Decompose numerical factor into orthog. poly parts - R-help

Mon, Sep 30, 2002 12:26 AM #

Multiple degrees of freedom terms can be split up in the anova table using

lsmod <- aov(time ~ spinner + order + d)  # using aov( ) makes things a bit
easier.
summary(lsmod, split = list(.....))

ie the splitting is done using summary.aov and the split= argument allows
the split to be controlled in an orderly way.  The details are just too long
to fit into this margin, though...

Bill Venables.

 -----Original Message-----
From: 	John Maindonald [mailto:john.maindonald at anu.edu.au] 
Sent:	Monday, September 30, 2002 3:58 PM
To:	Murray Jorgensen
Cc:	r-help at stat.math.ethz.ch
Subject:	Re: [R] Decompose numerical factor into orthog. poly parts

The following perhaps ought to work:

d <- ordered(diam[treat])
lsmod <- lm(time ~ spinner + order + d)
anova(lsmod)

Unfortunately, it gives exactly the same result as before.
The following, which is inelegant, does split up the orthogonal
terms:

d <- ordered(diam[treat])
p3 <- model.matrix(~ -1 + d)
lsmod <- lm(time ~ spinner + order + p3[,1]+p3[,2]+p3[,3])
anova(lsmod)

Note that orthogonal polynomial contrasts are the default for
ordered factors.

John Maindonald

Consider the following analysis of a class experiment done as a Latin

Square:

 > spinner <- gl(4,4,16,label=c("Murray","Angela","Shasha","Stephen"))
 order <- gl(4,1,16)
 treat <- scan()

1:  1 2 4 3
5:  4 3 1 2
9:  3 4 2 1
13:  2 1 3 4
17:
Read 16 items

 coin <- factor(treat,label=c("5c","10c","20c","50c"))
 time <- scan()

1: 12.0 13.3 13.0 8.9
5: 9.7 7.2 7.3 8.6
9: 9.2 9.0 7.6 7.4
13: 10.1 5.7 7.5 8.9
17:
Read 16 items

 diam <- c(19,24,28,33)
 treat

 [1] 1 2 4 3 4 3 1 2 3 4 2 1 2 1 3 4

 diam[treat]

 [1] 19 24 33 28 33 28 19 24 28 33 24 19 24 19 28 33

 d <- diam[treat]

 lsmod <- lm(time ~ spinner + order + poly(d,3))
 > anova(lsmod)

Analysis of Variance Table

Response: time
           Df Sum Sq Mean Sq F value   Pr(>F)  
spinner     3 39.367  13.122  9.9476 0.009594 **
order       3  7.587   2.529  1.9172 0.228001  
poly(d, 3)  3 14.208   4.736  3.5900 0.085602 .
Residuals   6  7.915   1.319                   
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

I'm a bit disappointed: I thought that the poly(d,3) sum of squares would
be decomposed into its three parts. How would I do that?

(Usual apologies for mental laziness.)



Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz                            Fax +64-7 838 4155
Phone  +64-7 838 4773 wk    +64 7 849 6486 home     Mobile 021 395 862

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