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Updated: Jul 19, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
Generalized linear models with ordinally-observed covariates
1Department of Statistics, University of Idaho, Moscow 83844-1104, USA. trjohns@uidaho.edu
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.
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