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Abstract : |
Linear mixed-effects models are frequently used to analyze repeated measures data, because they model fiexibly the within-subject correlation often present in this type of data. The most popular linear mixed-effects model for a continuous response assumes normal distributions for the random effects and the within-subject errors, making it sensitive to outliers. Such outliers are more problematic for mixed-effects models than for fixed-effects models, because they may occur in the random effects, in the within-subject errors, or in both, making them harder to be detected in practice. Motivated by a real dataset from an orthodontic study, we propose a robust hierarchical linear mixedeffects model in which the random effects and the within-subject errors have multivariate t-distributions, with known or unknown degrees-of-freedom, which are allowed to vary with groups of subjects. By using a gamma-normal hierarchical structure, our model allows the identification and classification of both types of outliers, comparing favorably to other multivariate t models for robust estimation in mixed-effects models previously described in the literature, which use only the marginal distribution of the responses. Allowing for unknown degrees-of-freedom, which are estimated from the data, our model, |
