An imputation strategy for incomplete longitudinal ordinal data

Abstract

A new quasi-imputation strategy for correlated ordinal responses is proposed by borrowing ideas from random number generation. The essential idea is collapsing ordinal levels to binary ones and converting correlated binary outcomes to multivariate normal outcomes in a sensible way so that re-conversion to the binary and then ordinal scale, after conducting multiple imputation, yields the original marginal distributions and correlations. This conversion process ensures that the correlations are transformed reasonably, which in turn allows us to take advantage of well-developed imputation techniques for Gaussian outcomes. We use the phrase 'quasi' because the original observations are not guaranteed to be preserved. We present an application using a data set from psychiatric research. We conclude that the proposed method may be a promising tool for handling incomplete longitudinal or clustered ordinal outcomes.