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

[Junyan Luo]

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!
>
>
>