[R] How to get the adjusted R squared from GLS() estimator

[peter dalgaard]

On 13 Mar 2014, at 22:26 , Greg Snow <538280 at gmail.com> wrote:

> Oh, you mean the gls function, not GLS as my initials (my
> parents are OLS and WLS, perhaps I was destined to regress), sorry.

Fortune candidate?

> The gls function in the nlme package (is that the one that you are
> asking about? or is there another gls function?) fits using maximum
> likelihood (or restricted maximum likelihood) rather than looking at
> sums of squares, so an adjusted r-squared is not a direct result like
> in ordinary least squares.  The idea of r-squared does not really
> translate well to models beyond ordinary least squares (see
> fortune(252), fortune(253), and fortune(254)), so adjusted r-squared
> would not either.

Specifically, the usual adjusted R-squared is the percentwise reduction in variance from an intercept-only model. In WLS, the covariance is assumed to be of the form

	Sigma = lambda^2 W

where W is a known matrix, it makes sense to look at the percent reduction in the proportionality factor lambda^2 and call that adj. R-squared. However, if W depends on additional parameters, as it does in GLS, you may have a different W in the intercept-only model, and it becomes quite unclear what the adj. R-squared should even mean.

-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com