[R-sig-ME] Query

[Ian Dworkin]

Jake

 true, but relating the old ANOVA based mixed nomenclature to the newer one
is sometimes difficult, at least with respect to what people often think is
being modeled.

in the old terminology the interaction between a fixed factor and random
effect resulted in a new random effect that was usually interpreted to mean
something like what Ben had as
(1|r:f)

However, more often than not what the researcher meant to look at was more
of the second situation
(f|r)

In quantitative genetics this comes up all the time with Genotype by
Environment interactions. Genotype (g) is usually a random effect (i.e.
different families in a quantitative genetics design), while the
environmental (e) factor (say a diet manipulation) would be the fixed
effect.

It would be common to see models (usually in SAS) where it was the
equivalent of (1|g:e). Apologies I totally forget the SAS notation, so am
keeping it consistent with the lme4 notation.

i.e
~ 1 + e + (1|g) + (1|g:e)


However when you speak to most researchers what they are often interested
in was a model that was really
~ 1 + e + (1+e | g).

I am not disagreeing with any points, just pointing out that sometimes
relating the two has caused much confusion for some researchers.


On 13 September 2017 at 14:46, Jake Westfall <jake.a.westfall at gmail.com>
wrote:

> Well in the old ANOVA-based mixed model framework we talk about
> interactions between fixed and random factors, although in modern mixed
> models we call those interactions "random slopes." (The coefficient for a
> fixed predictor X "depends on" the level of the random factor.) So Ezequiel
> could just be using the ANOVA-type terminology (used a lot in DoE) to refer
> to random slopes.
>
> Jake
>
> On Wed, Sep 13, 2017 at 1:41 PM, Doran, Harold <HDoran at air.org> wrote:
>
> > Perhaps a bit OT, but what *is* an interaction between a fixed and random
> > factor? The fixed effects are estimates, BLUPs are not estimates really.
> >
> > I can't quite consider what the estimand is in this instance
> >
> > -----Original Message-----
> > From: R-sig-mixed-models [mailto:r-sig-mixed-models-
> bounces at r-project.org]
> > On Behalf Of Ben Bolker
> > Sent: Wednesday, September 13, 2017 2:34 PM
> > To: r-sig-mixed-models at r-project.org
> > Subject: Re: [R-sig-ME] Query
> >
> >
> >    I'm going to say something here to get the conversation started, but
> > this information comes with a giant caveat.  I hope that someone with
> more
> > knowledge of experimental designs comes forward ...
> >
> >   in general an interaction between a random factor r and a fixed factor
> f
> > is either
> >
> > (1|r:f)
> >
> > (assuming a positive, compound-symmetric variance-covariance matrix) or
> >
> > (f|r)
> >
> > (assuming an unstructured variance-covariance matrix).  The latter is
> > likely to be very expensive if f has more than a few levels.
> >
> >   Interaction between two random factors would be (1|r1:r2) (you would
> > have (1|r1) and (1|r2) in the model as well).
> >
> > On 17-09-13 02:12 PM, EZEQUIEL ROSSI wrote:
> > > Dears,
> > >
> > >
> > > I am working with a Federer's augmented block design in lmer function
> > > and I need indicate interaction between ramdom and fixed factors and
> > > between two ramdom factors . Can you say me how I should make this?
> > >
> > >
> > > Thank you very much,
> > >
> > >
> > > Best regards,
> > >
> > >
> > > Ezequiel Rossi
> > >
> > > [[alternative HTML version deleted]]
> > >
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-- 
Ian Dworkin
Department of Biology
McMaster University
Office phone 905 525 9140 ext. 21775
Lab phone 905 525 9140 ext. 20076
dworkin at mcmaster.ca

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