[R] time varying covariates

From: Martin Wagner <martin.wagner_at_ilr.tu-berlin.de>
Date: Thu 14 Sep 2006 - 14:36:53 GMT


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

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