Sampling Weights in a Bayesian Grade of Membership Model

The Grade of Membership (GoM) model is a hierarchical mixed-membership model used to characterize underlying latent classes based on categorical data. When using GoM models to analyze survey data, the sampling design needs to be appropriately modeled. Linear mixed-effect models (LME's) easily model the stratification and clustering in sampling designs. This paper introduces a modification of the GoM model to include a polytomous logistic mixed-effects regression prior, designed to take sampling design induced dependencies into account. In addition, there is a debate regarding the use of sampling weights in model based analyses. I developed a new type of weighting, weighting based on the estimated parameter, to incorporate the sampling weights in the updated GoM model. Finally, simulation studies demonstrate the effect of the sampling weights under different levels of informative sampling.