# How to deal with underdispersion with binomial data

I'm working with a pretty large dataset (n = 4,500) where 10% of my points (pixels in a GIS landscape) are 1s and the rest are 0s. The full model for my data looks something like this:

model.full = glm(pond~elev+slope+landform+strmord+wcover, family=binomial, data)


Independent variables are elevation, slope and vegetation cover (all continuous), landform (categorical 4 levels), and stream order (categorical 4 levels). The response is a variable that takes a value of one if the pixel was used by an animal and 0 otherwise.

The values of the residual deviance are 2220.6 with 4420 df. This is slightly above .5 which means my data are underdispersed. I have two questions:

1. Is this really a problem?
2. Is there any way to deal with this (i.e: alternative model structure)?
• Given the spatial nature of these variables and their naturally strong spatial correlations (pond pixels tend to be next to pond pixels, etc.), you should at least test for spatial correlation among the residuals--and if found--accommodate that through a geostatistical model or incorporating neighboring "spatially lagged" values among the covariates. I do not have a feel for how or what degree that would be associated with underdispersion. – whuber Sep 23 '14 at 23:07
• Thanks whuber. I actually incorporated in my best ranked model a random effect for " occupied pixel blocks", that is, a random effect for neighboring occupied pixels. As I expected, the result was a drastic decrease in the deviance (as now I'm accounting for this unexplained variance with the spatial random effects), thus, making underdispersion even more pronounced. – Alejandro Sep 23 '14 at 23:53
• Whether or not its a problem depends on what you're doing with the model. One suggestion is to fit a quasibinomial model. – Glen_b -Reinstate Monica Sep 24 '14 at 0:29
• Thanks Glen. I basically will use the coefficients of the logistic regression to parameterize a resource selection function. Underdispersion will likely affect the variances though. However, I feel the structure of the model is somehow wrong. I saw cases where quasibinomial was used to deal with overdispersion, but underdispersion is so rare that I may have missed that. – Alejandro Sep 24 '14 at 3:15