Question about misspecified multilevel model

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).

* 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

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