GLM, Poisson - non-integer count numbers (average)

Question

I’m doing GLM for frequency data of a behavior x. As I have day 1 and day 2 of observations, I averaged the frequencies of that two days, so my counting data is not integer numbers. However, I am not able to make the models when I use the distribution of Poisson.

How do I fix it?

I’m adjusting model as follows:

al1<-glm(cbind(al)~sp*sexo,poisson(link="log"),data=abfm) 

But I get the following error message:

Warning messages: 
1: In dpois(y, mu, log = TRUE) : non-integer x = 4.500000 
2: In dpois(y, mu, log = TRUE) : non-integer x = 7.500000

Answer 1

There is no way to use the average of the two observations and at the same time use the Poisson distribution. You might try to figure out what the probability distribution of the average of two Poisson i.i.d random variables is, but I think this is not the best way out.

For me, the best way out would be to use a model of repeated measures, and consider a random effect of individual for each day.

For this, considering that you have a database as follows:

> dados <- data.frame(
+   id = 1:100,
+   explicativa = runif(100, 0, 20)
+   )
> 
> dados$r1 <- rpois(100, dados$explicativa)
> dados$r2 <- rpois(100, dados$explicativa)
> 
> head(dados)
  id explicativa r1 r2
1  1    9.082513 16 14
2  2   17.741123 14 29
3  3   10.819865 13 12
4  4   18.527938 22 25
5  5    4.828392  6  7
6  6   13.986794 14 15 

r1 and r2 are the frequencies observed on day 1 and day 2.

Turn your data into format tidy/long:

library(tidyr);library(dplyr)
dados <- dados %>% gather(dia, resposta, starts_with("r"))

Then adjust a model as follows:

library(lme4)    
modelo <- glmer(resposta ~ explicativa + (0 + dia | id), data = dados, family = poisson)

Thus, you will be considering that for each individual there is a random variation related to the day it is being measured.