Covariate-assisted Grade of Membership Model

Music City Center 

The Grade of Membership (GoM) model is a popular individual-level mixture model for multivariate categorical data such as survey responses. In modern data collection, numerous covariates are often gathered alongside the target response data, many of which share a similar latent structure. To leverage this covariate information for improved estimation of the latent structure of the target data, we introduce Covariate-assisted Grade of Membership (CoGoM) models and develop an efficient estimation algorithm based on spectral methods. For model identifiability, we establish a weaker sufficient condition compared to the covariate-free case. For theoretical guarantee, we show consistency in high-dimensional settings, demonstrating how incorporating covariates can aid the estimation of the latent structure. Through simulation studies, our proposed method outperforms traditional approaches in terms of both computation efficiency and estimation accuracy. Finally, we demonstrate our method by applying it to a Trends in International Mathematics and Science Study (TIMSS) dataset.

Grade of Membership Model

Identifiability

Sequential Projection Algorithm

Covariate Assistance

Spectral Method 

Section on Statistical Learning and Data Science