# [R] test for factor effect with nested glm

From: Marie-Agnes Coutellec <marie-agnes.coutellec_at_rennes.inra.fr>
Date: Thu, 20 Dec 2007 16:52:19 +0100

Dear all,

I use a nested design with lm and glm, with factor2 nested within factor1. In order to test for the significance of both factors, I use anova tables on the obtained models such as follows:

/> mod1<-lm(A~factor1/factor2)
> amod1<-anova(mod1, test="F")

Analysis of Variance Table
Response: A

```                   Df Sum Sq Mean Sq F value    Pr(>F)
factor1            15  85.99    5.73  3.1332 8.702e-05 ***
factor1:factor2    42 131.75    3.14  1.7145  0.005654 **
Residuals         308 563.52    1.83                      /

```

and recalculate the Fvalue for factor1 as follows:

/> ffactor1<-(85.99/15)/(131.75/42)
> fpop

[1] 1.827491
> 1-pf(ffactor1,15,42)

[1] 0.06285258/

My question is: am I allowed to do the same with an Analysis of Deviance table, calculated on a glm model, as done hereafter:

```/> mod2<-glm(M~factor1/factor2, family=Gamma(link=identity))
```

> amod2<-anova(mod2,test="F")
> amod2

Analysis of Deviance Table
Model: Gamma, link: identity
Response: M
Terms added sequentially (first to last)
```                 Df Deviance Resid. Df Resid. Dev      F    Pr(>F)
NULL                               365    164.486
factor1          15   18.699       350    145.787 3.4365 1.997e-05 ***
factor1:factor2  42   38.973       308    106.814 2.5579 2.319e-06 ***
```
```---

> ffactor1<-(18.699/15)/(38.973/42)

[1] 1.343422

> 1-pf(ffactor1,15,42)/

[1] 0.2206373

Thanks in advance for your answer, and sorry if my question doesn't fit
with the R-help list.

Agnès Coutellec

--

Marie-Agnès Coutellec
UMR INRA-Agrocampus 985 EQHC
Equipe Ecotoxicologie et Qualité des Milieux Aquatiques
65 rue de Saint-Brieuc - CS 84215
35042 Rennes cedex - FRANCE

tél.: +33(0)2 23 48 52 48
fax:  +33(0)2 23 48 54 40

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Received on Thu 20 Dec 2007 - 15:55:50 GMT

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