# Solved – Bayesian mixed model regression with a between subjects factor

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.

Contents

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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