Understanding linear constraints

[timkdavies]

Can anyone help me interpret linear constraints?

If you think that a particular covariate affects a particular parameter - lets say that capture effort varies and you think it affects capture probability - you can add it into the CJS model within MARK. This model will then estimate capture probability as a linear function of effort. If you run a second model without effort as a constraint - just a straightforward time-dependent model - and this model has a better AIC score, this suggests that including effort does not result in more precise (i.e. better) model.

Does this then suggest that although effort does vary, it makes no real difference to the estimation of capture probability?

Any help is appreciated, even just a yes or no!

Cheers,
Tim

[cooch]

Can anyone help me interpret linear constraints?

If you think that a particular covariate affects a particular parameter - lets say that capture effort varies and you think it affects capture probability - you can add it into the CJS model within MARK. This model will then estimate capture probability as a linear function of effort. If you run a second model without effort as a constraint - just a straightforward time-dependent model - and this model has a better AIC score, this suggests that including effort does not result in more precise (i.e. better) model.

Does this then suggest that although effort does vary, it makes no real difference to the estimation of capture probability?

Any help is appreciated, even just a yes or no!

Cheers,
Tim

More or less 'yes' - in this instance, if a model p(t) (which has more parameters) has more support in the data than a model p(effort) (which has fewer parameters), then the increased precision of reconstituted parameter estimates in p(effort) does not compensate for reduced overall fit of the less parameterized model. Invoking parsimony, you select the model with lowest AIC, and conclude that effort does not explain much of the variation in p. A minimal model set for this sort of thing would typically consist of 3 models: p(t), p(.) and p(interesting covariate). The contrast of p(t) vs p(.) tells you if your data support temproal variation in p. We know conceptually that p must very over time (no parameter is true constant - I suppose the exception being probability of remaining in a dead absorbing state - I digress). However, we don't knw a priori if our data wil l provide evidence of this. So, say you find that p(t) has more support than p(.). Great. But temporal variation in and of itself is of *zero* interest. It is the 'magnitude' or said variation (in some contexts), or the drivers for the variation (in other contexts) which is of interest. In this case, you're considering the latter, where 'effort' is one of the drivers you think might contribution to variation in p. If p(t) has more support (based on AIC), or if p(effort) fits significantly less well than p(t) (based on a LRT or equivalent), then you'd conclude there is no strong support for effort being the driver.

This whole issue is covered in considerable detail in chapter 4 and chapter 6.