Dear Doug, Jarrod, and/or perhaps others,

A couple posters have previously asked about multiple membership models, and Doug has said he could provide code to fit such models (https://stat.ethz.ch/pipermail/r-sig-mixed-models/2010q2/003860.html), if given some sample data.

Jarrod has similarly suggested that MCMCglmm can handle multiple membership (https://stat.ethz.ch/pipermail/r-sig-mixed-models/2011q2/006195.html), though I can't find any reference to multiple membership models in the MCMCglmm documentation. (Maybe I missed it, however.)

Here's is a simple sample dataset (Scottish Lip Cancer):
library(foreign); lips <- read.dta("http://www.bristol.ac.uk/cmm/media/runmlwin/lips1.dta")[,c(1,3,5,9:30)]

I would be very grateful for any indication of how to fit a multiple membership model to such data. In this instance, the outcome ("obs") is Poisson-distributed (number of instances of lip cancer in an area), and "perc_aff" is a covariate (percentage of the population working in outdoor activities). Each unit ("area") is observed only once, but a mixed model could be useful for modelling the spatial dependence in the data, where each area is taken to be nested in a set of neighbours (identified in columns 4-14). Each area has anywhere from 1 to 11 neighbours, so each neighbour's share of the overall "neighbour" classification would have to be weighted somewhere from 1/11 to 1. Weights are given in columns 14-25.

So a starting model is:
summary(M1 <- glm(obs ~ 1, lips, family=poisson))

Then:
library(lme4)
(M2 <- lmer(obs ~ 1 + (1 | neigh1), lips, family=poisson))

However, the random effect in M2 should be replaced by a random effect for "neighbours" (not just "neigh1") where each of the 1 to 11 neighbours "counts equally" towards the classification, not just the area's first neighbour.

Can this indeed be done in lme4 and/or MCMCglmm? If so, can you please show how? A similar analysis of this dataset, using MLwiN, is described in chapter 17 of 
http://www.bristol.ac.uk/cmm/software/mlwin/download/mcmc-09.pdf.

Thanks,
Malcolm


	[[alternative HTML version deleted]]


