interpreting results of regression using ordinal predictors in R
On Jan 2, 2013, at 9:22 PM, Ranjan Maitra wrote:
Dear friends,
Being very new to this, I was wondering if I could get some pointers
and guidance to interpreting the results of performing a linear
regression with ordinal predictors in R.
Here is a simple, toy example:
y <- c(-0.11, -0.49, -1.10, 0.08, 0.31, -1.21, -0.05, -0.40, -0.01,
-0.12, 0.55, 1.34, 1.00, -0.31, -0.73, -1.68, 0.38, 1.22,
-1.11, -0.20)
x <- ordered(c(2, 3, 3, 3, 5, 1, 2, 2, 1, 6, 0, 3, 4, 2, 2, 4, 1, 1,
1,
1))
x
# [1] 2 3 3 3 5 1 2 2 1 6 0 3 4 2 2 4 1 1 1 1
# Levels: 0 < 1 < 2 < 3 < 4 < 5 < 6
lm(formula = y ~ x)
# Call:
# lm(formula = y ~ x)
# Coefficients:
# (Intercept) x.L x.Q x.C
x^4 x^5
# -0.01679 -0.20788 0.46917 -0.45520 -0.05721
-0.28696
# x^6
# -0.31417
....
Question: What exactly, does x.L, x.Q, x.C, x^4,
x.L, linear x.Q, quadratic x.C, cubic x^4 quartic
etc stand for? How do these names, etc get assigned in the coefficients? Where do I find more about this information?
Search on "orthogonal polynomials".
Note that my question is not on lm (I think), but rather on how lm outputs the results of regressions involving ordered predictors. Some references would be great. Please post responses to this mailing list.
As always.
Thanks very much again for all your help! --
David Winsemius, MD Alameda, CA, USA