I am planning to apply categorical cluster analysis for my social data (all variables coded in nominal type beginning from 1 value). As a result of feature selection stage (with LCAvarsel package) also some socio-economic variables (like working sector) eventuated as important. What i wonder is for LCA (Latent Class Analysis) if i should add socio-economic variables such as gender, age, and etc. as manifest variables in the analysis, is there a drawback in terms of the assumption of conditional independence or in terms of covariates. So as a second stage, should i take any other categorical clustering approach like k-medoids, or methods like complete linkage with Eskin measure, or any other method like factor mixture modeling. LCA method seems complex with its assumptions for this kind of data.