What is the difference between
- generalized linear mixed models, and
- linear mixed effect models (lmer function in package lme4)
in terms of distributions of the response variable? Do they both work with non gaussian distributions?
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Linear mixed-effects models describe the relationship between a response variable and independent variables, with coefficients that can vary with respect to one or more grouping variables. A mixed-effects model consists of two parts, fixed effects and random effects. Fixed-effects terms are usually the conventional linear regression part, and the random effects are associated with individual experimental units drawn at random from a population. The random effects have prior distributions whereas fixed effects do not.
The Generalised Linear Mixed Model as linear predictor contains random effects in addition to the usual fixed effects, but would be estimated as a one step regression rather than Expectation Maximisation model.
You might be mixing up general linear models and generalized linear models.
Linear mixed models assume your response (or dependent) variable is normally distributed. Generalized linear mixed models do not; instead you have to provide a suitable distribution and link function for your data.