R help - Jan 2013 - interpreting results of regression using ordinal predictors in R

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



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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