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How to interpreting the exponential coefficent in poisson regression with offset?



Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)
2019 Moderator Election Q&A - Questionnaire
2019 Community Moderator Election ResultsStochastic gradient descent in logistic regressionpredict with Multinomial Logistic RegressionLinear regression with non-symmetric cost function?Do logistic regression and softmax regression do the same thing?Logistic regression with high cardinality categorical variableInterpreting lasso logistic regression feature coefficients in multiclass problemLogistic Regression with TensorflowLogistic regression in pythonHow do we solve this logistic regression question?Deriving new continuous variable out of logistic regression coefficients










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I am trying to find the village level risk factors for malaria. Therefore, I ran a poisson model in r with the prevalence of malaria(y) as dependent variable, altitude(x1) and Forestation(x2) as independent variable and log of Population(x3) as offset.



glmer(y~x1+x2+(1|cluster), family = poisson, offset = log(x3))


From what I have read, I understand that the interpretation of model with offset is different than a non-offset model.



It would be very helpful, If any one can clear the air on how to interpret the coefficients and exponential coefficient in the above-mentioned case.



Thanks










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    0












    $begingroup$


    I am trying to find the village level risk factors for malaria. Therefore, I ran a poisson model in r with the prevalence of malaria(y) as dependent variable, altitude(x1) and Forestation(x2) as independent variable and log of Population(x3) as offset.



    glmer(y~x1+x2+(1|cluster), family = poisson, offset = log(x3))


    From what I have read, I understand that the interpretation of model with offset is different than a non-offset model.



    It would be very helpful, If any one can clear the air on how to interpret the coefficients and exponential coefficient in the above-mentioned case.



    Thanks










    share|improve this question







    New contributor




    Mrinal9 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$














      0












      0








      0





      $begingroup$


      I am trying to find the village level risk factors for malaria. Therefore, I ran a poisson model in r with the prevalence of malaria(y) as dependent variable, altitude(x1) and Forestation(x2) as independent variable and log of Population(x3) as offset.



      glmer(y~x1+x2+(1|cluster), family = poisson, offset = log(x3))


      From what I have read, I understand that the interpretation of model with offset is different than a non-offset model.



      It would be very helpful, If any one can clear the air on how to interpret the coefficients and exponential coefficient in the above-mentioned case.



      Thanks










      share|improve this question







      New contributor




      Mrinal9 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      I am trying to find the village level risk factors for malaria. Therefore, I ran a poisson model in r with the prevalence of malaria(y) as dependent variable, altitude(x1) and Forestation(x2) as independent variable and log of Population(x3) as offset.



      glmer(y~x1+x2+(1|cluster), family = poisson, offset = log(x3))


      From what I have read, I understand that the interpretation of model with offset is different than a non-offset model.



      It would be very helpful, If any one can clear the air on how to interpret the coefficients and exponential coefficient in the above-mentioned case.



      Thanks







      logistic-regression






      share|improve this question







      New contributor




      Mrinal9 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











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      asked 14 mins ago









      Mrinal9Mrinal9

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          $begingroup$

          The offset means "exposure", so when you are calculating a regression with offset, instead of calculating absolute values, you are calculating ratios.



          You are changing "number of thefts" for "number of thefts for every 10.000 vehicles"



          $y = x1+x2+(1|cluster) + log(x_3)$: This is the equation you are calculating.



          I think you are missing a log in $y$ because the offset and the endogenous variable have to form a ratio:



          $log(y) = x1 + x2+(1|cluster)+log(x_3)$



          $log(y)-log(x_3) = x1 + x2+(1|cluster)$



          $log(fracyx_3) = x1 + x2+(1|cluster)$



          $log(ratio) = x1 + x2+(1|cluster)$





          share








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            0












            $begingroup$

            The offset means "exposure", so when you are calculating a regression with offset, instead of calculating absolute values, you are calculating ratios.



            You are changing "number of thefts" for "number of thefts for every 10.000 vehicles"



            $y = x1+x2+(1|cluster) + log(x_3)$: This is the equation you are calculating.



            I think you are missing a log in $y$ because the offset and the endogenous variable have to form a ratio:



            $log(y) = x1 + x2+(1|cluster)+log(x_3)$



            $log(y)-log(x_3) = x1 + x2+(1|cluster)$



            $log(fracyx_3) = x1 + x2+(1|cluster)$



            $log(ratio) = x1 + x2+(1|cluster)$





            share








            New contributor




            Juan Esteban de la Calle is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
            Check out our Code of Conduct.






            $endgroup$

















              0












              $begingroup$

              The offset means "exposure", so when you are calculating a regression with offset, instead of calculating absolute values, you are calculating ratios.



              You are changing "number of thefts" for "number of thefts for every 10.000 vehicles"



              $y = x1+x2+(1|cluster) + log(x_3)$: This is the equation you are calculating.



              I think you are missing a log in $y$ because the offset and the endogenous variable have to form a ratio:



              $log(y) = x1 + x2+(1|cluster)+log(x_3)$



              $log(y)-log(x_3) = x1 + x2+(1|cluster)$



              $log(fracyx_3) = x1 + x2+(1|cluster)$



              $log(ratio) = x1 + x2+(1|cluster)$





              share








              New contributor




              Juan Esteban de la Calle is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
              Check out our Code of Conduct.






              $endgroup$















                0












                0








                0





                $begingroup$

                The offset means "exposure", so when you are calculating a regression with offset, instead of calculating absolute values, you are calculating ratios.



                You are changing "number of thefts" for "number of thefts for every 10.000 vehicles"



                $y = x1+x2+(1|cluster) + log(x_3)$: This is the equation you are calculating.



                I think you are missing a log in $y$ because the offset and the endogenous variable have to form a ratio:



                $log(y) = x1 + x2+(1|cluster)+log(x_3)$



                $log(y)-log(x_3) = x1 + x2+(1|cluster)$



                $log(fracyx_3) = x1 + x2+(1|cluster)$



                $log(ratio) = x1 + x2+(1|cluster)$





                share








                New contributor




                Juan Esteban de la Calle is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.






                $endgroup$



                The offset means "exposure", so when you are calculating a regression with offset, instead of calculating absolute values, you are calculating ratios.



                You are changing "number of thefts" for "number of thefts for every 10.000 vehicles"



                $y = x1+x2+(1|cluster) + log(x_3)$: This is the equation you are calculating.



                I think you are missing a log in $y$ because the offset and the endogenous variable have to form a ratio:



                $log(y) = x1 + x2+(1|cluster)+log(x_3)$



                $log(y)-log(x_3) = x1 + x2+(1|cluster)$



                $log(fracyx_3) = x1 + x2+(1|cluster)$



                $log(ratio) = x1 + x2+(1|cluster)$






                share








                New contributor




                Juan Esteban de la Calle is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.








                share


                share






                New contributor




                Juan Esteban de la Calle is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.









                answered 6 mins ago









                Juan Esteban de la CalleJuan Esteban de la Calle

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