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I'm still fundamentally confused how one should evaluate how well a GLM Poisson regression model fits the data. Here is an example, using R and the dataframe total_data, whereby food_type is a categorical variable.

Call:                                                                                                                      
glm(formula = discrete_counts ~ food_type, family = poisson, data = total_data)                                
Deviance Residuals:                                                                                                                                        
 Min       1Q   Median       3Q      Max              
 -0.1808  -0.1808  -0.1698  -0.1530   2.7221                                                                                          
Coefficients:                                                                                                                                                          
Estimate Std. Error  z value Pr(>|z|)                                                                                                  
(Intercept)         -4.11341    0.01711 -240.456  < 2e-16 ***                                                                     
food_typeVEG1    -0.12623    0.02910   -4.337 1.44e-05 ***                                                           
food_typeVEG2    -0.58227    0.03530  -16.495  < 2e-16 ***                                                               
food_typeVEG3 -0.14338    0.04392   -3.264   0.0011 **                                                             
food_typeVEG4 -0.10044    0.04365   -2.301   0.0214 *                                                                 
food_typeVEG5    -0.33368    0.03632   -9.187  < 2e-16 ***                                                                     
 ---                                                                                                                                                        
 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1                                                                        

(Dispersion parameter for poisson family taken to be 1)                   

     Null deviance: 72673  on 617065  degrees of freedom                                                                   
Residual deviance: 72340  on 617060  degrees of freedom                                                                  
AIC: 89300                                                                                                                                                                                                                                                                                                                     
Number of Fisher Scoring iterations: 6   

So, the residual deviance is less than the degrees of freedom. So, this model doesn't suffer from overdisperson. The AIC score is huge, which means the model has little predictive value.

How else can I evaluate how good this model is?

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use the function P_disp() found in the "msme" package. It will give you the dispersion parameter (dp). if the dp<1 your model is good;conversively, if the dp>1 the model is not fitting well your data.

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  • $\begingroup$ Welcome to the site! We favour thorough answers. Could you expand on yours to make it more helpful? $\endgroup$ – mkt Apr 4 '18 at 11:04
  • $\begingroup$ Thanks for the answer. A few more details and references would be helpful for others. Otherwise, this is a great answer. $\endgroup$ – ShanZhengYang Apr 4 '18 at 15:18

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