"This coming edition of _Political_Analysis_ is a special issue on such
modeling issues & implementations; you might check those out," he said,
more than a little self-servingly.
A more-direct answer to your query (simply adding to Luke's good answer
already posted): Sure multi-level analysis is appropriate with low
2nd-unit sample-size/variation. However, the cautions you found are also
appropriate. With that little variation across contexts, you don't have
much information about how context affects outcomes or affects the
effects of other variables on outcomes, but you can and should still try
to use what info you do have as efficiently and honestly as possible.
Therefore, some multilevel modeling strategy that imposes some
assumptions about the nature--i.e., put some functional structure on the
nature of the heterogeneity based on your theory, not just fixed effects
or linear-interaction by default--&/or distribution of the heterogeneity
across contexts (e.g., multivariate normal?) will probably be a good
idea. A strategy that does so with some honesty about the uncertainty of
your estimates would be a very good idea.
So, for example, with <15 macro-level units, and especially if your
model is not simply linear-regression, the sort of "keep it simple &
just apply cluster std-err" approach that I defend in my contribution to
the afore-mentioned PA volume is probably not going to be so great: you
can't afford the inefficiency & sample size/variation not big enough for
'consistent' std errs to be terribly reassuring. A 2-stage approach (see
Jusko & Shively andLewis & Linzer in same PA) or, better, some fuller
hierarchical modeling strategy that imposes some stronger assumptions is
likely to be a better bet. Just be honest & up-front about those
assumptions & how strong they are (see Bowers & Drake in same PA). Thing
is: you have little info. No magic methods are going to save you--only
thing you can do is bring more information & structure to the problem
(i.e., theory or (a.k.a.?) assumption).
Hope this helps,
Rob
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Robert (Rob) J. Franzese, Jr. US Mail: (ISR Room
4256)
Assoc. Prof. Political Science P.O. Box
1248
The University of Michigan Ann Arbor, MI
48106-1248
Research Assoc. Prof. TeleComm:
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http://www-personal.umich.edu/~franzese
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> -----Original Message-----
> From: H-NET/APSA List for Political Methodology [mailto:H-POLMETH@H-
> NET.MSU.EDU] On Behalf Of Stevens, Daniel
> Sent: Friday, September 16, 2005 3:26 PM
> To: [log in to unmask]
> Subject: Re: [H-POLMETH] H-POLMETH: Multi-level model question
>
> [log in to unmask]
>
> ________________________________
>
> From: H-NET/APSA List for Political Methodology on behalf of Political
> Methodology
> Sent: Wed 8/25/2004 1:45 PM
> To: [log in to unmask]
> Subject: H-POLMETH: Multi-level model question
>
>
>
> From: "Alan E. Kessler" <[log in to unmask]>
> Subject: H-POLMETH: Multi-level model question
> Date: Wed, 25 Aug 2004 00:03:12 -0500 (CDT)
>
> I am seeking advice on the preferred estimation technique
> for multi-level data with a "small" number of level 2 units.
> Consider Steenbergen and Jones 2002 AJPS piece. The authors
> provide a great introduction to mutli-level analysis. Their
> application is a 3 level model with ~6300 level 1 observations
> (individuals), 100 level 2 observatiosn (parties), and 15
> level 3 observations (EU member states).
>
> I am interested in a simpler 2 level model that looks at
> only individuals and countries. Is multi-level analysis
> appropriate with 15 or fewer level 2 units? Some of the
> mutli-level textbooks I've glanced at suggest caution
> with low numbers of level 2 units. (The question is what
> this translates to in practice -- >10, >50?)
>
> Thanks for any advice.
> Best,
> Alan
>
>
> ____________________________
> Alan E. Kessler
> Department of Government
> University of Texas at Austin
> Burdine Hall 536
> Austin, TX 78712
> (512) 471-5121
> [log in to unmask]
>
>
>
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