I have a survey data with strata, clusters and weights. I have run SEM, accounting for survey design, with three latent factors as independent variables and Y as a dependent variable. Now, in a separate regression, I would like to see what other variables (say, demographics) affect one of the factor's scores. In this regression, demographics would be my independent variables and one of the latent factor would be the dependent variable. Should I account for the survey design again in this regression, given that the factor scores were generated in the first place using the survey design options? I did not combine all these into one SEM because of the model complexity and also because this second bit is more exploratory. Thank you
I think you should use the survey design again, i.e., also in the second step. Strata and clusters affect only the standard errors of the parameter estimates and essentially they had no impact yet on your analysis in the first step. Weights should also be used though. If you have a detailed explanation of how the weights were constructed you might be able to make further progress though. If the weights were constructed using X and X is included in the analysis then you don't need to include the weights (or you can use only the portion of the weights that is not based on X).