Multisample Analysis of Multivariate Ordinal Categorical Variables

Estimating the polychoric correlation from misclassified data

Many variables that are used in social and behavioural science research are ordinal categorical or polytomous variables. When more than one polytomous variable is involved in an analysis, observations are classified in a contingency table, and a commonly used statistic for describing the association between two variables is the polychoric correlation. This paper investigates the estimation of the polychoric correlation when the data set consists of misclassified observations. Two approaches for estimating the polychoric correlation have been developed. One assumes that the probabilities in relation to misclassification are known, and the other uses a double sampling scheme to obtain information on misclassification. A parameter estimation procedure is developed, and statistical properties for the estimates are discussed. The practicability and applicability of the proposed approaches are illustrated by analysing data sets that are based on real and generated data. Excel programmes with visual basic for application (VBA) have been developed to compute the estimate of the polychoric correlation and its standard error. The use of the structural equation modelling programme Mx to find parameter estimates in the double sampling scheme is discussed.

A latent normal distribution model for analysing ordinal responses with applications in meta-analysis

We consider the comparison of two treatments (or a treatment and a control/placebo) with responses that are classified into ordinal categories. By operating on the assumption that the responses are manifestations of some underlying continuous variables and that the definitions of the categories for the treatment group and the placebo group are the same in the same clinical test centre, we develop a model to examine the possible treatment effects. These treatment effects can be identified as location effect or dispersion effect. The method can be generalized to analyse clinical test results coming from different centres, where each centre may have its own standard in classifying responses. The method is technically undemanding and can be implemented in a very simple and straightforward way by using easily accessible software that can be downloaded at no cost. Real data sets are analysed for illustration.