This open access book offers an introduction to mixed generalized linear models with
applications to the biological sciences basically approached from an applications perspective
without neglecting the rigor of the theory. For this reason the theory that supports each of
the studied methods is addressed and later - through examples - its application is illustrated.
In addition some of the assumptions and shortcomings of linear statistical models in general
are also discussed. An alternative to analyse non-normal distributed response variables is the
use of generalized linear models (GLM) to describe the response data with an exponential family
distribution that perfectly fits the real response. Extending this idea to models with random
effects allows the use of Generalized Linear Mixed Models (GLMMs). The use of these complex
models was not computationally feasible until the recent past when computational advances and
improvements to statistical analysis programs allowed users to easily quickly and accurately
apply GLMM to data sets. GLMMs have attracted considerable attention in recent years. The word
Generalized refers to non-normal distributions for the response variable and the word Mixed
refers to random effects in addition to the fixed effects typical of analysis of variance (or
regression). With the development of modern statistical packages such as Statistical Analysis
System (SAS) R ASReml among others a wide variety of statistical analyzes are available to
a wider audience. However to be able to handle and master more sophisticated models requires
proper training and great responsibility on the part of the practitioner to understand how
these advanced tools work. GMLM is an analysis methodology used in agriculture and biology that
can accommodate complex correlation structures and types of response variables.
