Generalized mixed models for poisson distributions
Page E. Van Meter wrote:
Thanks! To clarify the simple mistake I was making for possible future novice readers of this mailing list: I did not understand that the glm function cannot handle random effects (which Faraway NEVER mentions in his book). I also did not understand that glmer and lmer can both handle non-linear data as long as the "family" is specified. I am very comfortable with linear models, linear mixed effect models, and non-linear models, but I have been having a lot of trouble tackling non-linear mixed effect models. I really do wish we could all agree on terms for these models (GLM is used for both general linear mixed models and generalized mixed models in many fields). Anyway, these were very rudimentary stumbling blocks that were not immediately apparent to me, so hopefully this will clarify for others.
1. It is too bad about the GLM thing, but I think both usages
("general" and "generalized" are here to stay).
2. Just to clarify a tiny bit more: "nonlinear mixed effect models"
usually implies normally distributed data (i.e. error terms) with
non-linear, NON-linearizable dependence of expected values on continuous
covariates (if they were linearizable then one could handle a
normal-error model with family(gaussian,link="..."))
nlmer handles these -- it doesn't complain about a "family" argument,
but based on a quick look on the output it looks like the function
actually ignores it.
3. GLMMs handle exponential-family data and linearizable
nonlinearities -- and they are indeed much harder than LMMs or GLMs.
Ben Bolker wrote:
glm doesn't do mixed effects models at all. You might (?) be confused about this because some software packages (SAS in particular, I don't know about SPSS) use the acronym GLM to refer to "general linear models" (rather than general*ized* linear models). Some particular kinds of linear mixed models (nested, balanced designs) can be estimated using the same general approaches used for ANOVA (in R, this would correspond to using aov with an Error term in the model). Linear models: lm (or aov) Generalized linear models: glm For linear mixed models you need lme (in the nlme package) or lmer (lme4). For generalized linear mixed models you need glmmPQL (MASS/nlme) or glmer (lme4). Ben Bolker