model{ ################## ##### MODELE ##### 4 = final model with added interaction terms ################## between ttt effect and secondary RP # submodel for the number of crises : fixed and random effects for (i in 1:Nmesures) { nb.crises[i] ~ dpois(lambda.crise[i]) log.lambda.crise[i] <- b.crise.cst + r.crise.indiv[indiv[i]] + ( b.crise[1] + b.crise.indiv[1,indiv[i]] )*ttt1[i] + ( b.crise[2] + b.crise.indiv[2,indiv[i]] )*ttt2[i] + b.crise.ttt1.second*(ttt1[i]*second[i])+ b.crise.ttt2.second*(ttt2[i]*second[i])+ b.crise.temp*temp[i] + b.crise.humid*humid[i] + b.crise.age*age[i] + b.crise.homme*homme[i] + b.crise.inhib*inhib[i] + b.crise.second*second[i] lambda.crise[i] <- exp(log.lambda.crise[i]) } # submodel for the RCS : fixed and random effects # gamma distribution parameters for R and JAGS # r = a = "shape" # lambda = 1/s = "rate" = 1/"scale" = "dispersion" # shape = lambda x Expectation # lambda = Expectation / Variance for (i in 1:Nmesures) { rcs[i] ~ dgamma(shape.rcs[i], dispersion.rcs)T(,10) log.E.rcs[i] <- b.rcs.cst + r.rcs.indiv[indiv[i]] + ( b.rcs[1] + b.rcs.indiv[1,indiv[i]] )*ttt1[i] + ( b.rcs[2] + b.rcs.indiv[2,indiv[i]] )*ttt2[i] + b.rcs.ttt1.second*(ttt1[i]*second[i])+ b.rcs.ttt2.second*(ttt2[i]*second[i])+ b.rcs.temp*temp[i] + b.rcs.humid*humid[i] + b.rcs.age*age[i] + b.rcs.homme*homme[i] + b.rcs.inhib*inhib[i] + b.rcs.second*second[i] E.rcs[i] <- exp(log.E.rcs[i]) shape.rcs[i] <- E.rcs[i] * dispersion.rcs } # submodel for the daily duration : fixed and random effects for (i in 1:Nmesures) { duree[i] ~ dgamma(shape.duree[i], dispersion.duree[i]) log.E.duree[i] <- b.duree.cst + r.duree.indiv[indiv[i]] + ( b.duree[1] + b.duree.indiv[1,indiv[i]] )*ttt1[i] + ( b.duree[2] + b.duree.indiv[2,indiv[i]] )*ttt2[i] + b.duree.ttt1.second*(ttt1[i]*second[i])+ b.duree.ttt2.second*(ttt2[i]*second[i])+ b.duree.temp*temp[i] + b.duree.humid*humid[i] + b.duree.age*age[i] + b.duree.homme*homme[i] + b.duree.inhib*inhib[i] + b.duree.second*second[i] E.duree[i] <- exp(log.E.duree[i]) shape.duree[i] <- nb.crises[i]+0.000001 dispersion.duree[i] <- shape.duree[i] / E.duree[i] } # submodel for the number of crises : random effects distribution for (m in 1:Nindivs) { r.crise.indiv[m] ~ dnorm(0, pow(sigma2.crise.indiv,-1)) b.crise.indiv[1,m] ~ dnorm(0, pow(sigma2.crise.indiv.b1,-1)) b.crise.indiv[2,m] ~ dnorm(0, pow(sigma2.crise.indiv.b2,-1)) } # submodel for the RCS : random effects distribution for (m in 1:Nindivs) { r.rcs.indiv[m] ~ dnorm(0, pow(sigma2.rcs.indiv,-1)) b.rcs.indiv[1,m] ~ dnorm(0, pow(sigma2.rcs.indiv.b1,-1)) b.rcs.indiv[2,m] ~ dnorm(0, pow(sigma2.rcs.indiv.b2,-1)) } # submodel for the daily duration : random effects distribution for (m in 1:Nindivs) { r.duree.indiv[m] ~ dnorm(0, pow(sigma2.duree.indiv,-1)) b.duree.indiv[1,m] ~ dnorm(0, pow(sigma2.duree.indiv.b1,-1)) b.duree.indiv[2,m] ~ dnorm(0, pow(sigma2.duree.indiv.b2,-1)) } ################## ##### PRIORS ##### ################## # number of crises, fixed effects moy.crise.cst <- 0.184458 moy.crise.ttt1 <- 0 moy.crise.ttt2 <- 0 moy.crise.ttt1.second <- 0 moy.crise.ttt2.second <- 0 moy.crise.temp <- 0 moy.crise.humid <- 0 moy.crise.age <- 0 moy.crise.homme <- 0 moy.crise.second <- 0 moy.crise.inhib <- -0.7142857 sd.crise.cst <- 1.168326 sd.crise.ttt1 <- 10 sd.crise.ttt2 <- 10 sd.crise.ttt1.second <- 10 sd.crise.ttt2.second <- 10 sd.crise.temp <- 10 sd.crise.humid <- 10 sd.crise.age <- 10 sd.crise.homme <- 10 sd.crise.second <- 10 sd.crise.inhib <- 0.2922741 # RCS, fixed effects moy.rcs.cst <- 1.444178 moy.rcs.ttt1 <- 0 moy.rcs.ttt2 <- 0 moy.rcs.ttt1.second <- 0 moy.rcs.ttt2.second <- 0 moy.rcs.temp <- 0 moy.rcs.humid <- 0 moy.rcs.age <- 0 moy.rcs.homme <- 0 moy.rcs.second <- 0 moy.rcs.inhib <- -1.39 sd.rcs.cst <- 0.3600715 sd.rcs.ttt1 <- 10 sd.rcs.ttt2 <- 10 sd.rcs.ttt1.second <- 10 sd.rcs.ttt2.second <- 10 sd.rcs.temp <- 10 sd.rcs.humid <- 10 sd.rcs.age <- 10 sd.rcs.homme <- 10 sd.rcs.second <- 10 sd.rcs.inhib <- 0.4132653 moy.dispersion.rcs <- (moy.rcs.cst / pow(sd.rcs.cst,2)) inf.dispersion.rcs <- 0 sup.dispersion.rcs <- moy.dispersion.rcs +5 # duration, fixed effects moy.duree.cst <- 0 moy.duree.ttt1 <- 0 moy.duree.ttt2 <- 0 moy.duree.ttt1.second <- 0 moy.duree.ttt2.second <- 0 moy.duree.temp <- 0 moy.duree.humid <- 0 moy.duree.age <- 0 moy.duree.homme <- 0 moy.duree.second <- 0 moy.duree.inhib <- 0 sd.duree.cst <- 10 sd.duree.ttt1 <- 10 sd.duree.ttt2 <- 10 sd.duree.ttt1.second <- 10 sd.duree.ttt2.second <- 10 sd.duree.temp <- 10 sd.duree.humid <- 10 sd.duree.age <- 10 sd.duree.homme <- 10 sd.duree.second <- 10 sd.duree.inhib <- 10 ### submodel for the number of crises : fixed and random effects distributions # fixed effects b.crise.cst ~ dnorm (moy.crise.cst, pow(sd.crise.cst,-2)) b.crise[1] ~ dnorm (moy.crise.ttt1, pow(sd.crise.ttt1,-2)) b.crise[2] ~ dnorm (moy.crise.ttt2, pow(sd.crise.ttt2,-2)) b.crise.ttt1.second ~ dnorm (moy.crise.ttt1.second, pow(sd.crise.ttt1.second,-2)) b.crise.ttt2.second ~ dnorm (moy.crise.ttt2.second, pow(sd.crise.ttt2.second,-2)) b.crise.temp ~ dnorm (moy.crise.temp, pow(sd.crise.temp,-2)) b.crise.humid ~ dnorm (moy.crise.humid, pow(sd.crise.humid,-2)) b.crise.age ~ dnorm (moy.crise.age, pow(sd.crise.age,-2)) b.crise.homme ~ dnorm (moy.crise.homme, pow(sd.crise.homme,-2)) b.crise.second ~ dnorm (moy.crise.second, pow(sd.crise.second,-2)) b.crise.inhib ~ dnorm (moy.crise.inhib, pow(sd.crise.inhib,-2)) # random effects sigma2.crise.indiv ~ dunif(0.01,5) sigma2.crise.indiv.b1 ~ dunif(0.01,5) sigma2.crise.indiv.b2 ~ dunif(0.01,5) ### submodel for the RCS : fixed and random effects distributions # fixed effects b.rcs.cst ~ dnorm (moy.rcs.cst, pow(sd.rcs.cst,-2)) b.rcs[1] ~ dnorm (moy.rcs.ttt1, pow(sd.rcs.ttt1,-2)) b.rcs[2] ~ dnorm (moy.rcs.ttt2, pow(sd.rcs.ttt2,-2)) b.rcs.ttt1.second ~ dnorm (moy.rcs.ttt1.second, pow(sd.rcs.ttt1.second,-2)) b.rcs.ttt2.second ~ dnorm (moy.rcs.ttt2.second, pow(sd.rcs.ttt2.second,-2)) b.rcs.temp ~ dnorm (moy.rcs.temp, pow(sd.rcs.temp,-2)) b.rcs.humid ~ dnorm (moy.rcs.humid, pow(sd.rcs.humid,-2)) b.rcs.age ~ dnorm (moy.rcs.age, pow(sd.rcs.age,-2)) b.rcs.homme ~ dnorm (moy.rcs.homme, pow(sd.rcs.homme,-2)) b.rcs.second ~ dnorm (moy.rcs.second, pow(sd.rcs.second,-2)) b.rcs.inhib ~ dnorm (moy.rcs.inhib, pow(sd.rcs.inhib,-2)) # random effects sigma2.rcs.indiv ~ dunif(0.01,5) sigma2.rcs.indiv.b1 ~ dunif(0.01,5) sigma2.rcs.indiv.b2 ~ dunif(0.01,5) # gamma distribution dispersion for RCS dispersion.rcs ~ dunif(inf.dispersion.rcs,sup.dispersion.rcs ) ### submodel for the daily duration : fixed and random effects distributions # fixed effects b.duree.cst ~ dnorm (moy.duree.cst, pow(sd.duree.cst,-2)) b.duree[1] ~ dnorm (moy.duree.ttt1, pow(sd.duree.ttt1,-2)) b.duree[2] ~ dnorm (moy.duree.ttt2, pow(sd.duree.ttt2,-2)) b.duree.ttt1.second ~ dnorm (moy.duree.ttt1.second, pow(sd.duree.ttt1.second,-2)) b.duree.ttt2.second ~ dnorm (moy.duree.ttt2.second, pow(sd.duree.ttt2.second,-2)) b.duree.temp ~ dnorm (moy.duree.temp, pow(sd.duree.temp,-2)) b.duree.humid ~ dnorm (moy.duree.humid, pow(sd.duree.humid,-2)) b.duree.age ~ dnorm (moy.duree.age, pow(sd.duree.age,-2)) b.duree.homme ~ dnorm (moy.duree.homme, pow(sd.duree.homme,-2)) b.duree.second ~ dnorm (moy.duree.second, pow(sd.duree.second,-2)) b.duree.inhib ~ dnorm (moy.duree.inhib, pow(sd.duree.inhib,-2)) # random effects sigma2.duree.indiv ~ dunif(0.01,10) sigma2.duree.indiv.b1 ~ dunif(0.01,10) sigma2.duree.indiv.b2 ~ dunif(0.01,10) }