The Complementary Log-Log Model for Continuous-Time Processes

As already noted, the logit model presumes that events can only occur at discrete points in time. For most applications, however, ties occur because event times are measured coarsely even though events can actually occur at any point in time. Aside from the implausibility of the logit model for such data, the model suffers from a lack of invariance to the length of the time interval. In other words, switching from person-months to person-years changes the model in a fundamental way, so that coefficients are not directly comparable across intervals of different length.

To avoid these difficulties, we can first specify a model for continuous-time data and from that derive a model for ...

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