7. Generalized Linear Models

The preceding chapters were all about specifying an appropriate (and often sophisticated) predictor term. In this chapter, we will give the outcome variables their due respect. First, the assumptions of Gaussian linear model are reviewed and generally discarded. Next, the framework of Generalized Linear Models is explained from ground up. After that is established, I will introduce a good dozen of model families, organized by types of measures. Next to some commonly known families, such as Poisson or Logistic regression models, this chapter will cover outcome variables for which good defaults have been lacking, such as rating scale responses and ToT measures. For RT and ToT data, I will suggest exponentially-modified Gaussian models and for (quasi) continuous rating scales, I will introduce a rather novel approach, Beta regression. The chapter closes with a look beyond GLMs. Distributional models allow to link predictors to the mean, but also other properties of the outcome distribution. I will show how a distributional model covers differences in individual answer styles to rating scales.