[R] extend summary.lm for hccm?

[Achim Voß]

Dear John (and other readers of this mailing list),


thanks for your help. It now raises two further questions, one directly 
related to R and probably easy to answer, the other one a little off-topic.

John Fox wrote:
> ... (BTW, one
> would not normally call summary.lm() directly, but rather use the
> generic summary() function instead.) ...

Is there any difference for R between using summary.lm() and using 
summary()? Or is it just that in the second case, R recognizes that the 
input is lm and then calls summary.lm()?

> That said, it's hard for me to understand why it's interesting to have
> standard errors for the individual coefficients of a high-degree
> polynomial, and I'd also be concerned about the sensibleness of fitting
> a fifth-degree polynomial in the first place.

I am trying to estimate some Engel curves - functions of the 
relationship between income of a household and the demand share of 
certain goods. As I want to estimate them for only one good, the only 
restriction that arises from Gorman (1981) seems to be that in a pure 
Engel curve model (including only income and the demand share) the 
income share should be the sum of some multiplications of polynomials of 
the natural logarithm of the income.

I have not yet found a theoretical reason for a limit to the number of 
polynomials and I know to little maths to say if it's impossible to 
estimate the influence of x^5 if you've already included x to x^4. So I 
thought I might just compare different models with different numbers of 
polynomials using information criteria like Amemiya's Prediction Criterion.

I guess using x^1 to x^5 it will be hardly possible to estimate the 
influence of a single one of these five polynomials as each one of them 
could be approximated using the other four, but where to draw the line? 
So if anybody could tell me where to read how many polynomials to 
include at most, I'd be grateful.


Regards,
Achim



Gorman (1981) is: Gorman, W. M. (1981), "Some Engel Curves," in Essays 
in the Theory and Measurement of Consumer Behaviour in Honor of Sir 
Richard Stone