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A variable with a fixed coefficient of 1. Offsets are commonly used in Poisson regression to allow the modeling of rates instead of counts.

A variable with a fixed coefficient of 1. Offsets are commonly used in Poisson regression to allow the modeling of rates instead of counts. The offset indexes the opportunity for an event to have occurred. For example, a researcher may want to investigate the number of events per unit time, but some study units were observed for a week and others for a month, thus it is expected that there will have been more events for the latter units. This can be accounted for by including an offset variable that indexes the length of time each unit was observed. For example, below is a Poisson regression that has been adapted with an offset to model rates:
$$ \ln\bigg(\frac{{\rm count}}{{\rm time}}\bigg) = \beta_0 + \beta_1X $$ $$ \ln({\rm count})-\ln({\rm time}) = \beta_0 + \beta_1X $$ $$ {\rm count} = {\rm time}\cdot\exp(\beta_0 + \beta_1X) $$ The most common offsets are time and spatial area.

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