I'm trying to specify a model in JAGS/rjags with one between subjects factor (**a**, with two levels – *Y*, *N*) interacting with one repeated measures continuous variable **x** plus subject varying slopes and intercepts that correlate. I can specify this model simply enough with the lmer function:

`lmer(y ~ a + x + a:x + (1 + a | id)) `

My JAGS/rjags is very rusty (or very fresh). The below seems to me to be fitting a model with subject varying intercepts and subject varying slopes while estimating the slope for both levels of **a**, but I'm not sure I'm doing what I think I'm doing. There's also no correlation specified between the two.

`modelstring = " model { for ( i in 1:Ntotal ) { y[i] ~ dnorm( mu[i] , tau ) mu[i] <- a1[aLvl[i]] + s1[sLvl[i]] + a2[aLvl[i]] * x[i] + s2[sLvl[i]] * x[i] } # Prior: tau <- pow( sigma , -2 ) sigma ~ dunif(0,1000) for ( j in 1:2 ) { a1[j] ~ dnorm( 0.0 , aTau ) a2[j] ~ dnorm( 0.0 , aTau ) } aTau <- 1 / pow( aSD , 2 ) aSD <- abs( aSDunabs ) + .1 aSDunabs ~ dt( 0 , 1.0E-7 , 2 ) # for ( j in 1:NsLvl ) { s1[j] ~ dnorm( 0.0 , sTau ) s2[j] ~ dnorm( 0.0 , sTau ) } sTau <- 1 / pow( sSD , 2 ) sSD <- abs( sSDunabs ) + .1 sSDunabs ~ dt( 0 , 1.0E-7 , 2 ) } " `

The framework for this comes from Kruschke and this has been of some help too. I would appreciate some pointers or links to examples of similar analyses.

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#### Best Answer

I eventually figured this one out with much help from Doing Bayesian Data Analysis (Kruschke) and Data Analysis Using Regression and Multilevel/Hierarchical Models (Gelman). This model gives varying intercepts and slopes and the correlation between them.

y = dependent variable

sLvl = participant id at each data point

aLvlx = between subjects factor for each id

NaLvl = Number of levels for the between subject's factor

Ntotal = total length of data in long form

`modelstring = " model { for( r in 1 : Ntotal ) { y[r] ~ dnorm( mu[r] , tau ) mu[r] <- b0[ sLvl[r] ] + b1[ sLvl[r] ] * x[r] } #General priors tau ~ dgamma( sG , rG ) sG <- pow(m,2)/pow(d,2) rG <- m/pow(d,2) m ~ dgamma(1, 0.001) d ~ dgamma(1, 0.001) #Subject level priors for ( s in 1 : NsLvl ) { b0[s] <- B[s,1] b1[s] <- B[s,2] B[s, 1:2] ~ dmnorm( B.hat[s, ], Tau.B[ , ] ) B.hat[s,1] <- hix1[aLvlx[s]] B.hat[s,2] <- hix2[aLvlx[s]] } Tau.B[1:2 , 1:2] <- inverse(Sigma.B[,]) Sigma.B[1,1] <- pow(tau0G, 2) Sigma.B[2,2] <- pow(tau1G, 2) Sigma.B[1,2] <- rho * tau0G * tau1G Sigma.B[2,1] <- Sigma.B[1,2] tau0G ~ dunif(0.001,100) tau1G ~ dunif(0.001,100) rho ~ dunif(-1,1) #Between subjects level priors for ( k in 1:NaLvl ) { hix1[k] ~ dnorm( 0 , 0.0000001 ) hix2[k] ~ dnorm( 0 , 0.0000001 ) } }" writeLines(modelstring,con="model.txt") `

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