I have a global model using a GLMM with 5 fixed effects with interactions, as well as two random effects.
x ~ a*b + a*c + a*d + a*e + (1|f) + (1|g)
I am using an information theoretic approach and have used the dredge() function in MuMIn on this global model.
The null model is ranked very low (95) which I had assumed meant that fixed effects are important to the system, as there are 94 possible model combinations which are better than random.
However, a colleague asked if the random effects were included in the null model, as otherwise, of course many models are better than null, because they take into account variation from the random effects, but the null model would not.
However, I assumed that the model would still have these random effects, just no fixed effects. Is this correct?
Yes.
Here's an experimental illustration that dredge() drops only fixed effects, leaving the null model as (intercept + all random effects)
library(lme4) library(MuMIn) m1 = lmer(Reaction~Days+(Days|Subject),sleepstudy,na.action=na.fail,REML=FALSE) dd = dredge(m1) Fixed term is "(Intercept)" ## Global model call: lmer(formula = Reaction ~ Days + (Days | Subject), data = sleepstudy, ## REML = FALSE, na.action = na.fail) ## --- ## Model selection table ## (Intrc) Days df logLik AICc delta weight ## 2 251.4 10.47 6 -875.970 1764.4 0.0 1 ## 1 257.8 5 -887.738 1785.8 21.4 0 ## Models ranked by AICc(x) ## Random terms (all models): ## ‘Days | Subject’
The first point here is that the end of the printed output explicitly shows the random effects included for all terms.
Fitting the null model manually and comparing AICc with the table above:
m0 <- update(m1, . ~ . - Days)
formula(m0)
## Reaction ~ (Days | Subject)
AICc(m0)
## [1] 1785.821