Distribution‐free fitting of logit models with random effects for repeated categorical responses

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Abstract
This article discusses random effects models for within‐subject comparisons of repeated responses on the same categorical scale. The models account for the correlation that normally occurs between repeated responses. The standard way of fitting such models maximizes the marginal likelihood after integrating with respect to a distribution for the random effect. An alternative non‐parametric approach does not assume a distributional form for the random effects. Recent literature shows that for certain simple logit models, this approach yields essentially the same model parameter estimates as conditional maximum likelihood. Moreover, these estimates also result from fitting corresponding quasi‐symmetric log‐linear models. For simple data sets in which primary interest relates to subject‐specific comparisons of the repeated responses, one can easily obtain the estimates with standard software for log‐linear models. Examples include data from crossover designs and from comparisons of treatment and control groups regarding the change between baseline and follow‐up observations.