Values of Deviance

[Sch. Lucie]

Hi,

My aim is to study the age variations of the residence time at a colony for greater flamingos I’m considering a multistates model applied to the reobservations of banded flamingos at a colony with the following states: « 1 » flamingo with an egg, « 2 » Flamingo with chick on island « 3 » Flamingo with chick in creche out of island. The season of reproduction is divided in 16 time intervals of 10 days. (/For example for each time interval, a flamingo seen at least once during these 10 days will be noted as state “1”)

First I began to run models from a simple .inp file, containing only capture histories:

0110001111030000 1;
0110001120033000 1;
0110001200000000 1;

Then, I integrated an individual covariate (age) at my first .inp file
(it is exactly the same dataset, only the covariate is added):
1110000000000000 1 12;
1112001110000000 1 12;
0000000000000003 1 13;

By building from the PIM chart the same model (same parameter fixed to zero, same link function, same adjustment of ĉ) with these two files (thus without taking into account the covariate in the second one) I obtain very different values of Deviance??

ĉ = 1,56

Simple file QAICc #Par QDeviance
S(state*t) p(state*t) Psi (state*t) 6087,286 112 1869,11
File with covariate
S(state*t) p(state*t) Psi (state*t) 7825,323 112 7592,745

Thanks in advance for your help.

Lucie.

[cooch]

Hi,
<snip>

I obtain very different values of Deviance??
.

The deviance of a model is measured relative to -2 log L of the 'saturated' model. In many (but not all) cases, the saturated models is a model where the number of model parameters is equal to the number of data points (which usual means the observed outcome of a binomial process like number of animals surviving out of some initial number known alive).

Thats basically the approach for models without individual covariates. For any of the models with individual covariates, the sample size for each encounter history is 1. The saturated model then has a -2 log likelihood value of zero. The deviance for any model with individual covariates is then just its -2 log likelihood value.

So, even if you don't use the individual covariates in a model, if they're in the .inp file, and you *tell* MARK that they are there, then MARK uses a different saturated model for computing the deviance. This doesn't influence model selection at all - provided you are doing the comparisons among models with the same saturated model.

I should probably add something about this into 'the book' somewhere.