Spatial multilevel models

[Raphael]

Hi George and other runmlwin users,

I am currently in the planning stage for a research project for which I would like to use spatial multilevel models.

The project: In this project I am planning to run discrete event history models (logistic regression with stacked data) in a multilevel framework to predict household-level (level-1) out-migration in relation to environmental measures (operating at the community - level-2). In addition, I would like to account for the spatial proximity between states (level-3), perhaps by specifying a cross-classification (multiple membership model) based on a contiguity matrix (derived from GIS) that defines which states are neighbors.

The background: There are few ways in how researchers have tried to add a spatial component to multilevel models. A series of articles by Morenoff and colleagues (Sampson, Morenoff, and Earls 1999, Morenoff, Sampson, and Raudenbush 2001, Swaroop, and Morenoff 2006) employed a two stage procedure to join multilevel and spatial models (by using the HLM software). First, the authors used the multilevel model to obtain adjusted y – values which they sometimes call posterior modes (Morenoff et al. 2001). “That is, before the spatial analysis, the neighborhood-level measures were adjusted for the potentially confounding effects of individual-level covariates within neighborhoods” (Sampson et al. 1999, p.646). In a second step the multilevel model adjusted scores of y were entered as dependent variables in the spatial analysis (the authors employed spatial lag models). As such the spatial analysis was then conducted only with aggregate-level data.
Another methodology is to split the higher level (in my case level-3) variance component into a spatially structured component and an unstructured component. Such models have been termed hierarchical geostatistical models (Chaix et al. 2005). Methodologically the splitting of the level-2 variance component can be accomplished through the use of multiple membership models or CAR (conditional autoregressive) models, which are usually estimated using Bayesian estimation procedures available in MLwiN or WinBUGS (see Lawson, Browne, and Vidal Rodeiro 2004). More recently spatial multilevel models have also been implemented using an empirical Bayes spatial (EBS) estimator (Verbitsky Savitz and Raudenbush 2009). It has been shown that spatial multilevel models provide a better model fit and more precise and stable estimates of the higher level intercepts than conventional aspatial multilevel models (Chaix et al. 2005, Verbitsky Savitz and Raudenbush 2009). Spatial multilevel models may not only provide a better model fit and therefore more precise and reliable estimates, they can also be used to measure the magnitude of diffusion, feedback, and spillover effects resulting from spatial proximity.

The question: Does anyone know about a description of how to implement spatial multilevel models in runmlwin? Are there any publications (besides the pretty dated book by Lawson et al., 2004) that uses these models in MLwiN? Thanks so much for your help with these questions!
Have a nice day!

Best,
Raphael

References:
Chaix, B., J. Merlo, S. V. Subramanian, J. Lynch, and P. Chauvin. 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 Malmo, Sweden, 2001." American Journal of Epidemiology 162:171-182.
Lawson, A. B., Browne, W. J., and C. L. Vidal Rodeiro. 2004. Disease Mapping with WinBUGS and MLwiN. Malden, MA: Wiley-Blackwell.
Morenoff, J. D., R. J. Sampson, and S. W. Raudenbush. 2001. "Neighborhood inequality, collective efficacy, and the spatial dynamics of urban violence." Criminology 39:517-559.
Sampson, R. J., J. D. Morenoff, and F. Earls. 1999. "Beyond social capital: Spatial dynamics of collective efficacy for children." American Sociological Review 64:633-660.
Savitz, N. V., & Raudenbush, S. W. (2009). Exploiting spatial dependence to improve measurement of neighborhood social processes. Sociological Methodology 2009, 39, 151-183.
Swaroop, S., and J. D. Morenoff. 2006. "Building community: The neighborhood context of social organization." Social Forces 84:1665-1695.

[GeorgeLeckie]

Hi Raphael,

For general details on discrete time event history models (logistic regression with stacked data) in a multilevel framework, with a particular focus on MLwiN, see:

http://www.bristol.ac.uk/cmm/software/s ... s/eha.html

The only examples that I am aware of for how to specify and fit spatial models using runmlwin are found at

http://www.bristol.ac.uk/cmm/media/runm ... l_Data.log

CAR models are often specified in the disease mapping literature and those researchers tend to use WinBUGS to fit these models. You should find lots of examples online.

I suspect Peter Congdon has examples of WinBUGS code for these types of models online (he has written several Statistical modelling books).

It would be interesting to try to refit some WinBUGS where possible in MLwiN to compare model results

Note that you can call WinBUGS from Stata using the winbugs suite of Stata commands

I hope this helps

George

[Raphael]

Hi George,
thanks a lot for the helpful information!
Have a good night!

Best,
Raphael