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
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