forcing multiple individual covariate betas identical?

[WHochachka]

I have a "simple" CJR model that I cannot figure out how to write in MARK. I'm looking at local survival probabilities of migrating birds passing through a banding station, trying to estimate the daily probability that a bird, if present, will leave. My problem is that I have two classes of explanatory variables that are on different time scales. On the within-year time scale, weather variables (wind, rain) change daily and affect both the probability of local survival and re-trapping probability. On the among-year time scale, I am interested in knowing whether there has been systematic change in local survival and retrapping probability over the last 30 years. Coding the within-year linear constraints in no problem when analysing a single year's data. Coding the among-year changes is no problem when within-year variation is ignored. My problem is trying to combine the within-year and among-year linear constraints into the same model.

I can create a design matrix that gets me most of the way to where I want to be. In this design matrix, each individual day's weather variables are treated as individual covariates (I have over 200 of these: 51 trapping sessions, 4 weather variables per day). And then year is just treated as a routine linear constraint in the design matrix. In GLM terms, weather is nested within year.

However, my problem is that it makes no biological sense that I should be estimating 200 weather-related regression coefficients. There are actually 4: wind-on-Phi, rain-on-Phi, wind-on-p, and rain-on-p. I.e., in GLM terms, both weather and year should be treated as main effects with no nesting. Can I persuade MARK to force a series of individual-covariate beta values to be estimated as identical? I know that I can fix the beta values to be identical by hard-wiring specific values into MARK, but I could not find (the Gentle Guide, help files, CSU pdf lecture notes, or this forum) an explanation of how the values could be estimated as identical.

I have attempted the cheesy (and wrong) approach of estimating daily beta values for only a single weather-predictor at one time, with the thought of then fixing these values in a subsequent MARK run that would try to estimate other weather effects. However, after about 48 hours of running on a very fast computer, with well over 1000 iterations, MARK seems to have suffered a memory leak and bailed out of the analysis. So, I do not think that this sort of work-around is even logistically feasible, let alone correct.

Any insights on how to code a model that constrains several individual covariates to be estimated as having the same beta value would be greatly appreciated.

Wesley Hochachka

[gwhite]

Wesley:
You would only estimate 4 weather variables, but each of these 4 columns would contain all 50 observations. That is, you would end up with a design matrix that looks like:
1 Rain1 Wind1 Temp1 Cloud1
1 Rain2 Wind2 Temp2 Cloud2
1 Rain3 Wind3 Temp3 Cloud3
...
1 Rain50 Wind50 Temp50 Cloud50

Note that you do not want to use the "Standardize Individual Covariates" option here, or the measurement scale of the 50 variables in a column will change. IF you need to scale them, use the product individual covariate function. So, to reduce all the values of rain by a factor of 10, use product(rain1,0.01) instead of just rain1.

I think you just about had this figured out on your own -- but hadn't realized what it means to put the different values of individual covariates all in the same column, so that they are all contributing to the same beta estimate.

Gary