i have 2 models: Model 1 has the AIC of 1355.477 and BIC of 1403.084. Model 2 has the AIC of 1347.578 and BIC of 1408.733...which model is the best, based on the AIC and BIC? i know we want the smallest value, but since both models have different smaller values, which one do i chose? i had put that: One cannot determine which model to chose, because the AIC is 1347.578 in Model 3 compared to Model 2 that has the BIC of 1403.084.
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.
suggests that BIC works better than AIC. But I would tend to conclude that we can't be sure in this case and you should consider how interpretable your solutions are. If you have categorical outcomes, you can also check TECH10.