Link-Barker model-averaged lambda CI looks wrong

[stshroye]

I am using Link-Barker models to estimate population parameters of adult Muskellunge in a lake in Minnesota. I have done this for other lakes with no apparent problems. However, for this particular lake my model-averaged lambda estimates are perplexing. The capture histories were grouped by sex. The 95% CI for females (below) looks reasonable. However, the 95% CI for males (below) looks much too wide, considering that the estimates from individual male models are generally more precise than the estimates from individual female models, and there is also less model variation. I assume this has something to do with the logit transformation for males, since simply using the weighted average estimate +- (1.96 * Unconditional SE) looks much more reasonable. Any ideas why the logit transformation does not seem to work for males? Thanks.

Code: Select all

                  Derived Parameter Lambda Population Change -- Females
Model                                     Weight    Estimate      Standard Error
---------------------------------------- -------   -------------- --------------
{Phi(g) p(t) f(g)}                   0.56988   0.9074241      0.0366917     
{Phi(g) p(t) f(.)}                   0.27016   0.9190508      0.0383457     
{Phi(.) p(t) f(g)}                   0.14734   0.9001447      0.0357391     
{Phi(.) p(t) f(.)}                   0.01263   0.9491867      0.0305778     
---------------------------------------- -------   -------------- --------------
Weighted Average                                   0.9100200      0.0369210     
Unconditional SE                                                  0.0377368     
95% CI for Wgt. Ave. Est. (logit trans.) is 0.8038599 to 0.9614750
Percent of Variation Attributable to Model Variation is 4.28%

                  Derived Parameter Lambda Population Change -- Males
Model                                     Weight    Estimate      Standard Error
---------------------------------------- -------   -------------- --------------
{Phi(g) p(t) f(g)}                   0.56988   0.9860799      0.0337181     
{Phi(g) p(t) f(.)}                   0.27016   0.9770472      0.0325609     
{Phi(.) p(t) f(g)}                   0.14734   0.9796126      0.0336665     
{Phi(.) p(t) f(.)}                   0.01263   0.9491867      0.0305778     
---------------------------------------- -------   -------------- --------------
Weighted Average                                   0.9822209      0.0333582     
Unconditional SE                                                  0.0338176     
95% CI for Wgt. Ave. Est. (logit trans.) is 0.5538389 to 0.9995934
Percent of Variation Attributable to Model Variation is 2.70%


[gwhite]

The model-averaged estimate for males is 0.98, much closer to the upper bound of 1 than the estimate for females of 0.91. The female confidence interval is close to symmetrical around the estimate, whereas the male estimate is quite asymmetric with the upper value ~1, forcing the lower value down considerably.

Play around in a spreadsheet and see how moving the estimate closer and closer to 1 generates a more and more skewed confidence interval.

Normally we might consider a profile likelihood confidence interval, but the model-averaged estimate is not a maximum likelihood estimate so no profile likelihood interval possible.

Gary

[jhines]

Since lambda is not bounded between zero and one, the plogit transformation is not appropriate. The log link function should be used for lambda as it allows the estimate to be greater than one.

[gwhite]

My error -- didn't notice you were model-averaging lambda, and not phi. Like Jim says, the logit CI is not appropriate for lambda. You could just do a confidence interval on the real scale (the usual +/- 2 SE), or do a confidence interval on the log scale and back-transform.

Gary