[R] Decompose numerical factor into orthog. poly parts

[John Maindonald]

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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-- 
John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Bioinformation Science, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
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