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interpreting results of regression using ordinal predictors in R

4 messages · Ranjan Maitra, Bert Gunter, David Winsemius

#
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, etc stand for? How do
these names, etc get assigned in the coefficients? Where do I find more
about this information?

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.

Thanks very much again for all your help!

Best wishes,
Ranjan
#
On Jan 2, 2013, at 9:22 PM, Ranjan Maitra wrote:

            
x.L,   linear
x.Q,  quadratic
x.C,  cubic
x^4   quartic
Search on "orthogonal polynomials".
As always.
David Winsemius, MD
Alameda, CA, USA
#
On Jan 2, 2013, at 10:09 PM, Bert Gunter wrote:

            
The material in "Intro to R" is, I think all will agree, rather  
sketchy. I think this strategy will be more productive:

http://lmgtfy.com/?q=%22orthogonal+polynomials%22+linear+models

Second link was:

www.stats.ox.ac.uk/pub/StatMeth/Linear2_04.pdf