On linear mixed models and their influence diagnostics applied to an actuarial problem

In this paper, we motivate the use of linear mixed models and diagnostic analysis in practical actuarial problems. Linear mixed models are an alternative to traditional credibility models. Frees et al. (1999) showed that some mixed models are equivalent to some widely used credibility models. The main advantage of linear mixed models is the use of diagnostic methods. These methods may help to improve the model choice and to identify outliers or influential subjects which deserve better attention by the insurer. As an application example, the data set in Hachemeister (1975) is modeled by a linear mixed model. We can conclude that this approach is superior to the traditional credibility one since the former is more flexible and allows the use of diagnostic methods.