st: Three-Four Level Meta-Analysis in Stata

[Jillian Turanovic <Jillian.Turanovic@asu.edu>]

Hello,

I am carrying out a meta-analysis with a three-level hierarchical data
structure containing effect size estimates (N = 318) nested within
individual studies (N = 67), nested within independent data sets (N =
43). There are significant variance components at each level. Each
effect size estimate at level 1 also has a known variance (equal to
the square of its standard error).

To properly carry out this analysis in HLM 7, I would have to specify
a four-level "variance known" model, where level 1 contains only the
precision weights for the known variance of effect size estimates
(with a constrained variance of 1.00), level 2 contains effect size
estimates within studies (along with various moderator
characteristics), level 3 corresponds to studies within datasets, and
level 4 corresponds to independent data sets. Unfortunately, HLM 7
cannot specify a four-level "variance known" model. Given these
issues, I was wondering if I could use Stata to estimate my
hierarchical multivariate models.

To adequately analyze this meta-analytic data, I need to use a
modeling strategy that:

1. Allows for the input of raw (non-normalized) sampling weights at level 1.
I am aware that this can be done using pweights in xtmixed (in Stata
12), specified using [pw = 1/known variance] in the fixed portion of
the model.

2. Constrains the lowest level variance to 1.
This is where I am facing problems. How can I constrain the lowest
level variance to 1 in Stata, as HLM does with their v-known models?
Is there a way?

I am a seasoned Stata user and familiar with many user-written
meta-analysis programs, yet am not aware of any that can help me
estimate 3-4 level hierarchical models with known/constrained variance
at level 1. I have searched the gllamm manual as well and have not
been able to find a clear answer. I am aware that MLwin has the
capacity to run these models (as outlined in Hox, 2010, by specifying
a three-level model with the known standard error specified as a
coefficient with a random effect at level 1), but am facing numerous
challenges with the software.

A previous thread from 2011 has raised this concern but a solution was
not offered (see:
http://www.stata.com/statalist/archive/2011-07/msg00432.html)

Any help would be tremendously appreciated.

Thank you,

Jillian J. Turanovic, M.S.
Doctoral Student
School of Criminology and Criminal Justice
Arizona State University
Mail Code:  4420
411 N. Central Ave., Suite 600
Phoenix, AZ   85004-0685
602-496-1292 (office)
602-496-2366 (fax)

References: Hox, Joop. 2010. Multilevel Analysis: Techniques and
Applications (2nd ed.). New York: Routledge.
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