Using variance components with lots of boundary estimates

[jbauder]

Could someone please give me some input on using variance components to estimate a mean value of survival? I would like to calculate an overall mean estimate of survival from my 14 year data set (I am using a CJS model). I would also like to calculate an overall mean for the three populations in my study. The model phi(population + time[Trend])p(population*time) has virtually all my support (w = 0.93) and indicates a positive linear increase in survival during the study. I understand from the GIM that I should use my phi(group*time)p(group*time) model to estimate an overall mean with variance components. However, I have several inestimable parameters on the boundary (sparse data set) and Appendix D (D-44 and D-45) indicates that these can throw off estimates from variance components. My overall mean estimates using variance components from my global model are a fair amount higher than survival using the phi(.) or phi(population) models, or even just looking at the mid-point value from the phi(population + time[Trend]) model.
I know you are not supposed to use a reduced model for variance components but in this case would it be acceptable to get my overall means from my phi(population + time[Trend])?
I am also a little confused about how process variation (sigma^2) is interpreted when I use variance components to estimate overall means for multiple groups (all three populations in my case). There is only one process variance given so does is it the same for all three estimates? Or am I thinking about it all wrong. It has been hard to wrap my head around how to interpret process variance when there are multiple groups. I would like to use these overall means to calculate effect sizes among populations but how does the process variance fit into this?

Thanks again
Javan

[cooch]

Could someone please give me some input on using variance components to estimate a mean value of survival? I would like to calculate an overall mean estimate of survival from my 14 year data set (I am using a CJS model). I would also like to calculate an overall mean for the three populations in my study. The model phi(population + time[Trend])p(population*time) has virtually all my support (w = 0.93) and indicates a positive linear increase in survival during the study. I understand from the GIM that I should use my phi(group*time)p(group*time) model to estimate an overall mean with variance components. However, I have several inestimable parameters on the boundary (sparse data set) and Appendix D (D-44 and D-45) indicates that these can throw off estimates from variance components. My overall mean estimates using variance components from my global model are a fair amount higher than survival using the phi(.) or phi(population) models, or even just looking at the mid-point value from the phi(population + time[Trend]) model.
I know you are not supposed to use a reduced model for variance components but in this case would it be acceptable to get my overall means from my phi(population + time[Trend])?
I am also a little confused about how process variation (sigma^2) is interpreted when I use variance components to estimate overall means for multiple groups (all three populations in my case). There is only one process variance given so does is it the same for all three estimates? Or am I thinking about it all wrong. It has been hard to wrap my head around how to interpret process variance when there are multiple groups. I would like to use these overall means to calculate effect sizes among populations but how does the process variance fit into this?

Thanks again
Javan

If you have a trend, then talking about the 'mean' doesn't make a lot of sense.

[cooch]

I am also a little confused about how process variation (sigma^2) is interpreted when I use variance components to estimate overall means for multiple groups (all three populations in my case). There is only one process variance given so does is it the same for all three estimates? Or am I thinking about it all wrong.

See example D.4.3. The key quote is

We’ll assume, however, that σ2(low) = σ2(high). This is not directly testable using the moments-based variance components approach in MARK, but is testable using an MCMC approach (see appendix E)

In other words, using the RE model (based on the moments estimator), it is not possible to estimate a separate process variance for each level of some 'treatment'. What you estimate is in fact a function of the process variance for each level, and the variation among levels. To get an estimate of process variation at the individual treatment level, you need to use another approach (as noted).