Estimation of Two-Level Hierarchical Generalized Linear Models Given a Mixture of Ordinal and Continuous Missing Data

• Activity Number: 583
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Yongyun Shin*+
• Companies: Virginia Commonwealth University
• Keywords: ignorable missing data ; hierarchical ; generalized linear model ; likelihood ; correlated probit model ; multiple imputation

Abstract

A hierarchical generalized linear model is estimated where p continuous and K ordinal variables have ignorable missing data. The key idea is to: estimate the joint model for the (p+K) variables, given known covariates; multiply impute complete data given the estimated joint model by maximum likelihood for subsequent analysis of the hierarchical model. However, it is difficult to define and estimate the joint model for the (p+K) variables correlated at multiple levels. My approach is to: express the joint distribution as a correlated probit model where ordinal variables have underlying latent variables, jointly normal with continuous variables; estimate the distribution of p continuous variables; sort ordinal variables in the ascending severity of missingness, estimate the conditional probit model for each kth ordinal variable given multiply imputed random effects of p continuous and (k-1) less severely missing ordinal variables, and transform into the joint model for p continuous and k latent variables at lower level; repeat the same for ordinal variables at higher level. Estimated joint model and multiply imputed random effects generate multiple imputation of complete data.