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I am trying to draw some conclusions about the fitting of one model, but after looking at some examples in the internet I just can't get a hold of it, the interpretation of the results I mean. Since all of the example reach a different conclusion with results I see really similar. I have some count data with high variability so I tried fitting a negative binomial model to the data and got the following results

summary(monb)

Call:
glm.nb(formula = Counts ~ Hour + weekday, data = modtab, init.theta = 0.2910141397, 
    link = log)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
   -0.8156  -0.7714  -0.6790  -0.5941   2.5479  

Coefficients:
                   Estimate Std. Error z value Pr(>|z|)  
(Intercept)       -0.520449   0.284584  -1.829   0.0674 .
Hour              -0.007665   0.013999  -0.548   0.5840  
weekdayDonnerstag  0.044863   0.343570   0.131   0.8961  
weekdayFreitag    -0.742229   0.365964  -2.028   0.0425 *
weekdayMittwoch   -0.448842   0.381636  -1.176   0.2396  
weekdayMontag     -0.493662   0.353680  -1.396   0.1628  
weekdaySamstag    -0.006994   0.336181  -0.021   0.9834  
weekdaySonntag    -0.235636   0.343460  -0.686   0.4927  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for Negative Binomial(0.291) family taken to be 1)

    Null deviance: 383.88  on 633  degrees of freedom
    Residual deviance: 375.59  on 626  degrees of freedom
    AIC: 1067.4

Number of Fisher Scoring iterations: 1


      Theta:  0.2910 
      Std. Err.:  0.0453 

      2 x log-likelihood:  -1049.4140 

I think that the model does not fit the data properly but I really can say any valid arguments of why. Can you say what are the reasons for a bad fitting or if I am wrong what are the evidences for a good fitting by looking at this summary?

Thank you

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Maybe you could plot the model with plot(monb) and look at the QQ plot and the residual vs. fitted plot.

The P-values (column "Pr(>|z|)") are quite large, which is sometimes interpreted as bad model.

If you have an alternative model, for instance glm.nb(Count~1, data=modtab), you can compare the AIC of both models.

If you look at the coefficient estimates +/- standard error, you find that the estimates are sometimes not distinguishable from 0, in which case they have no influence.

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  • $\begingroup$ Thank you. For the AIC value is it some acceptable value? for example a model's with AIC 1277 and another with AIC 1067. Can I say that the second model is better? or the AIC is still to high for making that assumption? $\endgroup$ – Tarigarma Aug 27 '13 at 7:54
  • $\begingroup$ The model with AIC 1067 is "better", assuming it did run on the same dataset. AIC gives no information on the absolute quality of the model. See wikipedia for more information. $\endgroup$ – Karsten W. Aug 27 '13 at 21:46

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