Can violations of the assumption of local independence among manifest variables be assessed?
One straight-forward approach is to assign individuals to the latent class in which they have the highest posterior probability of membership (these probabilities can be saved in a SAS data file using the OUTPOST option). Then, relationships among all indicators of your latent class variable can be explored separately for each group of individuals (i.e., for each class). More sophisticated (and statistically sound) ways to explore local dependence have been explored. One of these procedures is outlined by Bandeen-Roche, Migloretti, Zeger, and Rathouz (1997), where they multiply impute latent class membership and look for violations of this assumption within each imputation. This procedure requires Bayesian estimation, which will be included in a future release of PROC LCA and PROC LTA. For now, the WinLTA software (available at http://methodology.psu.edu/downloads/winlta) can be used to impute the latent class variable for models with no covariates.
