MCMC known fate - no data for group in year 1

[jlaufenb]

Hello All,

I am using the MCMC procedure in MARK to estimate annual survival, process variance, and process correlations for radio-collared individuals on 3 study areas using monthly known-fate data collected over 11 years. I constructed a DM where monthly survival was constant throughout the year but differed by year and group (g*t; group = study area). Because there were no animals collared in group 3-year 1, I fixed S{3,1}=0 to obtain fixed effects MLEs for initial values in the MCMC procedure. When setting up the MCMC procedure, I selected all parameters EXCEPT S{3,1} (i.e., parameter 23 for this dataset). I specified 3 hyperdistributions (1 for each study area) using a 3-column DM and specified 3 separate rhos making sure that rho(2) and rho(3) corresponding to correlations between groups 2&3 and groups 1&3, respectively, were appropriately placed in the V-C matrix to account for the missing parameter (i.e., parameter 23). When I run the estimation procedure, each iteration produces the following warning:

* * WARNING * * Error number 23 returned from DPOCO in MCMC.
Sigma(1) = 0.5618496
Sigma(2) = 0.7799723E-01
Sigma(3) = 0.5215052
Rounding errors are dominating calculations
Sigma(1) = 0.5618496
Sigma(2) = 0.7799723E-01
Sigma(3) = 0.5215052
VCDET = 0.6929720E-48
RCOND = 0.1130466-316
DET = 6.929720 -49.00000

My question is am I setting up this analysis appropriately given I have no data for 1 group in 1 year? If not, how should I be doing this? Is the MCMC procedure in MARK capable of handling this?

Thanks
Jared

[jlaufenb]

I have a follow-up question. Although I have not resolved the error produced in my previous post, I pressed on and tried to fit a model where S(t) for areas 1 and 2 are constrained to be equal (a valid hypothesis for this system). I obtained the MLEs for initial values and constructed a bivariate normal prior where mu1=areas1-2, mu2=area3, corresponding sigmas, and a single rho. I did this excluding the first year for group 3 as I previously did. When I ran the MCMC procedure expecting to see a similar error as before, I received none. I am perplexed why I received the previous warnings and what I should do about them. Can anyone provide some advice or insight to what might be the issue?

Related to the model in this post but more so to design, I have yet another question. Is it better to constrain areas 1 and 2 (as I did here) resulting in 11 S(t)s in my case to estimate the mu1 and sigma1 of the bivariate posterior or not to constrain from the onset but use the MCMC design matrix to include all 22 S(t)s in estimation of those hyperparameters? I expect it comes down to whether one believes annual survival rates in areas 1 and 2 are random draws from the same distribution or are actually equal. Thoughts?