Building design matrices for age-structured models

[NMichel]

I'm building design matrices for a dataset where both young and adults were marked, and I'm assuming that there is no effect of age at marking on adult survival (i.e., Phi should be the same for intervals 2+ for the two groups).

I've been working through the examples of similar matrices in chapter 8.1.2 in the Introduction to MARK. Here, the authors first build a design matrix for a model where adult survival differs for individuals marked as young vs. marked as adult, using an "age at marking" column, an "age" column, 5 "time" columns, 5 columns for an interaction of age at marking and time, and 4 columns for an interaction of age and time (no interaction for the first time interval). They then state, on p. 8-24, that you can create a model where survival is equal for all adults - regardless of age at marking - by simply removing the columns for the "age at marking" X "time" interaction.

This doesn't make sense to me, as you're still including an effect of age at marking, and indeed the survival values are different for adults marked as young and adults marked as adults in each time period. When I build the model using PIMs as demonstrated on p. 8-23, I do NOT come up with the same results - as they state on p. 8-24 you should. The only way I come up with the same results as the PIMs is by removing the "marked" column and adding a column for an interaction of age and time at interval T1. This model has a slightly higher deviance, but it does have equivalent survival values for each time period for individuals marked as young or adults.

Can anyone explain to me the rationale for including an age at marking column - and excluding the age X T1 interaction - when you're assuming there is no effect of age at marking on survival? Is it not better to exclude age at marking completely? If you do need to include the age at marking column, how do you get the design matrix specified on p. 8-24 to produce the same results as the PIM matrix shown on p. 8-23?

[cooch]

I'm building design matrices for a dataset where both young and adults were marked, and I'm assuming that there is no effect of age at marking on adult survival (i.e., Phi should be the same for intervals 2+ for the two groups).

Why assume this? Why not test it? Of the dozens (and dozens) of analyses I've seen that work with data from individuals marked as adults, and as young, at least half the time, there turns out to be some evidence that adult survival does vary as a function of age of marking. Why? Simple - individual marked as young, and subsequently encountered as adults, are (clearly) natal recruits. Individuals marked as adults are potentially an undefined mix of local individuals, transients, and other bits of strangeness - sufficiently often that their apparent survival rates are often 'demonstrably' different than adult survival for individuals marked as young. So, my general suggestion is, don't make assumptions you don't have to, especially when its easy to test the particular assumption analytically.

I've been working through the examples of similar matrices in chapter 8.1.2 in the Introduction to MARK. Here, the authors first build a design matrix for a model where adult survival differs for individuals marked as young vs. marked as adult, using an "age at marking" column, an "age" column, 5 "time" columns, 5 columns for an interaction of age at marking and time, and 4 columns for an interaction of age and time (no interaction for the first time interval). They then state, on p. 8-24, that you can create a model where survival is equal for all adults - regardless of age at marking - by simply removing the columns for the "age at marking" X "time" interaction.

You spotted an error in the description in the book - thanks! What you need to do (in general terms) is (1) delete the 'age at marking' column, and (2) delete the 'age at marking X time' interaction. For some reason, step (1) was omitted (althougn it appears in some version of the chapter I have on my computer - strange). I'll post a corrected version of that section sometime today.

[cooch]

You spotted an error in the description in the book - thanks! What you need to do (in general terms) is (1) delete the 'age at marking' column, and (2) delete the 'age at marking X time' interaction. For some reason, step (1) was omitted (althougn it appears in some version of the chapter I have on my computer - strange). I'll post a corrected version of that section sometime today.

I just posted a corrected Chapter 8 - in fact, I've re-worked the entire text devoted to this particular problem.

[NMichel]

Thanks - that clears things up! You're right, checking for differences in survival between those banded as young vs. adults is a good idea, and I plan on doing that. But first I wanted to make sure I had the matrices built correctly.

Thanks for your prompt reply.

Cheers,
Nicole Michel

[cooch]

Thanks - that clears things up! You're right, checking for differences in survival between those banded as young vs. adults is a good idea, and I plan on doing that.

Good idea...

But first I wanted to make sure I had the matrices built correctly.

Indeed, and better still, the fact you 'found an error' (the only one in the entire book...really! means you have a ery good grasp of the concepts underlying design matrices, for a fairly complex model.