Sampling Weights in a Bayesian Grade of Membership Model

<p>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, <em>weighting based on the estimated parameter</em>, 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.</p>