[R] strucchange Nyblom-Hansen Test?

[Achim Zeileis]

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!
>
> --
> View this message in context: http://r.789695.n4.nabble.com/strucchange-Nyblom-Hansen-Test-tp3887208p3887208.html
> Sent from the R help mailing list archive at Nabble.com.
>
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