Linear trends

[Mariana Mira]

I'm studing population dynamics of two toad species in Brazil, and I have two years of mark-recapture data, so I decided to run a preliminary analysis (CJS model) with the sampling periods being months, instead of years. But, the recapture rates in amphibians can vary a lot in response of climatic factors or season. Then, I constrained the time variation in recapture rates with the month variable, assuming equal recapture rates for the same months in different years. This improved my model. But, I would like to insert the combined effect of this month-dependence with the rainfall as a linear trend, with or without their interaction. But, the program gave me the same AIC of the model with only the month variable, when I performed the model with the combined effect. I would like to know if MARK can perform this linear trend with this monthly constraint. I would really appreciate if any one could help me or give me suggestions.
Thanks for your attention
Mariana

[cooch]

I'm studing population dynamics of two toad species in Brazil, and I have two years of mark-recapture data, so I decided to run a preliminary analysis (CJS model) with the sampling periods being months, instead of years. But, the recapture rates in amphibians can vary a lot in response of climatic factors or season. Then, I constrained the time variation in recapture rates with the month variable, assuming equal recapture rates for the same months in different years. This improved my model. But, I would like to insert the combined effect of this month-dependence with the rainfall as a linear trend, with or without their interaction. But, the program gave me the same AIC of the model with only the month variable, when I performed the model with the combined effect. I would like to know if MARK can perform this linear trend with this monthly constraint. I would really appreciate if any one could help me or give me suggestions.
Thanks for your attention
Mariana

It would help if you could post an example of the design matrix you're using (doesn't have to be the whole DM - just an example of what - in principle - you're trying to do).

[Mariana Mira]

I'll give an example of the part of the p (recapture rates) that I'm trying to model:
Out Nov Dez Jan Fev Mar
Bo B1 B2 B3 B4 B5 B6 B7
1 1 89.3
1 1 89
1 1 238
1 1 181.5
1 1 292
1 1 337
1 1 84
1 1 327.2
1 1 335.4
1 1 171
1 1 201
1 1 321

But, instead of 12 months in each year, I only put the wet months (just to ilustrate the example and do not take too long) in the two years (6 months) and the total monthly rainfall in the study area. Note that the model are p(month+rainfall), because I didn't put the intercation terms. Where there are no value, this means zero.
I hope that now you can understand what I am trying to do.
Thanks for every one that could help me.

[Mariana Mira]

I'm sorry, I did wrong! Now it is fine!
I'll give an example of the part of the p (recapture rates) that I'm trying to model:
Mês - Ou No De Ja Fe Ma
Bo B1 B2 B3 B4 B5 B6 B7
1 1 0 0 0 0 0 89.3
1 0 1 0 0 0 0 89
1 0 0 1 0 0 0 238
1 0 0 0 1 0 0 181.5
1 0 0 0 0 1 0 292
1 0 0 0 0 0 1 337
1 1 0 0 0 0 0 84
1 0 1 0 0 0 0 327.2
1 0 0 1 0 0 0 335.4
1 0 0 0 1 0 0 171
1 0 0 0 0 1 0 201
1 0 0 0 0 0 1 321

But, instead of 12 months in each year, I only put the wet months (just to ilustrate the example and do not take too long) in the two years (6 months) and the total monthly rainfall in the study area. Note that the model are p(month+rainfall), because I didn't put the intercation terms.
I hope that now you can understand what I am trying to do.
Thanks for every one that could help me.

[cooch]

I'm sorry, I did wrong! Now it is fine!
I'll give an example of the part of the p (recapture rates) that I'm trying to model:
Mês - Ou No De Ja Fe Ma
Bo B1 B2 B3 B4 B5 B6 B7
1 1 0 0 0 0 0 89.3
1 0 1 0 0 0 0 89
1 0 0 1 0 0 0 238
1 0 0 0 1 0 0 181.5
1 0 0 0 0 1 0 292
1 0 0 0 0 0 1 337
1 1 0 0 0 0 0 84
1 0 1 0 0 0 0 327.2
1 0 0 1 0 0 0 335.4
1 0 0 0 1 0 0 171
1 0 0 0 0 1 0 201
1 0 0 0 0 0 1 321

But, instead of 12 months in each year, I only put the wet months (just to ilustrate the example and do not take too long) in the two years (6 months) and the total monthly rainfall in the study area. Note that the model are p(month+rainfall), because I didn't put the intercation terms.
I hope that now you can understand what I am trying to do.
Thanks for every one that could help me.

OK, several issues (problems). First, to constrain your estimates of p to be functions of a continuous covariate, you generally use the covariate alone - you should not have a covariate column in addition to the columns coding for time. Your DM should have a basic intercept column, and then a column for each of your covariates. See section 7.8 in 'the book' (e.g., DM at top of p. 30). While you can - structurally - have columns coding for temporal heterogeneity (time columns) and the covariate - in the same DM, interpretation can be complex. I'm guessing that in your case, this isn't exactly what you want to do.

Second, your DM (as written) seems to imply that you're pooling over 2 groups (since you have the same identity coding for time replicated over two blocks of rows). Fine, but then why do your covariates differ between the groups? Look closely at the DM on p. 30 in Chapter 7. The first column is the intercept, the second column is the group coding, and the third column in the covariate. Note that the value of the covariates is duplicated between the two groups.

So, at least two major problems with what you've presented. I'd suggest you work through Chapter 7 in its entirety, since the basic problems I've outlined are fairly fundamental.

[gwhite]

Mariana:
The design matrix you provided should give a different deviance than the pure time model because you have repeated the time effect for the 6 months, but have different rainfall values. I assume that the rainfall effect is not being estimated -- which makes me ask if you have the latest version of MARK. The newer versions automatically scale values in the design matrix, so that the "large" entries that you have will not cause a problem.
Gary