Re: [R] logistic regression

From: Chris Lawrence <chris_at_lordsutch.com>
Date: Thu 16 Feb 2006 - 18:55:01 EST

On 2/16/06, Prof Brian Ripley <ripley@stats.ox.ac.uk> wrote:
> On Thu, 16 Feb 2006, Chris Lawrence wrote:
>
> > On 2/15/06, Taka Matzmoto <sell_mirage_ne@hotmail.com> wrote:
> >> I have two bianry variables (X and Y) and one continuous variable (Z).
> >>
> >> I like to know, after controlling for the continuous variable, where one of
> >> the binary is significantly related to the other binary variable using
> >> logistic regression
> >>
> >> model <- glm(Y ~ X + Z, family=binomial)
> >>
> >> Is checking the significance of the coefficient of X a proper way for doing
> >> that ?
> >
> > Yes, that will do it.
>
> Sorry, not so. That is a Wald test, and its power goes to zero as the
> true effect increases. You need to do a likelihood ratio test via
> anova() to get a reasonable test.

MASS, 3rd edition - p. 225-26. (I haven't collected my pennies yet for MASS 4.) Incidentally, at least the 3rd ed. doesn't suggest doing the LR test as an alternative to relying on the Wald chi-square test or z/t test.

For what it's worth, Long's Regression Models for Categorical and Limited Dependent Variables (1997, p. 97) disagrees in terms of the practical significance of Hauck and Donner's result (sorry, no JASA access from home to check):

"In general, it is unclear whether one test is to be preferred to the other [e.g., Wald or LR]. Rothenberg (1984) suggests that neither test is uniformly superior, while Hauck and Donner (1977) suggest that the Wald test is less powerful than the LR test. In practice, the choice of which test to use is often determined by convenience." (Long then goes on to discuss the need to estimate nested models for the LR test, versus the need to do matrix algebra to calculate the Wald test, as an illustration of the contrast in convenience.)

Rothenberg (1984) is in Econometrika vol 52, pp. 827-42, according to Long's bibliography, for anyone fascinated enough by this question to go digging.

Off to bed...

Chris



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