number of parameters, assessable parameters etc

[Guest]

multible questions...
Dear all

I was wondering about the number of parameters in some of my models until I discovered the discussion between White/Cooch in the old MARK forum (No 266). So I am aware that in the result browser the number of parameters is the ones, which were assessable and not the number one might expect considering the selected model. (i.e. due to sparse data).

My data set contains 24 trapping occasions. I run the full time dependent model – as an option under pre defined models. The result browser shows me 45 parameters. 22 for phi and 22 for p - plus the beta estimate for the last of both. Fine. Then I open the PIM’s and run the same analysis again- fully time dependent. I did not even open the design matrix. In the result browser the model has the same deviance as before but a lower AIC and only 40 parameters.
Why?

In the full output of the model – after the input and before the summary (AIC, deviance, c hat etc) MARK states the number of function evaluations for (in my case) 46 parameters.
After the beta and real estimates MARK states
Attempted ordering of parameters by estimatibility:
38 37 41 40 43 36 44 39 45 35 34 32 31 29 42 23 33 30 18 28 27 8 12 21 15
26 25 5 14 16 1 24 10 22 7 4 6 11 3 2 46 17 19 20 13 9
Beta number 9 is a singular value.

The order of models is quiet different in (my) both cases. Again why?

In general if I expect i.e. 45 parameters and the result browser tells me 40 – does that mean the last 5 of the above mentioned statement are the ones which were not identified (or problematic). In fact they were - I can view them. How should they be treated?

I discovered this while playing with covariates and linear models. I tried to include effort in my model (for p) but not as a substitute for time but as an addition – meaning I run the analysis with the interaction model ( p= time + effort + time effort + error) and the additive model )p = time + effort + error).
In my case the additive model was really much better than the only time dependent one and the interaction model.
BUT = I could not compute most of the LRT tests. Additive model against interaction model. Additive (time + effort) model against time. The only ones which gave me a result was additive against effort. So – the basic question is - did it make sense in the first place to combine time and effort – after all I used the effort as a linear model plus time dependency.
Secondly - which lead me to all the first questions in the beginning: has the number of parameters (assessable or not) something to do with the LRT test. I tested as stated above only the nested models.

Sorry for the length of the message – I just wanted to be clear.

Many thanks in advance.
Christian

By the way – it might be useful to give a link to the old forum for new subscribers – a lot of subjects are discussed there. Maybe it is there – but it does not hit me when browsing the new forum.

[cooch]

By the way – it might be useful to give a link to the old forum for new subscribers – a lot of subjects are discussed there. Maybe it is there – but it does not hit me when browsing the new forum.

Actually, such a link already exists - simply look at the MARK FAQ, which is a "sticky" posting in this forum (which is the item which is 'stuck' at the top of the list).

[Mark Trinder]

just a note on evan's mention that the old forum is listed in the 'sticky' posting - the address there is wrong!

this is the one that works for me.

http://www.cnr.colostate.edu/~gwhite/mark/mark.htm

[Mark Trinder]

or perhaps this one!

http://canuck.dnr.cornell.edu/HyperNews ... arked.html

[egc]

just a note on evan's mention that the old forum is listed in the 'sticky' posting - the address there is wrong!

No, it's not wrong - it works fine. The link should not have a period at the end...that has been corrected.

[Res]

Christian,

I think I have an answer to part of your question. When you fit a model with full time dependence, this model is already explaining all the variation between years (or time steps). So, there is no variation left to be explained by a time-covariate, such as effort. If I understand this correctly, I would expect that your model p(time+effort) has as many estimable parameters as model p(time), and the LRT will not work. However, if you compare models p(time) and p(effort), you can ask how much of the variation between the years is explained by variation in effort. And AIC will tell you whether time variation is more parsimoniously modelled as a funtion of effort, or whether you should retain the fully time dependent structure.

Does this help?

Res

[Guest]

Res

Thanks for your answer. Well, I agree that p (t) should explain all the variance between years – but I was interested if I could separate the influence of the effort. After all one assumption of the model is more or less equal effort – which is not the case for my data – especially in the first 7-8 years. So to look at the variance in-between years – and their “ ecological “ meaning I wanted to subtract effort and see how this changes the model. In theory the effort could be the only reason that p is time dependent and with an equal effort I would have a constant p. It is NOT the case but this was my intention to prove.
The full time dependent model phi (t) p (t) has 45 parameters (24 years) – which is correct – phi (t) p (t + effort) has 21 – the model phi (t) p (effort) has 6 – phi (t) p (t * effort) has 25. This is my problem _ I do understand that MARK only reports the number of parameter it could estimate. But why are there such huge differences?
( By the way – the interaction model had the exact same deviance as the full time dependent model – so proving your point about the explanation of the variance – though the AIC was smaller – well it had 20 parameters less .)

The additive model and the interaction model should have more parameters than the full time dependent model –since they are even more general – as you see above they haven’t and MARK takes them in the LRT test as the reduced model and phi (t) p(t) as general model – and I get a negative chi square value.

