Random effects in occupancy robust design models

[nachoman]

Hola,

I am using occupancy robust design models in MARK in order to estimate probability of colonisation and extinction plus derived prameters (parameterisation psi(1), epsilon, gamma) for time series (18 primary sessions) coming from four different experimental treatments. After model selection, I have arrived to a couple of candidate models, and now I want to fit random effects (Appendix D Gentle Introduction) to epsilon and gamma parameters in order to account for random variation, but I am having some problems.

One of the models that I am interested is a (model 1) model with additive intercepts for time and treatment for both epsilon and gamma, plus detection probability with treatment effects but no time variation. The other model is (model 2) a model with a similar structure but where epsilon and gamma follow a three level factor for both epsilon and gamma (say bad, regular and good year) instead of time, otherwise same structure as model 1. I have used the Desing Matrix to fit all the set of models. I am interested in fitting random effects to epsilon and gamma in both models to extract estimates for every treatment and also to compare model fit between them and also to fixed effects versions (similar to Appendix D D4.2 and D4.3, but with occupancy models).

When I run say, model 1 without random effects, I only need 48 BETA parameters. When it comes to run the random effects model, I choose the "user specified" option and code the additive time+treatment effects on the design matrix that pop's up. Here I code it for only one of the parameters (say epsilon, 20 BETAS), because otherwise would assume that epsilon and gamma come from the same distribution. The resulting model fits 52.something parameters with worse AICc. Then I do the same for gamma in a separate model.

I have two doubts. First, I am right to interpret that this means that while the fixed effects model fits only 48 BETA parameters with 20 BETAS for epsilon, the random effects model fits 52.something BETAS hence 24.something BETAS for epsilon? In the examples in Appendix D D4.2 and D4.3, random effects models have always LESS parameters than their fixed effects counterparts, so might be missing something...

Second, I am not sure whether my procedure is right or I should fit a random model for every parameter*treatment (say one model for epsilon*treat1, another model for epsilo*treat2, etc..., same for gamma) or whether I am fiddling nonsense and should do it in a complete different way.

Gracias,

N