Generalized linear models with ordinally-observed covariates

Abstract

An ordinally-observed variable is a variable that is only partially observed through an ordinal surrogate. Although statistical models for ordinally-observed response variables are well known, relatively little attention has been given to the problem of ordinally-observed regressors. In this paper I show that if surrogates to ordinally-observed covariates are used as regressors in a generalized linear model then the resulting measurement error in the covariates can compromise the consistency of point estimators and standard errors for the effects of fully-observed regressors. To properly account for this measurement error when making inferences concerning the fully-observed regressors, I propose a general modelling framework for generalized linear models with ordinally-observed covariates. I discuss issues of model specification, identification, and estimation, and illustrate these with examples.