I am having a problem with my real parameter estimates. They are not coming out as I would expect based on my design matrix. I am using a multi-state live and dead recovery model. I have 3 states and 4 attribute groups.
I think the problem stems from the fact that my 4 groups have different interval lengths. I dealt with this by including a column in the design matrix with the number of days that corresponds to each interval for each group (repeating for each stage) and using the log link with survival as was recommended:
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
The models run, but when I look at the real parameter estimates, they are not as I expect. For example, when I run a model with phi(group), I expect to see every survival estimate for each interval within a group to be the same number. This is not the case. Estimates that correspond to intervals with the same length (within a group) result in the same number, but otherwise they are different. Being in the same group is not enough even though that is how I have the design matrix set up. I believe I have my matrix set up correctly as far as which parameters belong to which grouping.
When I delete my column with my interval length information, everything works out correctly. All estimates for a given group end up being the same, as I expect. However, I can't just leave that column out because I believe including the interval length is crucial to getting better estimates. Perhaps I am missing something obvious, but I would really appreciate any help I can get. Thank you very much.
Heidi