. Please, any ideas will be very much appreciated. (The model is type=complex with cluster; PS: Modification índices do not indicate any change). 


Modeling the measurement error does not translate into better fit, but rather better slope estimates. Your measurement model implies a structure for the covariance matrix and when that structure does not fit the data well it results in poor overall chisquare fit. First check that the measurement (factor) model fits well, that is, analyze the 5 indicators only. 

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