[R] time varying covariates

[Martin Wagner]

Hello,

I am trying to model an intensity function with time-varying covariates.
Before, I have successfully defined a log likelihood function for a 
Power-Law Process (lambda(t)=alpha*beta*t^(beta-1))  with two paramters 
and no covariates for a repairable systems with failure times (t).
This function was maximized with R optim. No problem!

But now I want to include a covariate indicating a time-varying value at 
each failure time t. For constant covariates, the procedure is feasible :


leads to following log likelihood funciton:


here zi are the covariates which are constant for each unit i under 
observation. tij are the failure time for failure j of unit i.

Do you know how to formulate a log likelihood function for covariates 
which vary for each tj of each unit i ?

Thank you very much
Best regards

Martin Wagner
Berlin University of Technology