Specify model with polynomial interaction terms up to degree n
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 advance.
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
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Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
David Winsemius, MD West Hartford, CT