I am an MSc Biostatistics student working on a study of willingness to quit smoking. I derived a 3-class latent variable using Latent Class Analysis (LCA) from FTND and two motivational indicators. Since these variables were used to construct the latent class, I excluded them from my logistic regression to avoid modelling both the component indicators and their derived latent construct simultaneously.

I first fitted a full logistic regression using the remaining conventional predictors, performed AIC-based backward model selection to obtain a parsimonious model, and then added latent class membership to evaluate its incremental explanatory value using changes in AIC and BIC.

Would you consider this a statistically sound and defensible modelling strategy? Are there any methodological references or alternative approaches that you would recommend?