[R-sig-ME] Replicating type III anova tests for glmer/GLMM

[Fox, John]

Dear Emmanuel,

With proper contrast coding (i.e., a coding that's orthogonal in the *basis* of the design, such as provided by contr.sum() ), a "type-III" test is just a test that the corresponding parameters are 0. The models in question are generalized linear (mixed) models and so sums of squares aren't really involved, but one could do the corresponding Wald (like car::Anova) or LR test. The Wald test is what you'd get with multcomp:glht or car:linearHypothesis. BTW, I don't think that it would be hard for car::Anova to be extended to provide LR tests in this case.

Best,
 John

> -----Original Message-----
> From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces at r-
> project.org] On Behalf Of Emmanuel Curis
> Sent: February 23, 2016 10:32 AM
> To: Francesco Romano <francescobryanromano at gmail.com>
> Cc: r-sig-mixed-models at r-project.org
> Subject: Re: [R-sig-ME] Replicating type III anova tests for glmer/GLMM
> 
> On Tue, Feb 23, 2016 at 01:06:18PM +0100, Francesco Romano wrote:
> < On the other hand, I don't understand how Cai et al. (2012) p.842, <
> "combined analysis experiments 1 and 2", reported the main effect < of a
> factor with 4 levels via a single estimate, SE, z, p coefficient.
> < How did they obtain this and is this the right way?
> 
> It's just a guess, but any sum-of-square can be seen as a particular contrast,
> that is a particular combination of the coefficients in the model (or of the
> different means, expressed another way) that is tested against 0. So I guess
> this single estimate is the value of the contrast associated to the
> corresponding sum-of-squares, and SE/z/p are derived similarly.
> 
> You can play with multcomp::glht to test this, but knowing which contrast is
> tested by which sum of square in a specific desing may be
> tricky: it depends on the coding, on the (un)balance...
> 
> Kowing if this is the < right > way is I think the same debate that knowing
> which kind of sum-of-square should be used and the question is very
> application dependent. Just, if you don't know what this single estimate
> estimates really, interpretation is at best difficult...
> 
> --
>                                 Emmanuel CURIS
>                                 emmanuel.curis at parisdescartes.fr
> 
> Page WWW: http://emmanuel.curis.online.fr/index.html
> 
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