Main effects-Interactions-Missing Data

posts related to the RMark library, which may not be of general interest to users of 'classic' MARK

Main effects-Interactions-Missing Data

Postby jlaake » Tue Nov 22, 2022 9:04 pm

Recently I received a query from a student about a formula something to the effect of ~-1+fac1:fac2 where fac1 and fac2 are factor variables. They were using this formulation to create an identity design matrix which allows use of the sin link. The student's major advisor was concerned that they were using a model with interactions and no main effects and they thought this was a problem. I have gotten messages like this all too frequently due to a lack of understanding about what the formula does and that you can have alternative design matrices for the exact same model. If there are data for each of the combination of fac1*fac2 then ~-1+fac1:fac2 and ~fac1*fac2 will produce the same models (ie same likelihood) but with different design matrices. The beta parameters which relate to the design matrix will differ but the real parameters will be the same.

Whether you use ~-1+fac1:fac2 or ~fac1*fac2 is a matter of personal preference and the former does allow use of the sin link. In section C15 of Appendix C of Cooch and White - Gentle Introduction I suggest using something like ~-1+age:time for a situation in which only young are released each year for a CJS model and you want to fit an age*time model because you want to drop the age 1+ for time 1 term. Both age and time here are factor variables. An alternative that I hadn't considered at the time was to relevel the time factor level so time1 wasn't the intercept value and then the missing value is dropped automatically when using age*time.

I describe the above issues in the pdf titled "Main Effects-Interactions-Missing data" that Evan kindly put into the RMark Documentation Archive (http://www.phidot.org/software/mark/rmark/RMarkDocumentation.zip. The link to the documentation archive appears the first time you type library(RMark) in an R session. If you haven't spend any time reading the documents, please do so. If you get questions like this from your major advisor share the pdf with them. If you have any feedback about this pdf or any of the other files in the archive, please let me know. I don't guarantee I'll get to changes right away but I'll do my best.
jlaake
 
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