modelANOVA.txt

model{
# N observations (subjects * withinX1 * withinX2 * betweenX3)
for(i in 1:N){ 
    Y[i] ~ dnorm(muY[i], tauY)
    muY[i] <- a0 + a1[X1[i]] + a2[X2[i]] + a3[X3[i]] + a12[X1[i],X2[i]] + a123[X1[i],X2[i],X3[i]] + aS[X1[i],X3[i],id[i]] 
}

for (j1 in 1:nX1) { 
    for (j2 in 1:nX2) {
        for (j3 in 1:nX3) {
            for (s in 1:nS[j3]) {
                m[j1,j2,j3,s] <- a0 + a1[j1] + a2[j2] + a3[j3] + a12[j1,j2] + a123[j1,j2,j3] + aS[j1,j3,s] # cell means
            } 
        }
    }
}
# Mean for each subject
for (j3 in 1:nX3) {
    for (s in 1:nS[j3]) {
        mS[j3,s] <- mean(m[1:nX1, 1:nX2, j3, s])
    }
}

# Means for each treatment condition (across subjects)
for (j1 in 1:nX1) {
    for (j2 in 1:nX2) {
        for (j3 in 1:nX3) {
            m123[j1,j2,j3] <- mean(m[j1,j2,j3,1:nS[j3]])
        }
    }
}

# Mean for between factor (across subjects and within factors)
for (j3 in 1:nX3) { 
    m3[j3] <- mean(m123[1:nX1,1:nX2,j3])
}
# Mean for within factor 1
for (j1 in 1:nX1) { 
        m1[j1] <- mean(m123[j1,1:nX2,1:nX3])
}
# Mean for within factor 2
for (j2 in 1:nX2) { 
        m2[j2] <- mean(m123[1:nX1,j2,1:nX3])
}
# Mean for 2 factor interaction
for (j1 in 1:nX1) { 
    for (j2 in 1:nX2) {
        m12[j1,j2] <- mean(m123[j1,j2,1:nX3])
    }
}
mTot = mean(m123[1:nX1,1:nX2,1:nX3])
# Intercept
intercept <- mTot
# Deflection for between factor
for (j3 in 1:nX3) { 
    group[j3] <- m3[j3] - mTot
}
# Deflection for within factors
for (j2 in 1:nX2) { 
    paradigm[j2] <- m2[j2] - mTot
}
for (j1 in 1:nX1) { 
    phase[j1] <- m1[j1] - mTot
}
# Deflections for interactions
for (j1 in 1:nX1) {
    for (j2 in 1:nX2) {
        phase_paradigm[j1,j2] <- m12[j1,j2] - (intercept + phase[j1] + paradigm[j2])
        for (j3 in 1:nX3) {
            phase_paradigm_group[j1,j2,j3] <- m123[j1,j2,j3] - (intercept + phase[j1] + paradigm[j2] + phase_paradigm[j1, j2] + group[j3])
        }
    }
}
# Deflection for each subject
for (j3 in 1:nX3) {
    for (s in 1:nS[j3]) {
        betaS[j3,s] <- mS[j3,s] - (intercept + group[j3])
    }
}
# Priors
tauY ~ dgamma(0.001, 0.001)
for (j1 in 1:nX1) {
    for (j3 in 1:nX3) {
    tauS[j1,j3] ~ dt(0, 1/2.5^2,7)T(0,)
    }
}

a0 ~ dnorm(0, 10^-6)
for (j1 in 1:nX1) {
    a1[j1] ~ dnorm(0, 10^-6)
}
for (j2 in 1:nX2) {
    a2[j2] ~ dnorm(0, 10^-6)
}
for (j3 in 1:nX3) {
    a3[j3] ~ dnorm(0, 10^-6)
}
for (j1 in 1:nX1) {
    for (j2 in 1:nX2) {
        a12[j1,j2] ~ dnorm(0, 10^-6)
    }
}
for (j1 in 1:nX1) {
    for (j2 in 1:nX2) {
        for(j3 in 1:nX3) {
            a123[j1,j2,j3] ~ dnorm(0, 10^-6)
        }
    }
}
# Random effects
for (j1 in 1:nX1) {
    for (j3 in 1:nX3) {
        for(s in 1:nS[j3]){
            aS[j1,j3,s] ~ dnorm(0, tauS[j1,j3])
        }
    }
}
}