In HCI we often encounter dependent variables which are not (conditionally) normally distributed: we measure response-times, mouse-clicks, or the number of dialog steps it took a user to complete a task. Furthermore, we often encounter nested or grouped data; users are grouped within companies or institutes, or we obtain multiple observations within users. The standard linear regression models and ANOVAs used to analyze our experimental data are not always feasible in such cases since their assumptions are violated, or the predictions from the fitted models are outside the range of the observed data. In this chapter we introduce extensions to the standard linear model (LM) to enable the analysis of these data. The use of [R] to fit both Generalized Linear Models (GLMs) as well as Generalized Linear Mixed Models (GLMMs, also known as random effects models or hierarchical models) is explained. The chapter also briefly covers regularized regression models which are hardly used in the social sciences despite the fact that these models are extremely popular in Machine Learning, often for good reasons. We end with a number of recommendations for further reading on the topics that are introduced: the current text serves as a basic introduction.