A Testing Fit in Latent Class Analysis

WWGD
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Hi All,
I am trying to wrap my brain around Latent Class Analysis (LCA). In the mean time, does anyone know how to test for goodness of fit and whether a given number of classes is somehow optimal? AFAIK, Log-Likelihood should decrease as a measure of improved fit when adding latent classes. Is this correct? Is there any other measure?
 

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