On Sun, 9 Oct 2011, buehlerman wrote:
I want to apply Nyblom-Hansen test with the strucchange package, but I
don't know how is the correct way and what is the difference between the
following two approaches (leeding to different results):
The difference is that sctest(formula, type = "Nyblom-Hansen") applies the
Nyblom-Hansen test statistic to a model which assesses both coefficients
_and_ error variance.
The approach via functional = meanL2BB, on the other hand, allows to apply
the same type of test statistic to the score functions of any model. In
your case, where you used the default fit = glm in gefp(), a linear
regression model is used where the error variance is _not_ included as a
full model parameter but only as a nuisance parameter. Hence, the
difference.
Of course, one may also add another score function for the error variance.
On example("DIJA", package = "strucchange") I provide a function normlm()
with corresponding estfun() method. If you load these, you can do:
R> sctest(gefp(Employed ~ Year + GNP.deflator + GNP + Armed.Forces, data =
longley, fit = normlm), functional = meanL2BB)
M-fluctuation test
data: gefp(Employed ~ Year + GNP.deflator + GNP + Armed.Forces, data = longley,
fit = normlm)
f(efp) = 0.8916, p-value = 0.4395
which leads to the same output as sctest(formula, type = "Nyblom-Hansen").
Finally, instead of using gefp(..., fit = normlm), you could have also
used efp(..., type = "Score-CUSUM"):
R> sctest(efp(Employed ~ Year + GNP.deflator + GNP + Armed.Forces, data =
longley, type = "Score-CUSUM"), functional = "meanL2")
Score-based CUSUM test with mean L2 norm
data: efp(Employed ~ Year + GNP.deflator + GNP + Armed.Forces, data =
longley, type = "Score-CUSUM")
f(efp) = 0.8916, p-value = 0.4395
I hope that this clarifies more than adding to the confusion ;-)
The reason for the various approaches is that efp() was always confined to
the linear model and gefp() then extended it to arbitrary estimating
function-based models. And for the linear model this provides the option
of treating the variance of a nuisance parameter or a full model
parameter.
Hope that helps,
Z
data("longley")
# 1. Approach:
sctest(Employed ~ Year + GNP.deflator + GNP + Armed.Forces, data = longley,
type = "Nyblom-Hansen")
#results in:
# Score-based CUSUM test with mean L2 norm
#
#data: Employed ~ Year + GNP.deflator + GNP + Armed.Forces
#f(efp) = 0.8916, p-value = 0.4395
#2. Approach:
sctest(gefp(Employed ~ Year + GNP.deflator + GNP + Armed.Forces, data =
longley), functional = meanL2BB)
#results in:
# M-fluctuation test
#
#data: gefp(Employed ~ Year + GNP.deflator + GNP + Armed.Forces, data =
longley)
#f(efp) = 0.8165, p-value = 0.3924
I could not find any examples or further remarks of the first approach with
sctest(..., type = "Nyblom-Hansen").
Maybe the first approach is unlike the second no joint test for all
coefficients?
Thank you in advance for your help!
--
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