ABSTRACT
In applications it is quite common to encounter data which are non-normal. For example, counts, data which are strictly positive, or skewed data. To model such data, distributions such as Bernoulli, Binomial, Poisson, Exponential, etc are often appropriate. However, with such distributions, the assumptions made in linear models are generally not satisfied. Generalized linear models (GLM) provide effective tools to handle such data. At the heart of GLM's is the view that, for non-Gaussian data, the mean of the response is usually not linearly related to the predictors. This chapter reviews the core concepts of scalar GLM. It shows how to handle functional predictors. The chapter examines functional response models, and discusses how the models can be fit using the refund package in R. The theory for generalized linear models is built upon exponential families, though this can be generalized.
