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

[Steven J. Pierce]

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!