On Fri, 24 Mar 2017, Sven Schreiber wrote:
Am 23.03.2017 um 19:05 schrieb Allin Cottrell:
> 1) The convention when calculating BIC from a model estimated by least
> squares is to set "k" to the number of regression coefficients (leaving
> aside the error variance), while the convention under MLE is to include
> the variance estimator in k. (Or at least I think that's a fair
> statement of the case.)
One more follow-up here: Can you give a source for the convention? I guess in
principle one can make the case that also the error variance could be fixed a
priori and not estimated, and so k should change accordingly. But right now I
don't see why that argument wouldn't apply to OLS as well.
(Or are there some block-diagonal and/or asymptotic independence arguments
that would apply to one estimator here and not the other?)
I don't know of any canonical source of the convention, and in fact
it's not universal. Some writers argue for including the variance
parameter in the "k" count for least squares, but it seems that most
software doesn't do that (Stata, SAS, SPSS at least). R does include
the extra term, however. William Greene doesn't include it, in his
account of info criteria in Econometric Analysis, but he doesn't
comment on the matter.
I guess using k = (number of regressors) in the least squares case is
motivated by the fact that k in that sense is the standard measure of
loss of degrees of freedom in estimation.