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1.15159898632138, 0.839624221762097, 0.313712961008834, 0.657302664968142, 0.580837779249633, 0.580837779249633, 1.2014142663676, -0.615663010844745, 0.573921056029091, 0.482949277823364, 0.382865819266382, 1.07601299982633, 0.271640184156157, 0.573921056029091, -1.34233288344333, -0.19934979925025, 0.964787364716102, -0.163677887101688, 1.2014142663676, -0.252299080447525, -0.252299080447525, -0.554968941924626, 0.600144249680229, 0.366906887079548, 0.00337619756147767, -0.163677887101688, -0.457838926112716, -0.121366688150845, 0.674109784566575, 0.964787364716102, 0.725770464064608, 0.897128715880298), ngr=255, totsam=412) $|О|О‚ђ0 €|О|О‚ђ эƒђ Я6‚ђ *рŒџ list(base.mu=0, base.tau=1, a.nonwhite=0, a.lincome=0, a.carstairs=0) list(base.mu=1, base.tau=5, a.nonwhite=-2, a.lincome=2, a.carstairs=-1) .|О|О‚ђ0 €Š*uTШ‚ёTextRulers.StdRulerDescёTextRulers.RulerDescђдЫƒёTextRulers.StdStyleDescёTextRulers.StyleDescђ‚‚ёTextRulers.AttributesDescђL ЃZG™Ÿo €ќ €Ц€€Z%€$.€ю6€И?€‚H€LQ ‚ђ *рŒМ:Hџeco2-agg-indiv: Ecological inference with one binary and one continuous exposure, and combined aggregate and individual data. Model for limiting long-term illness among men aged from 45 to 59 years in London, in terms of individual ethnicity, household income and area deprivation. Aggregate data are taken from the UK census small area statistics, and include ngr = 255 wards in London. Individual data are taken from the Health Survey for England, including 412 individuals in London. BUGS Model specification  { ## ecological data for (i in 1:ngr) { ## The number of individuals per ward reporting limiting long term illness ## is modelled as binomial, with risk py[i] constant over the area. N.llti[i] ~ dbin(py[i], N.pop[i]) ## This risk is obtained by integrating the individual level risk, firstly over the binary exposure, non-white ## ethnicity py[i] <- p.nonwhite[i] * pnw[i] + ( 1 - p.nonwhite[i] ) * pw[i] ## and secondly over the continuous variable, mean log income. Details of this calculation are given in ## Jackson et al., (2005) Improving ecological inference using individual-level data. logit(pw[i]) <- ( mu.base[i] + a.carstairs*carstairs[i] + a.lincome*mean.lincome[i] ) / sqrt(1 + pow(c*a.lincome, 2) / tau.x[i]) logit(pnw[i]) <- ( mu.base[i] + a.carstairs*carstairs[i] + a.nonwhite + a.lincome*mean.lincome[i] ) / sqrt(1 + pow(c*a.lincome, 2) / tau.x[i]) tau.x[i] <- 1 / pow(sd.lincome[i], 2) ## The risk includes a random area-specific effect mu.base[i], to account for heterogeneity between areas ## due to unobserved factors. mu.base[i] ~ dnorm(base.mu, base.tau) } ## Model for limiting long term illness in the individual-level data is just a logistic regression with the same ## coefficients for (i in 1:totsam) { llti[i] ~ dbern(pzy[i]) logit(pzy[i]) <- mu.base[ward[i]] + mu.scale + a.carstairs*carstairs[ward[i]] + a.nonwhite * nonwhite[i] + a.lincome * lincome[i] } c <- 16*sqrt(3) / (15 * pi) pi <- 3.141592654 ## Log odds ratios for area level Carstairs deprivation index, non-white ethnicity and log income a.carstairs ~ dnorm(0, 0.1) a.nonwhite ~ dnorm(0, 1.48) # 95% prior belief that OR(a.nonwhite) is between 1/5 and 5 a.lincome ~ dnorm(0, 1.48) ## Odds ratios for area level Carstairs deprivation index, non-white ethnicity and log income or.nonwhite <- exp(a.nonwhite) or.lincome <- exp(a.lincome) or.carstairs <- exp(a.carstairs) base.mu ~ dlogis(0, 1) base.tau ~ dgamma(1, 0.01) base.sig <- 1 / sqrt(base.tau) p.base <- exp(base.mu) / (1 + exp(base.mu)) mu.scale <- 0.7 # fixed difference in prevalence (logit scale) between HSE and census }  Data Click on the arrows to open the data Inits Click on the arrows to open the initial values After 30000 iterations from two parallel chains, with the first 4000 from each discarded, we obtain the following summary statistics. Results  node mean sd MC error 2.5% median 97.5% start sample base.mu -2.108 0.03027 0.001257 -2.171 -2.107 -2.052 4001 52000 base.sig 0.1843 0.01172 1.438E-4 0.1622 0.184 0.2082 4001 52000 or.carstairs 1.071 0.004904 1.836E-4 1.062 1.072 1.081 4001 52000 or.lincome 0.5617 0.04406 0.00158 0.4785 0.5608 0.6513 4001 52000 or.nonwhite 1.432 0.1649 0.007305 1.133 1.424 1.763 4001 52000 ‚ёTextControllers.StdCtrlDescёTextControllers.ControllerDescёContainers.ControllerDescёControllers.ControllerDescђ ‚ђaYƒђ?‚ђ$ ЃZG™Ÿo‚ђ *рŒ ј ј,›[ ј@‚ёDocuments.ControllerDescђ 2~s*Ѓ€ќ €ќ Вhš-˜