Poisson regression using Minitab

Tahirawan77

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Hi,

I have a Response variable Y which consist of 'count of events' on monthly basis.
I have 7 Predictor variables: X1 ...X7 (All are counts)

First I performed a uni-variant analysis by using Minitab 'Fitted line plot' for each X vs Y. (Although it is not statistically correct as Fitted line plot requires Continuous response variable). But X1, X4, X6 & X7 were identified as statistically significant predictors. See detail graphs attached

Next I performed a 'Poisson Regression' using Minitab. I used 'Backward elimination' method with 0.05 as 'Alpha to remove'. I got X2, X4 and X7 as statistically significant factors. See results attached.

Next I again performed a 'Poisson Regression' using Minitab. Again I used 'Backward elimination' method but this time I used 0.1 as 'Alpha to remove'. I got X1, X2, X5 and X7 as statistically significant factors. See results attached.

My questions is in my first Poisson regression analysis., why X1 & X6 were not identified as statistically significant as they were identified earlier in the Fitted Line Plot. Further X2 was not statistically significant on Fitted line plot but became significant in the Poisson regression?

Second question is why big difference between the two Poisson regression results.

Thanks
 

Attachments

  • Y vs X1.JPG
    Y vs X1.JPG
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  • Y vs X2.JPG
    Y vs X2.JPG
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  • Y vs X3.JPG
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  • Y vs X4.JPG
    Y vs X4.JPG
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  • Y vs X5.JPG
    Y vs X5.JPG
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  • Y vs X6.JPG
    Y vs X6.JPG
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  • Y vs X7.JPG
    Y vs X7.JPG
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  • Poisson regression Alpha 0.05.JPG
    Poisson regression Alpha 0.05.JPG
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  • Poisson regression Alpha 0.1.JPG
    Poisson regression Alpha 0.1.JPG
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Semoi

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Probably you have colinear variables. It might be a good idea to calculate the variance inflation factor as well.
 

Tahirawan77

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Hi Semoi,

thanks for your reply. Pls. see attached VIF and Correlations and i think this is not the issue here. Do you agree?
 

Attachments

  • Coorelation of predictors.JPG
    Coorelation of predictors.JPG
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  • VIF Poisson 0.1.JPG
    VIF Poisson 0.1.JPG
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  • VIF Poisson 0.05.JPG
    VIF Poisson 0.05.JPG
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Semoi

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You did not calculate the VIFs for (X1, X4, X6, X7) UNION (X2, X4, X7), which is (X1, X2, X4, X6, X7). However, your correlation plot shows that the parameters are not independent. So my guess is still that this might be an issue. In particular, because of X2:
* the linear regression yields p=30%,
* while the Poisson regression yields p<0.1%.
Therefore, for X2 this is not an issue of being just above or just below the critical p-value (= 5%). For X1 this might be different, because the linear regression yields p=4.8%.

However, if you are "pretty sure" that the variables are independent -- maybe due to the fact what the parameters represent --, you might want to check the model assumptions. Since you have a small dataset I doubt that this investigation is fruitful -- only extreme would be detectable. However, analysing the residuals and leverages must/should be part of every evaluation. E.g. judging from the linear regression plot for X6 it might be the case that you included a point with a "too large" leverage. In a linear regression the data-points are not weighted equally, but by their leverage. Thus, removing a single data-point could shift/alter the result significantly.
 
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