reconstituting p hat in Huggins CC with Ind. Cov.

[royworth]

Hi all,

I am attempting to reconstitute values for p-hat from Huggins CC models that include individual environmental covariates (continuous) and age (binary). Specifically, I am trying to create a spreadsheet in excel that will allow me to predict p-hat by age class given new values for the individual covariates. I have become confused because I can only seem to get the proper estimates for p-hat when age is set to 0 (juvenile size class in this case). In other words, when age is set to 0, and I use the mean values for the covariates, I get very nearly the exact p-hat estimated by MARK in the "real parameter" output. However, when age is set to 1 (adults), I get nothing close to the estimate from MARK and, in fact, an opposite trend is reflected than what the model is expected to predict (i.e. i get lower p-hats for Adults than Juveniles, even though the estimates from MARK reflect the opposite).

It has been a long day and I am sure I have just overlooked something silly, but I would be extremely grateful if someone were able to point out to me what I may have overlooked, either in "The Gentle Intro" or by simple cognitive lapse.

Thanks, in advance,

Roy

[royworth]

Hi all,

I am attempting to reconstitute values for p-hat from Huggins CC models that include individual environmental covariates (continuous) and age (binary). Specifically, I am trying to create a spreadsheet in excel that will allow me to predict p-hat by age class given new values for the individual covariates. I have become confused because I can only seem to get the proper estimates for p-hat when age is set to 0 (juvenile size class in this case). In other words, when age is set to 0, and I use the mean values for the covariates, I get very nearly the exact p-hat estimated by MARK in the "real parameter" output. However, when age is set to 1 (adults), I get nothing close to the estimate from MARK and, in fact, an opposite trend is reflected than what the model is expected to predict (i.e. i get lower p-hats for Adults than Juveniles, even though the estimates from MARK reflect the opposite).

It has been a long day and I am sure I have just overlooked something silly, but I would be extremely grateful if someone were able to point out to me what I may have overlooked, either in "The Gentle Intro" or by simple cognitive lapse.

Thanks, in advance,

Roy

I apologize, I should also have mentioned that I used a design matrix approach and modeled age as a group, not as an "individual covariate" per MARK nomenclature. My design matrix looks like this, for example:
/*Int Age Cov1 Cov2 Cov 3*/
1 1 1.1 2 20;
1 1 0.2 5 35;
1 1 0.4 8 120;
1 1 3.2 10 80;
1 0 1.5 7 75;
1 0 5.5 11 60;
1 0 6.2 14 100;
1 0 3.1 3 35;

Thanks again,

Roy

[royworth]

Hi all,

I am attempting to reconstitute values for p-hat from Huggins CC models that include individual environmental covariates (continuous) and age (binary). Specifically, I am trying to create a spreadsheet in excel that will allow me to predict p-hat by age class given new values for the individual covariates. I have become confused because I can only seem to get the proper estimates for p-hat when age is set to 0 (juvenile size class in this case). In other words, when age is set to 0, and I use the mean values for the covariates, I get very nearly the exact p-hat estimated by MARK in the "real parameter" output. However, when age is set to 1 (adults), I get nothing close to the estimate from MARK and, in fact, an opposite trend is reflected than what the model is expected to predict (i.e. i get lower p-hats for Adults than Juveniles, even though the estimates from MARK reflect the opposite).

It has been a long day and I am sure I have just overlooked something silly, but I would be extremely grateful if someone were able to point out to me what I may have overlooked, either in "The Gentle Intro" or by simple cognitive lapse.

Thanks, in advance,

Roy

I apologize, I should also have mentioned that I used a design matrix approach and modeled age as a group, not as an "individual covariate" per MARK nomenclature. My design matrix looks like this, for example:
/*Int Age Cov1 Cov2 Cov 3*/
1 1 1.1 2 20;
1 1 0.2 5 35;
1 1 0.4 8 120;
1 1 3.2 10 80;
1 0 1.5 7 75;
1 0 5.5 11 60;
1 0 6.2 14 100;
1 0 3.1 3 35;

Thanks again,

Roy

Alas, more information. In one example, using the logit link, MARK came up with these estimates for the betas:

Index Beta Parameter Estimate (p-hat)
1 Intercept 0.358539
2 AGE -0.2714707
3 MSW 0.1695609
4 GRD 0.1800057
5 COND 0.5886597


These are the means and std. dev. for the covariates:

Variable Mean SD
MSW 3.5749099 1.6710218
GRD 5.5867267 4.1009395
COND 49.335256 34.05281


This is the value I came up with for AGE = 0 using the means of the covariates: 0.58869 (MARK's actual estimate for Juvenile p-hat was 0.5886867)

This is the value I come up with for AGE = 1: 0.52175 (MARK's estimate was 0.7205515 for adults!!!)

Here is how I calculated p-hat for AGE = 0:
p-hat = 0.358539 + -0.2714707*(0) + 0.1695609*(3.5749) + 0.1800057*(5.5867267) + 0.5886597*(49.335256)

I did the same for AGE = 1, just substituting the 1 for the 0 obviously.

Thanks again,

Roy

[royworth]

Thanks a ton to Jeff Laake for taking the time to discuss this problem with me off-site where, after going over my output file, he discovered that my problem was simply an absent minded error (I had gotten the order of my betas mixed up).

Thanks again, Jeff!

Sincerely,
Roy