I am doing a LCA analysis, my sample size is also a little small. According to the sample size adjusted BIC, the four class solution is statistically reasonable, and it also make sense theoretically. However, the BIC support two-class solution which does not make any sense to the theory. In this case, do you think I should use aBIC? If so, is there any literature I can use as reference? Thank you very much
BIC underestimates the number of classes when samples are small. See the following paper which is available on the website for further information:
Nylund, K.L., Asparouhov, T., & Muthén, B. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling. A Monte Carlo simulation study. Structural Equation Modeling, 14, 535-569.