The value of generalized linear mixed models for data analysis in the plant sciences - Madden, Laurence V.; Ojiambo, Peter S. (Frontiers in Horticulture, 2024)
Modern data analysis typically involves the fitting of a statistical model to data, including the estimation of model parameters and their precision (standard errors), and testing hypotheses based on the parameter estimates. Linear mixed models (LMMs) fitted through likelihood methods have been the foundation for data analysis for well over a quarter of a century; these models allow the researcher to simultaneously consider fixed (e.g., treatment) and random (e.g., block, location) effects on response variables, and account for the correlation of observations, when it is assumed that the response variable has a normal distribution. Analysis of variance (ANOVA), developed about a century ago, can be considered a special case of the use of an LMM. A wide diversity of experimental and treatment designs, and correlations of the response variable, can be handled with these types of models. Many response variables are not normally distributed, of course, such as discrete variables that may or may not be expressed as a percentage (e.g., counts of insects or diseased plants), and also continuous variables with asymmetrical distributions (e.g., survival time). As expansions of LMMs, generalized linear mixed models (GLMMs) can be used to analyze the data arising from several non-normal statistical distributions, including the discrete binomial,