Generalized Linear Mixed Models for Non-normal Responses
Josafhat Salinas‐Ruíz, Osval Antonio Montesinos López, Gabriela Hernández Ramírez, José Crossa
Abstract
Abstract Generalized linear mixed models (GLMMs) have been recognized as one of the major methodological developments in recent years, which is evidenced by the increased use of such sophisticated statistical tools with broader applicability and flexibility. This family of models can be applied to a wide range of different data types (continuous, categorical (nominal or ordinal), percentages, and counts), and each is appropriate for a specific type of data. This modern methodology allows data to be described through a distribution of the exponential family that best fits the response variable. These complex models were not computationally possible up until recently when advances in statistical software have allowed users to apply GLMMs (Zuur et al. 2009; Stroup 2012; Zuur et al. 2013). Researchers in fields other than statistical science are also interested in modeling the structure of data. For example, in the social sciences there have been applications in the field of education when several tests are applied to students; in longitudinal personality studies when the occurrence of an emotion is repeatedly observed over time over a set of people; and in surveys to investigate the political preference of a population, among others.