# [R] Question on glm for Poisson distribution.

From: Ghislain Vieilledent <ghislainv_at_gmail.com>
Date: Thu 28 Jul 2005 - 00:26:32 EST

I REALLY try to answer to my question as an autonomous student searching in the huge pile of papers on my desk and on the Internet but I can't find out the solution.
Would you mind giving me some help? Please.

```#########################################

```

I'm trying to use glm with factors:

P(Pyrale=k)=exp(-m).[(m^k)/k!]
with log(m)=Intercept+Trait(i) (link function is log for Poisson distribution)

Then I test the significativity of Trait:

Response: Pyrale

Terms added sequentially (first to last)

Df Deviance Resid. Df Resid. Dev P(>|Chi|) NULL 19 49.813
Trait 3 31.281 16 18.532 7.419e-07

Which means that variable Trait is significant for determining the value of P(Pyrale=k).

I tried to order the effects of the modalities of my variable Trait using:

> summary(Pyr.1.glm)

Call:
glm(formula = Pyrale ~ Trait, family = poisson, data = DataRav)

Deviance Residuals:
Min 1Q Median 3Q Max
-1.7117 -0.8944 -0.6237 0.6390 1.5224

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.3350 0.2294 5.819 5.92e-09 *** TraitIns&Fong -2.9444 1.0259 -2.870 0.00410 ** TraitInsecticide -2.2513 0.7434 -3.028 0.00246 ** TraitTemoin -0.2364 0.3454 -0.684 0.49372

```---
Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

(Dispersion parameter for poisson family taken to be 1)

Null deviance: 49.813 on 19 degrees of freedom
Residual deviance: 18.532 on 16 degrees of freedom
AIC: 61.85

Number of Fisher Scoring iterations: 5

##############################################################

I have therefore two questions:

- Considering the values of estimated coefficients for Trait(i), does it
mean that the bigger is the coefficient, the lower is the probability
considering the mathematical expression (exp(-m))?

- How can I check that coefficients are significatively different one from
each other (as with function TukeyHSD for other models)?

Thanks for you help.

Regards

Ghislain.

--
Ghislain Vieilledent
30, rue Bernard Ortet 31 500 TOULOUSE
06 24 62 65 07

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