Say for example I want to see the rate of injury for firefighter vs police vs soldier.(adsbygoogle = window.adsbygoogle || []).push({});

##InjuryCount_{i}## The number of injuries recorded for the ith person over time

##T_{i} ## Time the person was followed. Varies from person to person.

##I(f)_{i}## indicator for ith person of being a firefighter or not, police is baseline

##I(s)_{i}## indicator for the ith person of being a soldier or not, police is baseline

Then I would model ##log(InjuryCount_{i}/T_{i})=\beta_{0} +\beta_{1}I(f)_{i}+\beta_{2}I(s)_{i}. ##

Where the regression model is either a poisson, negative binomial, or quasi poisson.

Now how would I intepret the coefficients?

Is ##exp(\beta{0} )## the estimated rate of injury for the baseline group. Or is it the estimated mean rate for the baseline group. I'm not sure which.

If we look at individuals, then I can say that it is the estimated rate of injury for someone belonging in the baseline group.

But if I look at the group, I can say that it is the estimated mean rate for the baseline group as a whole.

Not sure which one is right.

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# A Interpreting Poisson Regression Estimates across groups

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