[R] Hierarchical Version of Bayesian Change Detection Model in JAGS

[Llew Mills]

I am trying to create a hierarchical changepoint detection model in JAGS,
estimating group difference in changepoint based on individual changepoints
in scores for an outcome variable (fictional in this case). I can run a
non-hierarchical version of this same analysis, based on a single set of
scores, but am having trouble with the hierarchical structure in JAGS.

Here is code for creating the toy data. score is a fictional outcome
variable measured on each of 84 days (tracked by variable days) for forty
individuals ( variable id) divided equally among two groups (tracked by
variable group). Data is created so the individuals in group A tend to have
a later breakpoint (around day 34) than those in group B (around day 15).

Here is code for toy data.

    breakpointG1 <- NA
    for (i in 1:20) { breakpointG1[i] <- round(rnorm(1, 34, 5)) }
    breakpointG2 <- NA
    for (i in 1:20) { breakpointG2[i] <- round(rnorm(1, 15, 5)) }
    bps <- c(breakpointG1, breakpointG2)
    group <- rep(c("A", "B"), each = 20)
    df <- data.frame(id = NA, days = NA, group = NA, score = NA)
    for ( i in 1:length(bps) ) {
    pre <- rnorm(bps[i], 40, 3) #
    post <- rnorm(84-bps[i], 25, 3)
    dfi <- data.frame(id = i, days = 1:84, group = rep(group[i], 84), score
= c(pre, post))
    df <- rbind(df, dfi)
    }
    df <- df[-1,]

Plot all participants in one graph, but with a separate loess-smoothed line
for each group.

    ggplot(df, aes(x = days, y = score)) +
           geom_point(aes(colour = factor(id))) +
           geom_smooth(aes(group = group, linetype = group), colour =
"black", span = 0.5, se = F) + guides(colour = F)

The difference in group change thresholds is clearly visible on this graph.
Now for the Bayesian analysis verifying what we can see with our eyes.
First step is to create the data list from the dataframe.

    y <- df$score
    sdY <- sd(y)
    sid <- df$id
    days <- df$days
    nTotal <- nrow(df)
    nDays <- max(df$days)
    nID <- length(unique(sid))
    nG <- length(unique(g))

We also need a vector where each element is the group number of the subject
in question (i.e. there will be 40 elements in this vector)

    groupOfSubject = NULL
    for ( sIdx in 1:nID ) {
      groupOfSubject = c( groupOfSubject , unique(g[sid==sIdx]) )
    }

    dataList = list(y = y,
                    sdY = sdY,
                    g = g,
                    days = days,
                    sid = sid,
                    nTotal = nTotal,
                    nDays = nDays,
                    nID = nID,
                    nG = nG,
                    groupOfSubject = groupOfSubject)


Now the model string for jags. The main things I am interested in
estimating are the group changepoints `muChng[]` and the `muB[]`s for pre-
and post-breakpoint `score`. I have used nested indexing but I must confess
I am out of my depth here.

    cat("
        model{

        # likelihood
        for (oIdx in 1:nTotal) {
        y[oIdx] ~ dnorm(mu[sid[oIdx]], 1/sigma^2)
        mu[sid[oIdx]] <- b1[sid[oIdx]] + step(days[oIdx] -
chng[sid[oIdx]])*b2[sid[oIdx]]
        }

        # priors
            # on subject-level id for b
            for (sIdx in 1:nID) {
                 b1[sIdx] ~ dnorm( muB1[groupOfSubject[sIdx]], 1/10^2 )
                 b2[sIdx] ~ dnorm( muB2[groupOfSubject[sIdx]], 1/10^2 )
                 chng[sIdx] ~ dnorm( muChng[groupOfSubject[sIdx]], 1/10^2 )
                 }

                # prior on group
                for (gIdx in 1:nG) {
                     muB1[gIdx] ~ dnorm(0, 1e-6)
                     muB2[gIdx] ~ dnorm(0, 1e-6)
                     muChng[gIdx] ~ dunif(1,nDays)
                     }

        # prior on Sigma
        sigma ~ dunif(1/sdY*10,sdY*10)

        }", file = "temp.jag")

Next adapt the mcmc chains using `rjags::jags.model()`.

    library(rjags)
    jagsModel <- jags.model(file = "temp.jag",
                            data = dataList,
                            n.chains = 3,
                            n.adapt = 1000)

But the model doesn't run, returning the message

    Error in jags.model(file = "temp.jag", data = dataList, n.chains = 3,
:
      RUNTIME ERROR:
    Compilation error on line 7.
    Attempt to redefine node mu[1]

I am not as familiar with breakpoint models as with the general linear
model so am not sure where I am going wrong. Something to do with the
nested indexing in the definition of `mu[]` in the likelihood function I
think, but I can't see where, and none of the alternatives I have tried
seem to work. I am stuck. Will take any suggestions, from small to a
complete overhaul or a different method. Any help much appreciated.

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