Can we calculate BLRT (Parametic Bootstrapped Likelihood Ratio Test) with Stata?

[Eunhye Kang]

Dear researchers,

I am trying to conduct latent profile analysis with Stata and wonder if we can calculate BLRT (Parametric Bootstrapped Likelihood Ratio Test) in Stata 17.

[Frederic Theriault Couture]

Hello Eunhye,
Did you manage to find a way to calculate it on Stata ? I was wondering the same!
Thank you!
Frederic

[Weiwen Ng]

The bootstrap likelihood ratio test in latent class models is for model selection. Say you fit a 5-class model. The BLRT tells you if a 4-class model fits about as well as a 5-class model. It does this by:

1. Taking -2* the log likelihood (LL) from the 4-class and the 5-class models.
2. From the parameter estimates for the 4-class model, generate 100 (or however many) simulated datasets.
3. Fit 4- and 5-class models to each simulated dataset. (I assume they use the parameter estimates from the 4- and 5-class models in the original sample as start values.)
4. From point 3, you have an empirical estimate of the difference in -2LL values. We normally assume that this difference has a chi-square distribution. In the LCA context, we know this difference is not distributed chi-square. Anyway, that empirical distribution is now the basis of your test.
5. I'm not sure that this is the bootstrap as we know it. This seems more like a general simulation. But everyone calls it the BLRT.

This is a complex and computationally intensive process. And no, it's not implemented in Stata, and there doesn't seem to be an easy way to implement it. I believe that Penn State University's LCA plugin implements the BLRT, but it only takes categorical indicators. The R package polca does not implement the BLRT and it's also categorical variables only. The flexmix package does do the BLRT and it takes many types of indicator, but it's harder to use.

So, if not the BLRT, how do we select the correct number of latent classes? I use the BIC, plus I inspect the latent class solutions adjacent to my preferred one and I compare what they're telling me. In my dissertation work, the 5 class model is selected, but the 4- and 5-class solutions tell me about the same overarching thing. I'd compare the 6-class solution also, but it didn't converge.