GLM over time and space? is it possible to fit a GLM over space and time?
I have shrimp densities measured over 8 months, and in each month there are 4 stations sampled along a freshwater-saltwater gradient, so I have 32 observations of shrimp densities in total.
I have Temperature,Salinity,Turbidity,Oxygen,Depth as my environmental variables. I have 32 observations for each variable here as well.
So do I need to block for space or time? Do I have to use a manyglm?
thanks!
Pieter
 A: This, I believe, is the purpose of Generalized Estimating Equations. I'm not personally too familiar with them, but these slides seem to offer a good overview of their application to spatial regression.
A: I would look into using Integrated Nested Laplace Approximation, which is specifically for the type of data you have. There is also an R package for it here.
Otherwise I would perhaps use a generalized linear mixed effects model. If your primary question is how shrimp respond to those environmental variables, then you could use the month as a random effect. This is essentially correcting for the fact that your observations from month to month are likely to be related to each other, although this does not account for the spatial autocorrelation that might also be in your data. If the sampling sites are independent of each other then I wouldn't worry about spatial autocorrelation. This is a great guide to using GLMMs for ecological questions. 
I'm not sure what the distribution of your shrimp densities are, but that would change the distribution you would use for the GLMM. If it is normally distributed then you could use a linear mixed effect model. 
