# How do we correctly select the final number of classes in latent class analysis?

Hope this is not too basic: What Statistical, Mathematical methods do we use to determine number of

classes and class membership in Latent Class Analysis?

• It could help to clarify this: when you say determine number of classes, how is that distinct from class membership? Class membership is a function of the model we just fit. – Weiwen Ng Jun 28 at 23:38
• Well, I would say once we have the number of classes assuming an underlying model that says there are n classes, we would determine membership. I hope I am making sense here but ask otherwise. – MSIS Jun 29 at 0:16
• Determining class membership is inherent to the model. It's not a separate step. This may be just an issue of nomenclature, though. – Weiwen Ng Jun 30 at 13:40

She also mentions two modified likelihood ratio tests, the bootstrapped LRT (BLRT), and an adjusted likelihood ratio test proposed by Lo, Mendell, and Rubin (LMR LRT). You can't use a regular likelihood ratio test for reasons she explains. These modified LR tests compare models with $$K$$ versus $$K-1$$ latent classes; a test p-value <= 0.05 means that you would reject the $$K-1$$ class model in favor of the $$K$$ class model. p > 0.05 means both models explain the data about equally well, and because of Occam's Razor (i.e. prefer parsimonious explanations), you would keep the $$K-1$$ class model.
However, if you're considering the BLRT over the LMR LRT, note Nylund et al's discussion on page 565. With the BLRT, you're simulating data based on your model results and testing $$K$$ vs $$K-1$$ classes (I'm not sure this really qualifies as bootstrapping, but this is what everybody calls it). You're assuming that reality corresponds to the model you are testing, then you simulate data based off that model, and then you obtain the empirical distribution of the difference of -2 * the log likelihood. Now, latent profile analysis typically assumes normally distributed indicators. (Some programs/packages are capable of handling other indicator types, but the same critique would apply). What if that's not reality? What if you assumed normal indicators but they're really counts? What if the empirical distribution of the indicators is really skewed, but isn't well modeled by another distribution either? Then the BLRT results might mislead you. Again, Nylund et al show that when we know that the data generating process corresponds to how we model the indicators in LCA/LPA, the BLRT will outperform the LMR test - but in reality, we do not know the data generating process.