It's my first question here, I hope I'll ask it correctly. I am trying to find out how to analyse non-integer, count data (yes!). I am looking at the effect of a given treatment on habitat suitability for some birds, measured as number of territories. Some of the territories are inbetween two plots with different treatments, such that I had to distribute the territories between the plots. I end up with half and quarter territories.
EDIT My dataset looks like this:
year plot treatment territories location surface 1 1985 1569 ctrl 1.0 Cheyres 1.2 2 1986 1569 ctrl 1.0 Cheyres 1.2 3 1987 1569 1 0.0 Cheyres 1.2 4 1988 1569 2 2.0 Cheyres 1.2 5 1989 1569 3 6.5 Cheyres 1.2 6 1990 1569 1 1.5 Cheyres 1.2
Where year, plot, location and treatment are factors.
I've tried a GLMM with Poisson distribution (in R):
glmmacrsci1 <- glmer(territories ~ treatment * (1|year) * (1|location/plot), offset=surface, family="poisson", data=acrsci)
When running this, I get the usual non-integer warnings (e.g.):
In dpois(y, mu, log = TRUE) : non-integer x = 1.500000
and I get infinite AIC, BIC, and deviance:
$AICtab AIC BIC logLik deviance df.resid Inf Inf -Inf Inf 775
Most other questions related to non-integer counts were about rates, which can apparently be circumvented by using an offset. However I don't think it's possible in my case.
My questions to you:
1) Is it correct to use a GLMM with Poisson distribution with such data? (I don't think so but glmer seems to work anyway)
2) Can you think of any alternative to Poisson for my data?