by jhines » Thu Feb 02, 2012 4:01 pm
Hi Billie,
I was able to run a model with an identity design matrix for detection, but I used the 2nd parameterization (which computes conditional probabilities, psiA,psiBA,psiBa,pA,pB,rA,rBA,rBa, instead of interaction ratios). Also, I constrained colonization and extinction to be constant over time. The reason for this is that I don't think you have enough data (18 sites per species) to estimate time-specific colonization, extinction and all of the detection probabilities. In addition, I ran some simpler models for comparison.
If you had trouble with the default parameterization (phiA,phiB,phi,...), it's not surprising that you had trouble with some models. This parameterization attempts to estimate the species interaction factor, phi, directly, as opposed to the 2nd parameterization, which estimates the conditional probabilities. The program needs to compute the likelihood value for the model, given the parameters and if you're using the interaction factor, it has to translate that ratio back into conditional probabilities. This can result in numerical problems for the optimization routine when the denominator of the ratio is small. This problem is avoided when using the conditional probabilities (2nd parameterization).
If you're interested in the species interaction factor, you can compute it from the estimates of psiA, psiBA, and psiBa as:
phi = psiBA/(psiA*psiBA+(1-psiA)*psiBa)
Cheers,
Jim