[R-sig-ME] No need to handle between-group correlation structure in glmm in general?

[Steven J. Pierce]

Junyan,

Hofmann et al. (2000) and Raudenbush & Bryk (2002) both specifically say
that level 2 residuals are supposed to be independent in a 2-level model.
So, I think it is very important to directly test that assumption and modify
the model to account for autocorrelation if it is present. It may not always
make a huge difference in practice, but I consider that the conceptually
appropriate way to proceed. Ultimately geostatistical models performed
better than adding a conditional autoregressive (CAR) structure to a
traditional multilevel model in my own work. 

My dissertation (Pierce, 2010) was contrasting different ways of modeling
neighborhood effects on residents and lays out an argument for why
geostatistical approaches may be better tools than traditional multilevel
models for answering some kinds of questions. I used an exact Moran's I test
for regression residuals to detect autocorrelation in level 2 residuals in
my own work (see Bivand, Pebesma, & Gomez-Rubio, 2008, pp. 258-264 and the
lm.morantest.exact function from the spdep package in R). In terms of
software, I used a combination of R and WinBUGS to run my multilevel models
because I wanted to use Bayesian methods as similar as possible to the
geostatistical models implemented in the spBayes package. WinBUGS did the
real estimation work, but I used R for data management, calling WinBUGS,
then post-processing the WinBUGS results. 

Bivand, R. S., Pebesma, E. J., & Gómez-Rubio, V. (2008). Applied spatial
data analysis with R. New York, NY: Springer Science+Business Media.

Hofmann, D. A., Griffin, M. A., & Gavin, M. B. (2000). The application of
hierarchical linear modeling to organizational research. In K. J. Klein & S.
W. J. Kozlowski (Eds.), Multilevel theory, research, and methods in
organizations: Foundations, extensions, and new directions (pp. 467-511).
San Francisco, CA: Jossey-Bass.

Pierce, S. J. (2010). Using geostatistical models to study neighborhood
effects: An alternative to hierarchical linear models. (Doctoral
dissertation).  Available from ProQuest Dissertations and Theses database.
(UMI No. 3417821)
https://www.msu.edu/~pierces1/S_Pierce_Final_Dissertation_2010.pdf 

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

Regards,

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: Junyan Luo [mailto:jzl106 at gmail.com] 
Sent: Wednesday, March 14, 2012 9:16 AM
To: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] No need to handle between-group correlation
structure in glmm in general?

Hi Dr. Pierce,

Thanks for the reply! And the information you provided is very useful!
Do you know if any existing R tools can handle this type of analysis?

The suggestion of comparing model fit is a good idea, but probably a
more important issue is whether the presence of correlated random
effects biases the parameter estimation. I am aware of a few test
techniques related to this, but totally unsure about their
implications. For example, is it a good idea to perform Moran's I test
on the second level residuals? (Or random effects directly?) A more
important question is, if Moran's I suggests autocorrelation in second
level residuals, would it be corrected by incorporating an correlation
structure for random effects?

REGARDS,
Junyan

On Wed, Mar 14, 2012 at 8:37 AM, Steven J. Pierce <pierces1 at msu.edu> wrote:
> The best thing to do would be to empirically test whether modeling the
> spatial autocorrelation in the level 2 random effects improves model fit
> compared with a simpler model that assumes independence of those random
> effects. In my dissertation work, adding spatial autocorrelation at level
2
> improved a model (but not dramatically).
>
> Check out the following resources:
>
> Beard, J. R. (2008). New approaches to multilevel analysis. Journal of
Urban
> Health, 85(6), 805-806. doi: 10.1007/s11524-008-9314-7
>
> Browne, W., & Goldstein, H. (2010). MCMC sampling for a multilevel model
> with non-independent residuals within and between cluster units. Journal
of
> Educational and Behavioral Statistics, 35(4), 453-473. doi:
> 10.3102/1076998609359788
>
> Chaix, B., Leyland, A. H., Sabel, C. E., Chauvin, P., Råstam, L.,
> Kristersson, H., & Merlo, J. (2006). Spatial clustering of mental
disorders
> and associated characteristics of the neighbourhood context in Malmö,
> Sweden, in 2001. Journal of Epidemiology and Community Health, 60(5),
> 427-435. doi: 10.1136/jech.2005.040360
>
> Chaix, B., Merlo, J., & Chauvin, P. (2005). Comparison of a spatial
approach
> with the multilevel approach for investigating place effects on health:
The
> example of healthcare utilisation in France. Journal of Epidemiology and
> Community Health, 59(6), 517-526. doi: 10.1136/jech.2004.025478
>
> Chaix, B., Merlo, J., Evans, D., Leal, C., & Havard, S. (2009).
> Neighborhoods in eco-epidemiologic research: Delimiting personal exposure
> areas. A response to Riva, Gauvin, Apparicio and Brodeur. Social Science &
> Medicine, 69(9), 1306-1310. doi: 10.1016/j.socscimed.2009.07.018
>
> Chaix, B., Merlo, J., Subramanian, S. V., Lynch, J., & Chauvin, P. (2005).
> Comparison of a spatial perspective with the multilevel analytical
approach
> in neighborhood studies: The case of mental and behavioral disorders due
to
> psychoactive substance use in Malmö, Sweden, 2001. American Journal of
> Epidemiology, 162(2), 171-182. doi: 10.1093/aje/kwi175
>
> Fagg, J., Curtis, S., Clark, C., Congdon, P., & Stansfeld, S. A. (2008).
> Neighbourhood perceptions among inner-city adolescents: Relationships with
> their individual characteristics and with independently assessed
> neighbourhood conditions. Journal of Environmental Psychology, 28(2),
> 128-142. doi: 10.1016/j.jenvp.2007.10.004
>
>
>
> 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: Junyan Luo [mailto:jzl106 at gmail.com]
> Sent: Tuesday, March 13, 2012 7:33 PM
> To: R-sig-mixed-models at r-project.org
> Subject: [R-sig-ME] No need to handle between-group correlation structure
in
> glmm in general?
>
> Hi,
> Recently I have been working with a data set that contains individual
> samples from a set of connected geographical areal units. While I plan
> to use glmm to model the data with individuals as the 1st level units
> and the areal units as the 2nd level units, I am concerned with the
> potential spatial autocorrelation among the geographical areal units
> (i.e., at the second level). It is reasonable to think that the random
> effects at the second level will be spatial autocorrelated. I know
> nlme has the option to specify "within-group" correlation structure,
> but I couldn't figure out a way to specify "between-group"
> correlations structure for the geographical areal units.
>
> However, one of my colleagues told me it was totally unnecessary to
> specify a correlation structure at the second level. This is because
> the two assumptions of multi-level models are (1) the individual error
> term is independent; (2) the individual error term is uncorrelated
> with the random effects. It does NOT assume that the random effects
> should be independent. So unless (2) is violated, generally we don't
> need to worry about autocorrelation in the random effects. That's
> probably why nlme only has the option for specifying "within-group"
> correlation structure. I feel the assessment is reasonable, but I am
> unsure if that is correct. Can anybody help me clarify this? Thanks!
>
>
>