A common approach to analyzing longitudinal ordinal data is to apply generalized linear mixed models (GLMMs). The efficiency and validity of inference for parameters are affected by the random-effects distribution in GLMMs. A proposed test is developed based on the observed data and a reconstructed data set induced from the observed data for diagnosing the random-effects misspecification in cumulative logit models for longitudinal ordinal data, extending the idea presented by Huang (2009) for longitudinal binary data. The proposed test statistic has the quadratic form of the difference of maximum likelihood estimators between the observed data and the reconstructed data, and it follows a limiting chi-squared distribution when the model is correctly specified. The simulation studies are conducted to assess the performance of the proposed test, and a clinical trial example demonstrates the application of the proposed test.
Computational Statistics & Data Analysis 92, pp.126-133