And as I pointed out just fitting the phi (t) p (t) model – via pre defined model – via opening the PIMs by myself and via design matrix (identity and full) revealed – in the same order 45, 41 and 39 parameter respectively. (and slightly different AIC values)

Phi (t) p (effort) was less supported that phi (t) p (t) but in the end the model phi (.) p (t + effort) is the best supported model – so this model fits the data better than the full time dependent one. So time AND effort might explain more variances than time alone – but due to the reduced parameter _ I am not sure.

The problem (for me) is the differences in parameters in general – but also the consequences – regarding the definition of the AIC – is the model phi (t) p (t * effort) really better supported than phi (t) p (t )? Same deviance - the delta AIC is 42 (meaning of life - D. Adams) but it has less parameter than it should have. In the discussion between Coach and White in the old forum (posting 266) White stated usually such models (too many parameters for the data therefore less parameter are in fact assessable) are at the end of the list – well in my case it is the best supported – though I do not trust the AIC due to the “wrong” number of parameters.

Any ideas?
Thanks

Christian


----------------------------------------------------------------------------------------------------------------
{phi (t) p(t * effort)} 3934,164 0,00 0,98843 1,0000 25 2301,594
{phi (.) p( t + effort)}3944,346 10,18 0,00608 0,0062 22 2318,024
{Phi(.) p(t) PIM} 3948,508 14,34 0,00076 0,0008 24 2318,024
{phi (t) p(t) design} 3963,760 29,60 0,0 0,0000 39 2301,602
{Phi(t) p(t) PIM} 3976,653 42,49 0,0 0,0000 45 2301,594
{phi (effort) p (effort)} 4071,751 137,59 0,0 0,0000 4 2482,259
{phi (.) p(effort)} 4072,875 138,71 0,0 0,0000 3 2485,458
phi (t) p (t + effort)} 4080,700 146,54 0,00 0,0000 21 2456,453
{Phi(t) p(.) PIM} 4081,124 146,96 0,00 0,0000 24 2450,640
{Phi(.) p(.) PIM} 4086,695 152,53 0,00 0,0000 2 2501,226
{phi (.) p( t * effort)} 4110,895 176,73 0,00 ,0000 24 2480,411

[Res]

Christian,

Ok, you want to partition the variance in p between years into a component due to variable effort and another component for the rest? You cannot do this by including time AND effort into the same model, because effort cannot explain any more variation than the fully time dependent model already does. The fully time dependent model already accounts for any sort of differences between years. That is why you get the same deviance for both models. In principle, you should also get the same number of parameters (the one for effort not being estimated). I'm not sure why MARK gives you fewer parameters for the second model. Especially, I'm worried about the fact that there seem to be only 6 estimable parameters for model phi(t)p(effort); it should have 25 (intercept, 23 for the time effect on survival, and 1for effort). Did you always use the logit link function? With this link function, parameters near 1 or 0 sometimes get counted as non-estimable. Find out why these parameters are not estimated. E.g. what happens to the deviance if you fix one of these 'unestimated' parameters? If it is truly non-estimable, the deviance should not change. What happens if you use different starting values? If the model has converged, you should get exactly the same deviance and number of parameters as before. Did you have any years with very sparse data? Does the GOF test look ok?

Now about partitioning the variance: you can either look at the changes in deviance, or use the variance components option in MARK. For the first method: fit models p(t), p(effort), and p(.), where the last model is constant over time. The deviance should be lowest in the first model, and highest in the last. Intuitively, if the deviance of p(effort) is close to the deviance of p(.), effort explains very little of the variation over time (i.e. between years). On the other hand, if the deviance of p(effort) is close to the deviance of p(t), then almost all of the variation between years is explained by variation in effort. Formally, the proportion of variance (V) explained by effort is: V=(dev p(.) - dev p(effort))/(dev p(.) - dev p(t)). For the variance components method, please refer to the MARK help files, or Loison et al 2002 (Journal of Applied Statistics 29:289-304).

Cheers,
Res

[Guest]

Res

You are absolutely correct. I actually fixed the number of parameters in the result browser to the number it should estimate. I.e. for phi (t) p (effort) instead 6 I fixed it to 25. The order of the models changed quiet a bit phi (t) p (effort) was even worse than phi(t) p(.). The phi (t) p (t) was much better supported – in the end the model phi (.) p (t) seems to be the most reasonable.
Yes, I do have sparse data – actually in most years – blue whales in the St Lawrence – they are not many left….

It also seems that trap dependency influencing the data – well not in the real meaning of the word but as transients – irregular guests. Here I had also problems with the LRT – but after fixing the number of parameters – it made much more sense. Therefore it seems that I follow this approach and will leave the effort out completely.

Many thanks again – it really helped

All the best
Christian

By the way – I was on you www site – I presume the next time I can write in German to you?