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A Interpreting Poisson Regression Estimates across groups

  1. Apr 25, 2017 #1
    Say for example I want to see the rate of injury for firefighter vs police vs soldier.

    ##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.
     
  2. jcsd
  3. Apr 25, 2017 #2

    Dale

    Staff: Mentor

    Do you have subjects where the same subject is both a firefighter and a soldier?
     
  4. Apr 26, 2017 #3
    No, but what might happen if there is overlap?

    The way I set up the regression equation would result in log(response)=B_0+0+0 for the police(baseline group) since I suppose that would have to be the result from the categories being mutually exclusive.
     
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