Using General Mixed Effects models to address pseudo replication

Question

A common problem in animal studies is pseudoreplication of data points due to a limit in the number of animals available in a study population.

I need to address any pseudoreplication and influence of individual in my study. I had planned to model ID (individual animal) as a random factor in a glmr.

In my main study, with a large data set I am using permutation based logistic regressions for whether animals of a certain age class are underweight. Looking at a model :

mod1 <- glm(Underweight ~ Age.Class, family = binomial(), data = data)

against (likelihood ratio test) a permuted data set of the same data, this finds Age class predicts tendency to be underweight.

To factor in ID into this, I assign individual identity to a subset of my data (was not possible time wise to ID whole data set) I had planned to address pseudo replication as a post hoc assessment on the work with this subset of data.

I am confused as to the method for this, would I:

a) do a simple LRT test between a model that factors in ID and doesn't, if there is no sig difference then ID has no effect, i.e.:

glm1 <-  glmer(Underweight ~ Age.Class + (1 | ID.number), 
               family = binomial(), data = data)

glm2 <-  glmer(Underweight ~ Age.Class, 
               family = binomial(), data = data)


lrtest(glm1, glm2)

Or

b) Do I also need to interpret ID into some kind of permutation test like the original model?

Answer 1

A couple of points:

• It is not clear why you want to use permutation tests and not the classic $\chi^2$ distribution for the likelihood ratio test.
• Model glm2 uses glmer() but without including any random effects. Does this really work? You should better compare using anova() model mod1 the logistic regression without random effects (null hypothesis) with model glm1 that includes the random intercepts (alternative hypothesis).