# How to consider the duration of categorical independent variable?

I am trying to model the effect of weather condition on number of crashes in a road. Weather is categorized as dry and wet. Most of the cases, crashes in dry weather condition are frequent as the dry condition is dominating. For instance, after analyzing the weather data, I found that the weather was dry in 90% time of the whole year. Can you suggest me any modelling technique that can consider the duration of such variables? I have already tried with normalizing the dependent variable by the duration.

## 1 Answer

I assume your response variable is a count of number of accidents. Then you want to model the rate of accident events (rate is expected number of events per unit of time). That can be done with poisson regression (search this site for many examples). You should not divide by duration, you should use the logarithm of duration as an offset. This is explained in many posts here: When to use an offset in a Poisson regression? and Goodness of fit and which model to choose linear regression or Poisson