I have fit a binomial GLMM (glmer) to a response variable that is a proportion.
How my data looks:
ind_id total_off total_on total OFT1 MIS1 sex litterid 122 50 40 90 2.33 -1.32 F 5643 134 10 20 30 -1.00 -0.22 M 2345 145 1 10 11 3.19 0.89 F 8743
ind_id: individual identity
total_off: count of # of times off territory
total_on: count of # of times on territory
total: sum of # of times off and on territory
OFT1: continuous behaviour score
MIS1: continuous behaviour score
sex: categorical sex (M or F)
litterid: identity of litter
library(lme4) m.1<-glmer(cbind(total_off, total_on) ~ OFT1 + MIS1 + sex + (1|litterid), family=binomial, data=new) summary(m.1)
Fixed effects output:
Estimate Std. Error z value Pr(>|z|) (Intercept) 0.08019 0.19200 0.418 0.676 OFT1 -0.07030 0.06919 -1.016 0.310 MIS1 0.05392 0.04753 1.135 0.257 sexM 0.19664 0.19385 1.014 0.310
Based on chapter 16 in The R Book, I can back-transform the estimates with the following equation:
But, the examples Crawley goes over are for categorical explanatory variables with a
glm() model (no random effect), not
glmer() model (random effect).
I have two questions:
- For starters, should my
cbind(total_off, total)instead of
- How can I back-transform
glmermodel estimates? Once back transformed, how are they interpreted?
For continuous explanatory variables, such as
OFT1, I want to be able to say something like: for every 1 unit increase in
OFT1 score, an individual spends X% more/less time off their territory. For categorical explanatory variables, such as
sex, I want to be able to say: females spend X% more/less time off their natal territory compared to males.