Generalized linear models with ordinally-observed covariates.
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.
Johnson
Timothy R
TR
Department of Statistics, University of Idaho, Moscow 83844-1104, USA. trjohns@uidaho.edu
D000704:Analysis of Variance; D015982:Bias; D003625:Data Collection / Q000706:statistics & numerical data; D003627:Data Interpretation, Statistical; D006306:Health Surveys; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D015233:Models, Statistical; D016012:Poisson Distribution; D012044:Regression Analysis