[R-sig-ME] Question about misspecified multilevel model

[Christopher David Desjardins]

Thanks, Phillip. The concrete example was meant to be just an example, so
you would know what I am talking about. I am thinking about
misspecification in general. Thanks for the detailed response to that. I am
cutting your response below.

On Saturday, August 6, 2016, Phillip Alday <Phillip.Alday at unisa.edu.au>
wrote:

> Hi Chris,




>  Now, I'm not sure what will happen with more complex fixed-effects or
> random-effects structures, but my guess is that generally the variance will
> be allocated to whatever variable is "close enough" (here classroom is
> close enough to school because a collection of classrooms makes up a
> school) and if there are none close enough, the remaining variance will
> just contribute to the residual variance (which didn't happen here).
>

This is what I am wondering about out and this is what I expected happens
but wasn't sure if it was just for this example and wasn't sure if there
was a mathematical reason why.



>
> * The fixed-effects model matrix is the same for both models so that you
> could potentially compare REML-fitted models, but that also gets you into
> all sorts of fun debate about the pros and cons of REML and it's just
> easier to avoid all the issues with comparisons of REML-fit
>
> Best,
> Phillip
>
> > On 6 Aug 2016, at 05:19, Christopher David Desjardins <
> cddesjardins at gmail.com <javascript:;>> wrote:
> >
> > Hi,
> >
> > I have a question that's potentially off-topic but that I'm hoping that
> > someone here can shed some insight on.
> >
> > Assume that I know that I know my true model and that my true is a
> > three-level model. My observations are such that I have a measurement on
> a
> > student nested within a classroom nested within a school. The true model
> > would be:
> >
> > Y_ijk = pi_0jk + e_ijk  # student within classroom within schools (1st
> > level)
> >
> > pi_0jk = beta_j0k + r_p0k  # classroom within schools (2nd level)
> >
> > beta_j0k = gamma_pq0 + u_pqk  # schools (3rd level)
> >
> > The model in lmer would be:
> > classroom <- read.csv("http://www-personal.
> umich.edu/~bwest/classroom.csv")
> > library("lme4")
> > correct.mod <- lmer(mathgain ~ (1 | schoolid/classid), data = classroom)
> >
> > What I am wondering about is, if I were to omit that second level, the
> > whole classroom within schools equation, where would that variance that
> > would end up as the random intercept go? Would it go to the random
> > intercept for school or would it go down to the residual?  The model I am
> > referring to is below:
> >
> > misspecified.mod <- lmer(mathgain ~ (1 | schoolid), data = classroom)
> > summary(correct.mod); summary(misspecified.mod)
> >
> > It looks like the variances for both the residual and the random
> intercept
> > for school change. But maybe they do in a predictable way?
> >
> > If someone could suggest a paper has an answer or better that would be
> very
> > helpful.
> >
> > Chris
> >
> >       [[alternative HTML version deleted]]
> >
> > _______________________________________________
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> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
>

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