Linear Mixed Models with Random Effects Analysis of variance models that include random effects are called linear mixed models with random effects (LMM). For agricultural experiments, random effects are often reps, blocks, years, locations or subjects. Usually, random effects are not tested, but are used to adjust the standard errors for tests on the fixed effects. This broadens the inference by implying that one would expect the same results regardless of the block, location or year in which the experiment was conducted.

Linear Mixed Models with Repeated Effects Repeated effects are factors where the experiment unit is measured repeatedly. Common factors are time or spatial increments, such as dates or soil depth. The assumption of equal variance within each time or space measurement is no longer necessary because the variances can be estimated by the model. A repeated measures model can also include random effects.

Generalized Linear Mixed Models for Count Data Generalized linear mixed models (GLMM) allow for the modeling of non-normal response data within an analysis of variance framework. The distribution of the response data is included in these models so the assumption of normality is unnecessary. Count data usually has a Poisson or negative binomial distribution and was the focus of this seminar. Binomial and multinomial are two other types of response data often seen in agriculture experiments. They can also be modeled with a generalized linear mixed model.

Reference material from the seminars Several of the most useful papers and one book listed in the reference sections of the seminar handouts.