[R-sig-ME] nAGQ = 0

[Jake Westfall]

To further clear things up for other readers, this formula syntax is a nice
and very useful (if little known) trick for estimating separate intercepts
and x slopes for each level of Trt. It creates a design matrix like:

[1 0 x_1 0]
[1 0 x_2 0]
[0 1 0 x_3]
[0 1 0 x_4]

where the first two rows belong to Trt=1, the second two rows belong to
Trt=2; columns 1 and 2 are the Trt1 and Trt2 intercepts, respectively; and
columns 3 and 4 contain only the x values for Trt1 and Trt2, respectively,
so their associated coefficients give the group-specific slopes for each
level of Trt.

Jake

On Thu, Sep 7, 2017 at 2:41 PM, Phillip Alday <phillip.alday at mpi.nl> wrote:

> As mentioned previously, the formula syntax for this one is a bit
> confusing. The left-hand side was easy enough to figure out from the
> brms docs, but the division operator on the RHS was a trick I had never
> used before -- it took me looking at the output from the
> glmer(...,nAGQ=0) model to get that it's equivalent to
>
> ~ 0 + Trt + Trt:x + (x | Rep)
>
> Phillip
>
>
>
> On 09/07/2017 06:12 AM, Rolf Turner wrote:
> >
> > On 07/09/17 10:57, Poe, John wrote:
> >
> >> This is where my being a political scientist on a listserv full of
> >> definitely not political scientists is going to make me look dumb.
> >> I've never actually seen a model specification like that before for a
> >> multilevel model. Is the outcome supposed to be the proportion dead
> >> out of the total population for each row? I'm missing something about
> >> this that is probably very obvious.
> >>
> >> After fiddling with it I was able to get it to converge for one chain
> >> but I wouldn't trust it at all right now.
> >
> > Well, I hadn't seen a model specification quite like that either.  It's
> > brm() syntax, which is a bit different from glm() or glmer() syntax.
> >
> > The model being fitted is a binomial model, with success probability p
> > modelled by
> >
> >     g(p) = beta_0 + beta_1 * x + Z_0 + Z_1 * x
> >
> > where the Z_k are the random effects, and where g() is the link
> > function, e.g. cloglog(). (I *think* I've got that right.)
> >
> > Of course beta_0 and beta_1 depend on treatment group and Z_0 and Z_1
> > depend on "Rep", which is nested within treatment group.
> >
> > Note that we are talking *generalized* linear mixed models here; the
> > responses are binomial success counts.  "Success" = Dead, since one is
> > trying to kill the bugs.
> >
> > For what it's worth the glmer() syntax is
> >
> >    glmer(cbind(Dead,Alive) ~ (0 + Trt)/x + (x | Rep),
> >          family=binomial(link="cloglog"),data=X)
> >
> > I got the brm() syntax from the vignette; as I said, I'd never seen it
> > before.
> >
> > cheers,
> >
> > Rolf
> >
>
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