>
> The test implemented by -linktest- (known as Tukey's one-degree-of-
> freedom test for non-additivity) is a test of the null hypothesis
> that the effects of the covariates are additive against alternatives
> in which they are not (the introduction of the square of the linear
> predictor to the model may be thought of as capturing a range
> of such
> alternatives). Since one of the purposes of the link function in a
> GLM is to linearize the effect of the covariates, in this
> context, it
> may also be thought of as a test of the adequacy of the link
> function. This is discussed in detail by Pregibon (1980), who
> proposed a slightly different approach; the entry under [R] -
> linktest- provides the full references to Pregibon (1980) and to
> Tukey's original 1949 paper, and explains why Stata uses Tukey's
> original formulation. I strongly suggest reading Pregibon's paper,
> which provides a nice way to think about what is going on in the GLM
> context.
I know the Stata manual, the Pregibon paper and Tukey's paper.
Nonetheless, they did not clarify the issue sufficiently for me. So what
you are saying is that the linear predictor (i.e. -predict, xb-) should
be predictive of the observed dependent variable? I believe I
understand the concept, but I assumed that "the effects of the
covariates" should be expressed on the same scale as the dependent
variable not in the scale of the link-function-transformation.
>
> Your posting also raised another (minor) issue worth commenting on.
> In particular, you demonstrated the following
[snip]
>
> noting that the results obtained by manually regressing price on xb
> and xb2 are slightly different from those obtained via
> -linktest-. A
> quick look at the code for -linktest- (type -viewsource
> linktest.ado-) reveals why; namely, there is a -version 6- at the
> top, which means that when the model including _hatsq is fit, Stata
> is running under version control as if it were version 6. Under
> version 6, -glm- used Iteratively Reweighted Least Squares
> (IRLS) and
> reported standard errors based on the expected information matrix.
> One of the changes made in version 7 was to make use of Stata's -ml-
> the default, as well as reporting standard errors based on the
> observed information matrix. Thus, to replicate the results of -
> linktest-, you must use the -irls- option:
[snip]
Precisely, the version 6 control is producing these results although
they are of minor concern to me. But I saw that Stata is going to fix
that, so this is great.
Daniel
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