# binomial GLMM for Repeated Measure + overdispersion

My experiment is the following:

In a nutshel:

site ncolonie   Week 1                      Week2                       Week3
-   -           no treatment                3min freeze                 3min freeze
A   7control    remove pieces of paper      remove pieces of paper      remove pieces of paper
A   8treatment  remove pieces of paper      remove pieces of paper      remove pieces of paper
B   8control    remove pieces of paper      remove pieces of paper      remove pieces of paper
B   7treatment  remove pieces of paper      remove pieces of paper      remove pieces of paper


In words:

I have 30 colonies of ants ("id" is colony name) across two different labs ("site", 15 colonies in the first lab, 15 in the other one). In the first experiment ("pre-test"), there is no treatment and I introduce a certain amount (total) of pieces of paper with a bad smell in each nest and measure how many the ants removed after 1h (removed); in the second week ("week2") I put the test ("t") colonies in the freezer during 3min (cold shock, does not kill them but may affect performances), leave them some time to recover then I introduce smelly pieces of paper again in the nest; in the third week ("week3") I put the colonies in the freezer during 3min again, leave them some time to recover then I introduce smelly pieces of paper again.

My model is mod1=glmer(y~treatment*site*week+ (1|id),family=binomial(link=probit))

Here is a repeatable example, I used the same distributions as in the actual data set:

rm(list=ls())
treatment<-as.factor(rep(c("t","c"),45))
id<-as.factor(rep(1:30,3))
site<-as.factor(rep(c(rep("A",15),rep("B",15)),3))
week<-as.factor(c(rep("pre-test",30),rep("week1",30),rep("week2",30)))
removed<-trunc(rnorm(90,79,35))
total<-trunc(rnorm(90,139,30))
y=cbind(removed,total)

library(lme4)
require(car)
summary(mod1)


results of the summary

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation)
Family: binomial  ( probit )
Formula: y ~ treatment * site * week + (1 | id)

AIC      BIC   logLik deviance df.resid
1255.6   1288.1   -614.8   1229.6       77

Scaled residuals:
Min      1Q  Median      3Q     Max
-8.1031 -1.4258  0.0164  1.7890  5.5761

Random effects:
Groups Name        Variance Std.Dev.
id     (Intercept) 0.01919  0.1385
Number of obs: 90, groups:  id, 30

Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)                -0.41424    0.06143  -6.744 1.54e-11 ***
treatmentt                 -0.29816    0.08534  -3.494 0.000477 ***
siteB                      -0.04343    0.08538  -0.509 0.611014
weekweek1                   0.28284    0.04530   6.243 4.29e-10 ***
weekweek2                   0.08350    0.04583   1.822 0.068447 .
treatmentt:siteB            0.38427    0.12108   3.174 0.001506 **
treatmentt:weekweek1        0.02687    0.06415   0.419 0.675310
treatmentt:weekweek2        0.23246    0.06448   3.605 0.000312 ***
siteB:weekweek1            -0.01073    0.06403  -0.168 0.866906
siteB:weekweek2            -0.09807    0.06481  -1.513 0.130241
treatmentt:siteB:weekweek1 -0.24261    0.09132  -2.657 0.007890 **
treatmentt:siteB:weekweek2 -0.06146    0.09260  -0.664 0.506915
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


1) Am I doing this right or should I use something else to analyze my results? (repeated-measure ANOVA? same GLMM but using the removal percentage of the first week as random effect?)

2) Should I worry about overdispersion? (I know there are exceptions for Binomial GLMM but it looks like I am not in the 'binary' category?)

3) Is (1|id) enough to account for overdispersion?

• I'm not sure I understand what it is you are trying to do? Are you interested in predicting something? Are you trying to estimate the effect of something? Jun 9, 2017 at 15:04
• Sorry it is unclear, I am trying to estimate the effect of the treatment. I want to know if exposing my ants to 1 and then 2 freezing events affect their ability to perform tasks.
– Nakx
Jun 9, 2017 at 15:06

mod1=glmer(y~treatment*week*site+(1|id),family="binomial")

Assumptions were met and results consistent with the figures. I then compared my levels by using the package lsmeans.
library(lsmeans)