GAMLSS for high-variability data: an application to liver fibrosis case.

In this paper, we propose management of the problem caused by overdispersed data by applying the generalized additive model for location, scale and shape framework (GAMLSS) as introduced by Rigby and Stasinopoulos (2005). The idea of using a GAMLSS approach for handling our problem comes from the idea of Aitkin (1996) consisting in the use of an EM maximum likelihood estimation algorithm (Dempster, Laird, and Rubin, 1977) to deal with overdispersed generalized linear models (GLM). As in the GLM case, the algorithm is initially derived as a form of Gaussian quadrature assuming a normal mixing distribution. The GAMLSS specification allows the extension of the Aitkin algorithm to probability distributions not belonging to the exponential family. In particular, aim of this work is to show the importance of using a GAMLSS strutcure when a mixture is used to provide a natural representation of heterogeneity in a finite number of latent classes (Celeux and Diebolt, 1992).