Stage Based Models

[jras]

I'm looking for a little direction with multigroup models. Our data set has individuals classified into 3 size-based stages. We would like to be able to estimate parameters for each stage, but also any effects that may occur due to "transition paths" they take, such as transitioning from the first stage to the second as compared to going staight to the last stage in one year. To compound the problem individuals may also remain in a given stage for the entire four year study period. Originally, we thought something similar to an Age-based model, but the variability in stage transition makes this unfeasible. Any suggestions of how to approach this would be greatly appreciated.

[cooch]

I'm looking for a little direction with multigroup models. Our data set has individuals classified into 3 size-based stages. We would like to be able to estimate parameters for each stage, but also any effects that may occur due to "transition paths" they take, such as transitioning from the first stage to the second as compared to going staight to the last stage in one year. To compound the problem individuals may also remain in a given stage for the entire four year study period. Originally, we thought something similar to an Age-based model, but the variability in stage transition makes this unfeasible. Any suggestions of how to approach this would be greatly appreciated.

Have a look at the multi-state chapter of 'the book' (if you haven't already):

http://www.phidot.org/software/mark/docs/book/

Lays out the basics of how conceptually you can estimate the parameters you're interested in.

However, the problem with stage models - where transition probabilities are potentially a function of how long individuals have been in a given stage - is that they are in practice semi-Markov models, not first order Markov, as typically assumed by the classic M-S models (aka the Arnason-Schwarz models), as well as standard 'matrix modeling' approaches (sensu Caswell 2001). As such, they violate the assumption of the standard M-S models which assume no heterogeneity in the probability of a transition from a stage among individuals in that stage.

There are some approaches you could consider to handle this sort of 'stage duration' heterogeneity, but the best starting point is (i) read the M-S chapter, then (ii) the papers on application of M-S models to various things of interest (i.e., papers on the subject by Nichols, Kendall, Schwarz and the rest of the usual suspects).