On Fri, 14 Oct 2011, buehlerman wrote:
Thanks a lot for your immediate help and detailed explanation!
About one thing I'm not quite clear:
When the default fit = glm in gefp() is used:
sctest(gefp(Employed ~ Year + GNP.deflator + GNP + Armed.Forces, data =
longley, fit = lm), functional = meanL2BB)
To understand what exactly is tested, it may help to decompose this into
the steps (1) model fitting, (2) process setup, (3) test statistic
computation.
m <- lm(Employed ~ Year + GNP.deflator + GNP + Armed.Forces,
data = longley)
p <- gefp(m, fit = NULL)
sctest(p, functional = meanL2BB)
To see which parameters are assessed you can look at
estfun(m)
or the corresponding fluctuation process
plot(p, aggregate = FALSE)
both of which have one column per parameter. The visualization for the
Nyblom-Hansen test statistic
plot(p, functional = meanL2BB)
does not show the individual processes because you first aggregate across
parameters using the squared Euclidian norm (before taking its mean).
is this then the original Nyblom's Parameter Stability Test (1989) or is
it the joint (Nyblom-)Hansen test with theta = (beta) constant instead
of theta = (beta, sigma^2) constant ?
The original Nyblom suggestion was for ML estimation of a distribution
with one parameter (without covariates). Hansen extended this to the
linear regression model and proposed to either compute one test statistic
per parameter (which you can do with the "parm" argument of gefp) or a
joint statistic for all parameters. Hansen included in "all" parameters
also the variance, but the idea can be directly modified to any other
model with a vector of parameters.
The reason that estfun(lm_object) does not include the variance is that
coef(lm_object) and vcov(lm_object) etc. also do not include it. So it is
the conceptual question whether lm() computes the OLS estimator or the
full ML estimator. The normlm() wrapper on the ?DJIA man page is one
possibility to switch to the ML view for the purposes of using
"strucchange".
hth,
Z
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