Paul von Hippel <von-hippel.1@osu.edu> writes:
> I am fitting 3-level linear models to a data set containing about
> 60,000 test scores nested in 17,000 students nested in 1,000
> schools. I am considering introducing a 4th level (teachers or
> classrooms), which neither HLM software nor SAS PROC MIXED can
> handle. Can NLME fit a 4-level model to a data set of this size?
Probably not. The computational methods in the lme function are
optimized for strictly nested grouping factors. In an observational
data set of this size it is unlikely that strict nesting will hold,
even for the three level model, as that would mean that none of the
17,000 students changed schools during the observation period.
Introducing the fourth level of teacher or classroom will certainly
violate strict nesting.
Handling large scale mixed-effects models in which the grouping
factors (students, teachers, and schools, in this case) are partially
crossed (meaning that an individual student is observed in several
classrooms and possibly more than one school) is very difficult. The
computational methods will need to be redesigned and reimplemented,
essentially from scratch. I have written (with Saikat DebRoy) about
the computational methods
http://www.stat.wisc.edu/~bates/reports/MixedComp.pdf
and am working on implementations but it is not something that will be
done quickly.
> If so, let me ask about another capability. In my data, the level 1
> error variance is known from psychometric analysis. I would like to
> set this variance component to this known value before the other
> variance components are estimated. SAS PROC MIXED has a PARMS command
> which allows me to do this. Is there anything comparable in NLME?
I think there may be ways of doing that but I would not recommend it.
Instead I would recommend estimating the level 1 error variance and
comparing the estimate to the presumed value. If these estimates are
similar then you have greater confidence in your model. If they are
very different then you would need to ask yourself why they are so
different.
Sometimes comparisons like this are very valuable diagnostics. A
similar situation occurs with penalized quasi-likelihood (PQL)
estimation of parameters in generalized linear mixed models. For
binomial or Poisson distributions of the error term the scale
parameter should be unity but it gets estimated separately in the PQL
algorithm. We have found that estimates that are very different from
one usually indicate model failure.
--
Douglas Bates bates@stat.wisc.edu
Statistics Department 608/262-2598
University of Wisconsin - Madison http://www.stat.wisc.edu/~bates/
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