process var with var components

[amusante]

In a known fate model I have 4 groups with weekly encounter entries for a total of 20 entries or weeks for each group. I want to use the variance components procedure for S(t) model to obtain the process variance without samplng variance for use in a leslie matrix model. When I do the Beta-hat mean seems high and sigmas appear very small compared with data? Does this look right or what do I need to do to get process variance from weekly survival estimates? Thanks again. Tony

Beta-hat SE(Beta-hat)
------------------------
1.000000 0.000004

S-hat SE(S-hat) S-tilde SE(S-tilde) RMSE(S-tilde)
-------------------------------------------------------------
1.000000 0.000000 1.000000 0.000000 0.000000
0.982759 0.017092 0.999986 0.000014 0.017227
1.000000 0.000000 1.000000 0.000000 0.000000
1.000000 0.000000 1.000000 0.000000 0.000000
1.000000 0.000000 1.000000 0.000000 0.000000
1.000000 0.000000 1.000000 0.000000 0.000000
1.000000 0.000000 1.000000 0.000000 0.000000
0.982143 0.017697 0.999986 0.000014 0.017843
1.000000 0.000000 1.000000 0.000000 0.000000
1.000000 0.000000 1.000000 0.000000 0.000000
1.000000 0.000000 1.000000 0.000000 0.000000
1.000000 0.000000 1.000000 0.000000 0.000000
0.961538 0.026668 0.999980 0.000014 0.038441
1.000000 0.000000 1.000000 0.000000 0.000000
0.916667 0.039893 0.999970 0.000014 0.083304
0.904762 0.045295 0.999970 0.000014 0.095208
0.921053 0.043744 0.999975 0.000014 0.078922
0.971429 0.028160 0.999986 0.000014 0.028557
0.970588 0.028976 0.999986 0.000014 0.029397
1.000000 0.000000 1.000000 0.000000 0.000000

Naive estimate of sigma^2 = 0.0005461 with 95% CI (0.0001362 to 0.0016475)

Estimate of sigma^2 = 0.0000000 with 95% CI (0.0000000 to 0.0008469)

Estimate of sigma = 0.0000141 with 95% CI (0.0000087 to 0.0291009)

Trace of G matrix = 12.0041313

[ganghis]

1) I don't think it makes sense to rely on estimates of S-tilde in this case because they are influenced highly by the 0 SEs on survival rates that are 1.0

2) Look at Gould and Nichols' 1998 Ecology paper. In your case, there are no issues with detection<1. Thus the only extraneous sources of variation that you might want to accout for are demographic stochasticity and process covariance. You could get into the VC matrix and subtract estimates of requisite quantities from the total variance of your estimates (S^2). Be advised that this approach can result in estimates of process variance that are less than or equal to 0.

Paul Conn

[gwhite]

Tony:
One of the main reasons I put the MCMC estimation capabilities into MARK was to handle problems like yours, where enough of the survival estimates had zero standard errors, yet you want to estimate a process variance. However, I wouldn't advise using the MCMC procedure unless you have a pretty good understanding of how this estimation procedure works, so that you can diagnose potential problems.
Gary