I have a question concerning the use of log link and its impact on covariates in the design matrix. I am using a multi-state live and dead recovery model. I have 3 states and 4 attribute groups.
Each attribute group has time intervals of different lengths, so I used this method to deal with that:
Re: [ http://www.phidot.org ] groups with varying intervals
by Jon Runge » Wed Apr 25, 2007 9:30 am
I asked Gary White the same question awhile back, here's response:
"You will have to include the time interval between occasions (call it L) as a covariate in a log link for the parameter. So, assume you are estimating survival, S, across an interval of length L. Then, log(S)=B1*L, and S=exp(B1*L)=exp(B1)^L. So, the unit length of survival (day) is exp(B1), and the interval survival is exp(B1)^L = DSR^L where DSR = Daily Survival Rate."
Just to be complete (ie risk stating the obvious): You model the time interval covariate with a column for L in the design matrix. Then you need to have rows specific to each group and time period to capture the unique interval for each group/time combination. Also, make sure that phi has a log link. Don't constrain any parameters with log link to be 0--that won't work. Finally, note that DSR is just an example. You could use unit length = 1 week, 1 month, whatever you want your survival estimate to mean biologically.
--Jon
Jon Runge
However, I am concerned about what effect using this trick will have on a variable I included in my analyses. I created a column for temperature in the DM and temperatures tended to increase over time. The modeling found a negative effect of temperature. However, I expected (and all literature suggests) that there would be a positive effect of temperature. I also noticed that interval length had a negative effect (longer interval yielded lower survival probabilities). I am curious if perhaps MARK is not treating my temps as it should due to the trick I used to create time intervals of the correct lengths and this is why temperature is coming out with a negative effect. Am I modeling temperature incorrectly or is this really the effect of temperature in my models? Is there any fix for this? I am also concerned about the effect that the log link may have, if any, on the individual covariates I am modeling as well.
I would strongly appreciate any feedback I can get on this. I have searched the forum and read the manual, but I haven't seen anything that really addresses this. If I missed something, please tell me where to look. Thank you very much,
Heidi