[R] type III ANOVA for a nested linear model

[Mendiburu, Felipe (CIP)]

Dear Carsten

In this test, factor B would be representing to a factor of block or repetition according to as the levels of A, B, and C are in the data. Factor C this nested in A, then the model should include: B, A and C nested in A, the difference it is the error.

Model:
B	1
A	2
C(A)	6
Error	(2+6)*1 = 8
Total    

mydata<-read.table("mydata.txt",header=T)
mydata[,1]<- as.factor(mydata[,1])
mydata[,2]<- as.factor(mydata[,2])
mydata[,3]<- as.factor(mydata[,3])
model <- aov(resp ~ B + A + C/A, mydata)
summary(model)
            Df Sum Sq Mean Sq F value    Pr(>F)    
B            1 915.21  915.21 89.6476 1.274e-05 ***
A            2  33.12   16.56  1.6223   0.25621    
C            6 199.50   33.25  3.2570   0.06316 .  
Residuals    8  81.67   10.21

Best regards,

Felipe de Mendiburu
Statistician



-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch]On Behalf Of Carsten Jaeger
Sent: Tuesday, July 10, 2007 6:15 AM
To: R help list
Subject: [R] type III ANOVA for a nested linear model


Hello,

is it possible to obtain type III sums of squares for a nested model as
in the following:

lmod <- lm(resp ~ A * B + (C %in% A), mydata))

I have tried

library(car)
Anova(lmod, type="III")

but this gives me an error (and I also understand from the documentation
of Anova as well as from a previous request
(http://finzi.psych.upenn.edu/R/Rhelp02a/archive/64477.html) that it is
not possible to specify nested models with car's Anova).

anova(lmod) works, of course.

My data (given below) is balanced so I expect the results to be similar
for both type I and type III sums of squares. But are they *exactly* the
same? The editor of the journal which I'm sending my manuscript to
requests what he calls "conventional" type III tests and I'm not sure if
can convince him to accept my type I analysis.

R> mydata
      A     B     C  resp
1     1     1      1 34.12
2     1     1      2 32.45
3     1     1      3 44.55
4     1     2      1 20.88
5     1     2      2 22.32
6     1     2      3 27.71
7     2     1      6 38.20
8     2     1      7 31.62
9     2     1      8 38.71
10    2     2      6 18.93
11    2     2      7 20.57
12    2     2      8 31.55
13    3     1      9 40.81
14    3     1     10 42.23
15    3     1     11 41.26
16    3     2      9 28.41
17    3     2     10 24.07
18    3     2     11 21.16

Thanks a lot,

Carsten

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