Do “true” multi-level models require Bayesian methods?

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I agree with Jake. It is common practice to use cross-level interactions to
investigate the effects of covariates at different levels, even when one is
not using pure Bayesian methods to estimate the models. This happens a lot
in community psychology, industrial/organizational psychology, education,
medicine, and in a variety other disciplines from what I have seen in the
literature. Indeed, this feature lets multilevel models serve as a better
way to test certain theories and hypotheses than simpler methods such as OLS
regression because then the resulting model better aligns with the
conceptual structure of the theory and the phenomena of interest.

Aguinis, H., Gottfredson, R. K., & Culpepper, S. A. (in press).
Best-practice recommendations for estimating cross-level interaction effects
using multilevel modeling. Journal of Management.
http://mypage.iu.edu/~haguinis/pubs.html 

James, L. R., & Williams, L. J. (2000). The cross-level operator in
regression, ANCOVA, and contextual analysis. In K. J. Klein & S. W. J.
Kozlowski (Eds.), Multilevel theory, research, and methods in organizations:
Foundations, extensions, and new directions (pp. 382-424). San Francisco,
CA: Jossey-Bass.

Luke, D. A. (2005). Getting the big picture in community science: Methods
that capture context. American Journal of Community Psychology, 35(3/4),
185-200. doi: 10.1007/s10464-005-3397-z

Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models:
Applications and data analysis methods (2nd ed.). Thousand Oaks, CA: Sage
Publications.

Shinn, M., & Rapkin, B. D. (2000). Cross-level research without cross-ups in
community psychology. In J. Rappaport & E. Seidman (Eds.), Handbook of
community psychology (pp. 669-695). New York, NY: Kluwer Academic/Plenum
Publishers.


Steven J. Pierce, Ph.D. 
Associate Director 
Center for Statistical Training & Consulting (CSTAT) 
Michigan State University 
E-mail: pierces1 at msu.edu 
Web: http://www.cstat.msu.edu 

-----Original Message-----
From: Jake Westfall [mailto:jake987722 at hotmail.com] 
Sent: Tuesday, September 03, 2013 7:22 PM
To: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] Do "true" multi-level models require Bayesian
methods?

Hi Michael,

This is certainly possible in, e.g., lme4 or nlme packages. My perception is
actually that these kind of models are discussed pretty routinely in the
traditional multilevel literature under the term "cross-level interactions."
Taking a quick look at my bookshelf, I find discussions of cross-level
interactions in Snijders & Bosker (2011), Hox (2010), and Goldstein (2010).

Jake

Date: Tue, 3 Sep 2013 14:53:23 -0700
From: mwojnowi at uci.edu
To: r-sig-mixed-models at r-project.org
Subject: [R-sig-ME] Do "true" multi-level models require Bayesian methods?

I've been recently learning about mixed effects models (e.g. via
Fitzmaurice, Laird, and Ware 's book *Applied Longitudinal Analysis*) as
well as Bayesian hierarchical models (e.g. via Gelman and Hill's book

*Data

Analysis Using Regression and Multilevel/Hierarchical Models*)

One curious thing I've noticed: The Bayesian literature tends to emphasize
that their models can handle covariates at multiple level of analysis. For
example, if the clustering is by person, and each person is measured in
multiple "trials," then the Bayesian hierarchical models can investigate
the main effects of covariates both at the subject and trial level, as

well

as interactions across "levels."

However, I have not seen these kinds of models in the textbooks

introducing

frequentist methods.

I'm not sure if this is a coincidence, or an example of where Bayesian
methods can do "more complicated things." Is it possible to use mixed
effects models (e.g. the lme4 or nlme packages in the R statistical
software) to investigate interactions of fixed effect covariates across
"levels" of analysis?

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One curious thing I've noticed: The Bayesian literature tends to emphasize
that their models can handle covariates at multiple level of analysis. For
example, if the clustering is by person, and each person is measured in
multiple "trials," then the Bayesian hierarchical models can investigate
the main effects of covariates both at the subject and trial level, as well
as interactions across "levels."

However, I have not seen these kinds of models in the textbooks introducing
frequentist methods.

I'm not sure if this is a coincidence, or an example of where Bayesian
methods can do "more complicated things." Is it possible to use mixed
effects models (e.g. the lme4 or nlme packages in the R statistical
software) to investigate interactions of fixed effect covariates across
"levels" of analysis?

Some structural equation models need a more flexible setup than lme4 
offers: see the sem, lavaan (and OpenMX) packages for gaussian and probit 
options. Bayesian packages like BUGS are by nature able to fit pretty 
arbitrary models.


| David Duffy (MBBS PhD)                                         ,-_|\
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