[R] question about poisson regression

[Achim Zeileis]

On Tue, 14 May 2013, meng wrote:

> Many thanks.
> Another question:
> model<- glm(count ~ drug*result, family = poisson)
> 
> > anova(model,test="Chisq")
>          Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
> NULL                            3     47.522              
> drug         1    0.032         2     47.491   0.85858    
> result       1   41.187         1      6.304 1.383e-10 ***
> drug:result  1    6.304         0      0.000   0.01205 *  
> 
> T! he pvalue of drug is 0.85858,which indicates that the total count of
> drug1 and drug2 are not significantly different at 0.05 level.
> 
> But:
> 
> > summary(model)
> Coefficients:
>               Estimate Std. Error z value Pr(>|z|)    
> (Intercept)     2.0794     0.3536   5.882 4.06e-09 ***
> drug2           0.9163     0.4183   2.190   0.0285 *  
> result2         1.9095     0.3788   5.041 4.64e-07 ***
> drug2:result2  -1.1211     0.4650  -2.411   0.0159 *  
> 
> The pvalue of drug2 is  0.0285 *  ,which indicates that the total count of
> drug2 is significantly different from drug1 at 0.05 level,which contradict
> to the result of anova.
> 
> Can you give me some help about that ?

The anova tests the main effect of drug (without any other variable in the 
model) which is non-significant (62 vs. 64 observations).

The summary gives the drug2 effect which pertains to the reference group 
(i.e., result = 1) and this is significant (8 vs. 20 observations).

However, either result is probably not interesting. I guess the 
interaction (and possibly the result main effect) is the quantity of 
interest.
Z

> Many thanks.
> 
> 
> Best
> 
> 
> 
> 
> 
> 
> 
> At 2013-05-13 18:56:01,"Achim Zeileis" <Achim.Zeileis at uibk.ac.at> wrote:
> >On Mon, 13 May 2013, meng wrote:
> >
> >> Hi all:
> >> I have a question about poisson regression.
> >>
> >> My data:
> >> drug result count
> >> 1       1          8
> >> 1       2        54
> >> 2       1       20
> >> 2       2      44
> >>
> >> My model:
> >> model<- glm(count ~ drug*result, family = poisson)
> >>
> >> My result:
> >> summary(model)
> >>
> >> Coefficients:
> >>              Estimate Std. Error z value Pr(>|z|)
> >> (Intercept)     2.0794     0.3536   5.882 4.06e-09 ***
> >> drug2           0.9163     0.4183   2.190   0.0285 *
> >> result2         1.9095     0.3788   5.041 4.64e-07 ***
> >> drug2:result2  -1.1211     0.4650  -2.411   0.0159 *
> >>
> >> Calculation of coefficients:
> >> Intercept: drug=1 and result=1,the corresponding count is 8.So log(8) is 
> 2.079442 which is Intercept.
> >>
> >> My question: How is drug2 calculated? log(64)-log(62) or something like 
> >> that(indicates the difference between drug2 and drug1) ? I've searched 
> >> and tried many times for all possible solutions,but the result is not 
> >> 0.9163.So,how is drug2 calculated ?
> >
> >It's the drug2 effect (on a log-scale) for result=1, i.e.,
> >log(20) - log(8).
> >
> >The four coefficients are:
> >
> >R> y <- c(8, 20, 54, 44)
> >R> c(log(y[1]), log(y[2]) - log(y[1]), log(y[3]) - log(y[1]),
> >+    (log(y[4]) - log(y[3])) - (log(y[2]) - log(y[1])))
> >[1]  2.0794415  0.9162907  1.9095425 -1.1210851
> >
> >> Many thanks!
> >>
> >>
> >> Best
> >> 	[[alternative HTML version deleted]]
> >>
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> tml
> >> and provide commented, minimal, self-contained, reproducible code.
> >>
> 
> 
> 
>