Mean Individual Covariate Value w/ Dummy Covariate

[brp]

On page 11-42 in the MARK book, the author explains that using the mean individual covariate value option with a dummy covariate (sex in that example) will produce the weighted average of apparent survival for males and females.

The MARK help file "Individual Covariates and Real Estimates" states:

The second option is to use the mean value of each of the individual covariates in the model. This option normally makes a lot of sense, except in cases where dummy variables are included in the individual covariates. For example, suppose adults are coded as 1 and subadults coded as 0. What does it mean to compute real parameter values for the mean of this age variable?

I think the answer to that question is "the overall real parameter value across all ages". In other words, the weighted average.

It appears to me the MARK book and the help file are contradictory. Which of these lines of thought is correct?

[cooch]

On page 11-42 in the MARK book, the author explains that using the mean individual covariate value option with a dummy covariate (sex in that example) will produce the weighted average of apparent survival for males and females.

The MARK help file "Individual Covariates and Real Estimates" states:

The second option is to use the mean value of each of the individual covariates in the model. This option normally makes a lot of sense, except in cases where dummy variables are included in the individual covariates. For example, suppose adults are coded as 1 and subadults coded as 0. What does it mean to compute real parameter values for the mean of this age variable?

I think the answer to that question is "the overall real parameter value across all ages". In other words, the weighted average.

It appears to me the MARK book and the help file are contradictory. Which of these lines of thought is correct?

I don't believe they're contradictory at all. In the help file, which considers age, it may not make sense to consider average parameter value for an individual of average age, since average age may not be of particular importance (or biologically meaningful). There are cases, though, where average over sex might be important - say, if there was strong prior expectation of a 1:1 sex-ratio.

The common 'thread' is that using the mean individual covariate option produces a weighted mean. It's up to the end-user to decide if this is meaningful or not.

[brp]

If the average parameter value for an individual of average age (where age is a dummy covariate: 0=subadults, 1=adults) is not biologically meaningful (as suggested in the help file), then in my opinion, the average parameter value for an individual of average sex (whatever that means?) is also not biologically meaningful.

I think the weighted average interpretation makes sense for both age and sex dummy covariates. Do you agree?

I don't understand why it's necessary to expect a 1:1 ratio to be able to have a meaningful weighted average. Can you clarify? If we have a 1:1 ratio (50/50% split), then the weighted average simplifies to the regular average.

[cooch]

If the average parameter value for an individual of average age (where age is a dummy covariate: 0=subadults, 1=adults) is not biologically meaningful (as suggested in the help file), then in my opinion, the average parameter value for an individual of average sex (whatever that means?) is also not biologically meaningful.

I think the weighted average interpretation makes sense for both age and sex dummy covariates. Do you agree?

I don't understand why it's necessary to expect a 1:1 ratio to be able to have a meaningful weighted average. Can you clarify? If we have a 1:1 ratio (50/50% split), then the weighted average simplifies to the regular average.

Nothing to clarify. The mean is a weighted mean given the frequency distribution of the covariate. Whether or not that is meaningful is up to you.