# [R] Specify model with polynomial interaction terms up to degree n

David Winsemius dwinsemius at comcast.net
Mon Jul 2 17:04:11 CEST 2012

```On Jul 2, 2012, at 10:51 AM, David Winsemius wrote:

>
> On Jul 2, 2012, at 9:29 AM, YTP wrote:
>
>> I would like to specify a model with all polynomial interaction
>> terms between
>> two variables, say, up to degree 6. For example, terms like a^6 +
>> (a^5 *
>> b^1)  +  (a^4 * b^2) + ... and so on.  The documentation states
>>
>> The ^ operator indicates crossing to the specified degree.
>>
>> so I would expect a model specified as y ~ (a+b)^6 to produce these
>> terms.
>> However doing this only returns four slope coefficients, for
>> Intercept, a,
>> b, and a:b.  Does anyone know how to produce the desired result?
>> Thanks in
>
> You might try:
>
> poly(a,6)*poly(b,6)
>
> (untested   ... and it looks somewhat dangerous to me.)

Well, now it's tested and succeeds at least numerically. Also tested

( poly(a,6) +poly(b,6) )^2 with identical results.

Whether this is wise practice remains in doubt:

dfrm <- data.frame(out=rnorm(100), a=rnorm(100), b=rnorm(100) )
anova(lm( out ~ (poly(a,6) +poly(b,6) )^2, data=dfrm) )
#-----------------------
Analysis of Variance Table

Response: out
Df Sum Sq Mean Sq F value  Pr(>F)
poly(a, 6)             6 12.409 2.06810  3.0754 0.01202 *
poly(b, 6)             6  5.321 0.88675  1.3187 0.26596
poly(a, 6):poly(b, 6) 36 41.091 1.14142  1.6974 0.04069 *
Residuals             51 34.295 0.67246
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

--

David Winsemius, MD
West Hartford, CT

```