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# Offset in a multinomial logistic regression where exposure durations varied

Hello:  I would like to do a multinomial logistic regression.  There are three response levels, and two factors (class) variables as the explanatory variables.  My problem is the "exposure" to both of the class variables varies by observation.  In a binomial logistic regression I know I could include the exposure as an offset variable, but I can't figure out how to calculate what offset I should use when there are two factors, each with varying exposures.  Any ideas?

More detail:  I'm trying to model probabilities of a fish moving in a stream.

My 3 responses are the fish 1) moved upstream; 2) moved downstream, or 3) moved and returned to its former location.

The two nominal response variables are light level (coded as day or night) and tide (coded as flooding or ebbing).

The study took place over several months, so fish that were followed early in the study experienced shorter daylengths (exposure to light) than fish that were followed later in the study.  The same is true of the tides - fish were exposed to varying durations of flooding or ebbing tides.  So how do I take the different day lengths and tide durations into account when trying to evaluate the fish response to those factors?

Example code:

Proc Logistic;

Class DayOrNight  (ref='Day')

FloodOrEbb (ref='Ebb');

Model Movement = DayOrNight | FloodOrEbb / Offset = ????;

Run;

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