Empirical Bayes estimation of small area proportions based on ordinal outcome variables - ARCHIVED

Much research has been conducted into the modelling of ordinal responses. Some authors argue that, when the response variable is ordinal, inclusion of ordinality in the model to be estimated should improve model performance. Under the condition of ordinality, Campbell and Donner (1989) compared the asymptotic classification error rate of the multinominal logistic model to that of the ordinal logistic model of Anderson (1984). They showed that the ordinal logistic model had a lower expected asymptotic error rate than the multinominal logistic model. This paper also aims to compare the performance of ordinal and multinomial logistic models for ordinal responses. However, rather than focussing on classification efficiency, the assessment is made in the context of an application where the objective is to estimate small area proportions. More specifically, using multinominal and ordinal logistic models, the empirical Bayes approach proposed by Farrell, MacGibbon and Tomberlin (1997a) for estimating small area proportions based on binomial outcome data is extended to response variables consisting of more than two outcome categories. The properties of estimators based on these two models are compared via a simulation study in which the empirical Bayes methods proposed here are applied to data from the 1950 United States Census with the objective of predicting, for a small area, the proportion of individuals who belong to the various categories of an ordinal response variable representing income level.