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I have data on claim frequency and several predictors like age, gender of insured person and characteristic of vehicle. I have checked for the assumption of mean equal to variance of a Poisson model. Now I want to test for multicollinearity and homocedasticity. How am I supposed to proceed so that I choose a suitable model and fit it using the Poisson regression model?

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  • $\begingroup$ One possibility to overcome the mean equal variance issue in poisson-regression is, to look at a quasipoisson-model which estimates a scaling parameter for the variance being able to change w.r.t mean. To check whether multicollinearity and homoscedasitcity is really a propblem I would suggest to develope a model-framework and estimate the corresponding parameters. Then you should look at the residuals. $\endgroup$ – Druss2k Feb 21 '14 at 23:03
  • $\begingroup$ If your counts are typically high, the usual diagnostic approaches to checking the model's variance assumption apply (i.e. to look at one of the types of standardized residuals for GLMs and do a display suitable for checking that those have constant variance much as one would with linear models). $\endgroup$ – Glen_b Feb 21 '14 at 23:20
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If the variance equals the mean (the assumption for the Poisson that you say you have checked) then the only way to see homoscedasticity is if the mean does not change, i.e. you are fitting a straight line. So that is usually not something that we check in Poisson regression.

You can look for multicolinearity by looking at plots and correlations of the predictor variables. Then to see the effect of this on the regression fit the model with fewer predictor variables and see how much it changes the remaining slope estimates and how much it changes the overall fit (deviance or other measure).

Most important is to incorporate your knowledge of the variables and how they should work together.

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