Random effects in ordinal regression models

• Published in: Computational statistics & data analysis Vol. 22; no. 5; pp. 537 - 557
• Main Authors: Tutz, Gerhard, Hennevogl, Wolfgang
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 30.09.1996; Elsevier Science; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: EM algorithm; EM-type algorithm; Exact sciences and technology; Generalized linear models; Linear inference, regression; Mathematics; Mixed model; Ordinal regression; Probability and statistics; Random effects; Repeated measurements; Sciences and techniques of general use; Statistics; Ordinal regression; Mixed model; EM-type algorithm; Random effects; EM algorithm; Generalized linear models; Repeated measurements; Monte Carlo method; Generalized linear model; Numerical integration; Regression model; Repeated measurement; Gauss method; Covariate
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/0167-9473(96)00004-7

Ordinal regression models as special cases of multivariate generalized linear models are extended to include random effects in the linear predictor. Random effects may describe the shifting of thresholds in the cumulative model or they may describe subject-specific weights of covariates. In a more general case instead of the shifting of thresholds all thresholds may depend on the subject. The latter case makes alternative link functions advisable. Three alternative estimation procedures based on the EM algorithm are considered. Two of them make use of numerical integration techniques (Gauss-Hermite or Monte Carlo), and the third one is a EM type algorithm based on posterior modes. The estimation procedures are illustrated and compared by two examples.