Robustness for general design mixed models using the t-distribution

The t -distribution allows the incorporation of outlier robustness into statistical models while retaining the elegance of likelihood-based inference. In this paper we develop and implement a linear mixed model for the general design of the linear mixed model using the univariate t -distribution. This general design allows a considerably richer class of models to be fit than is possible with existing methods. Included in this class are semi-parametric regression and smoothing, and spatial models.