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-0.121366688150845, 0.674109784566575, 0.964787364716102, 0.725770464064608, 0.897128715880298), ngr=761, totsam=412) $|О|О‚ђ$ € ‚ђ 2ArialрŒ|О|О‚ђЂ‘ ˆ‘ƒђ j‘:‚ђ ArialрŒ&‘џlist(num=c(4, 3, 4, 2, 8, 5, 7, 4, 7, 8, 6, 6, 6, 4, 5, 5, 6, 6, 8, 6, 8, 5, 9, 7, 6, 6, 7, 6, 6, 5, 6, 7, 6, 5, 8, 6, 5, 4, 5, 9, 6, 6, 8, 6, 7, 7, 6, 3, 7, 6, 5, 6, 7, 5, 6, 7, 6, 5, 10, 7, 4, 6, 8, 6, 6, 5, 4, 5, 5, 5, 6, 4, 5, 7, 9, 6, 6, 6, 6, 6, 6, 7, 5, 4, 11, 6, 6, 6, 5, 6, 7, 5, 7, 5, 6, 6, 7, 6, 5, 4, 7, 6, 4, 9, 5, 9, 5, 6, 6, 7, 6, 9, 6, 7, 9, 5, 7, 6, 8, 8, 6, 6, 7, 4, 5, 6, 6, 6, 6, 5, 7, 6, 6, 8, 6, 5, 5, 5, 5, 3, 7, 3, 7, 6, 7, 5, 7, 5, 5, 4, 6, 7, 6, 4, 7, 8, 6, 5, 8, 7, 5, 9, 9, 6, 6, 6, 5, 7, 6, 5, 4, 6, 5, 7, 6, 6, 9, 4, 8, 7, 6, 6, 5, 7, 10, 7, 6, 6, 3, 5, 7, 6, 5, 5, 6, 6, 8, 6, 6, 8, 4, 8, 6, 6, 7, 6, 7, 7, 8, 6, 7, 5, 5, 4, 5, 5, 5, 7, 5, 7, 4, 5, 8, 6, 4, 6, 5, 4, 7, 4, 5, 7, 6, 8, 7, 9, 5, 7, 4, 6, 6, 7, 7, 5, 6, 1, 7, 4, 5, 6, 4, 6, 8, 7, 6, 4, 6, 6, 5, 5, 5, 7, 5, 4, 5, 7, 5, 7, 8, 6, 2, 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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)) P |О|О‚ђ+ €t|О‚ђІ Œƒђ n6‚ђ *№.џClick on the arrows to open the initial valuesЁt|О‚ђ0 €у*uTШ‚ёTextRulers.StdRulerDescёTextRulers.RulerDescђдЫƒёTextRulers.StdStyleDescёTextRulers.StyleDescђ‚‚ёTextRulers.AttributesDescђL ЃZG™Ÿo €ќ €Ц€€Z%€$.€ю6€И?€‚H€LQ ‚ђ *рŒМ:Цџeco2-agg-indiv-spatial: Ecological inference with one binary and one continuous exposure, combined aggregate and individual data, and spatially-correlated random effects 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 = 761 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. Here this is given a spatial, instead of an exchangeable, structure ## with the conditional autoregressive (CAR) distribution. (Besag et al., 1991) mu.base[i] <- base.mu + U[i] } U[1:ngr] ~ car.normal(adj[], weights[], num[], tau.u) ## 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]] + 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) tau.u ~ dgamma(0.5, 0.0005) sig.u <- 1 / sqrt(tau.u) sd.u <- sd(U[]) 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 Spatial dataClick on the arrows to open the extra data required for the spatial distribution Inits  list(base.mu=0, base.tau=1, a.nonwhite=0, a.lincome=0, a.carstairs=0, tau.u=1) list(base.mu=1, base.tau=5, a.nonwhite=-2, a.lincome=2, a.carstairs=-1, tau.u=5)  The simulation runs at about 78 seconds for 1000 iterations on a 2.4 GHz computer. After running 30000 iterations, discarding the first 4000 as burn-in, from two parallel chains, we obtain the following summary statistics. Results  node mean sd MC error 2.5% median 97.5% start sample base.mu -2.104 0.01997 9.202E-4 -2.142 -2.104 -2.065 4001 52000 base.sig 0.1759 0.3101 0.001362 0.05195 0.1198 0.6244 4001 52000 or.carstairs 1.068 0.003964 1.786E-4 1.06 1.068 1.076 4001 52000 or.lincome 0.4876 0.02623 0.001164 0.4389 0.4869 0.5399 4001 52000 or.nonwhite 1.216 0.08934 0.004068 1.046 1.213 1.388 4001 52000 sd.u 0.18 0.005133 1.061E-4 0.1702 0.1799 0.1901 4001 52000 sig.u 0.2828 0.01241 1.875E-4 0.2591 0.2826 0.3078 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-˜