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.
Keywords: Survey Sampling, GoM model, Inverse Probability
Weights, Linear Mixed-Effect Models