Missing Data – Handling Missing Values in Response Variable in JAGS

bugsjagsmissing data

Gelman & Hill (2006) say:

In Bugs, missing outcomes in a regression can be handled easily by
simply including the data vector, NA’s and all. Bugs explicitly
models the outcome variable, and so it is trivial to use this model
to, in eﬀect, impute missing values at each iteration.

This sounds like an easy way to use JAGS to do prediction. But do the observations with the missing outcomes also affect parameter estimates? If so, is there an easy way to keep these observations in the dataset that JAGS sees, but to not have them affect the parameter estimates? I was thinking about the cut function, but that's only available in BUGS, not JAGS.

Best Answer

Yes, it is really easy to use in BUGS or JAGS! It is actually a pleasure to use it!

But do the observations with the missing outcomes also affect parameter estimates?

Of course not. The parameters are only affected by the observed outcomes. The missing outcomes (NAs) will not affect anything, actually it is the other way: the missing outcomes will be derived from the parameters. Note that the missing outcomes will have its posterior distribution also. Then it is very easy to compute some derived quantities e.g. like a sum over indices of the outcome, and these derived quantities not only are handled for missing values, but also immediatelly have their posterior distribution. That's what is so sexy on BUGS & JAGS!

Have fun!

Related Solutions

Solved – JAGS: posterior predictive distribution

disclaimer I still don't fully understand your model; but without at least a reproducible example, this is the best I can offer. It is not clear exactly what you are doing here. For example, how are pvr and pir calculated? Would it make sense to calculate them inside the same model?

Answer

I am assuming that your data includes observations for mu[] but not pmu[] and you want to estimate pmu[j] given j values of pvr and pir.

Append the pir and pvr to the ir and vr columns, get rid of the second for loop, and then consider the values of mu[] estimated using pir and pvr to be the posterior predictive estimates of mu. Then replace the two for loops with this:

for (i in 1:length(ri)+length(pri)){
    ri[i] ~ dnorm(mu[i],tau)
    mu[i] <- alpha + b.vr*vr[i] + b.ir*ir[i]
}

I have done something similar, but without predicted regressors, similar to the example given by Gelman et al in 'Bayesian Data Analysis' (pp 598-599 starting under posterior predictive simulations).

Solved – Vector multiplication in BUGS and JAGS

Unlike JAGS, WinBUGS and OpenBUGS does not do this form of vectorization; you have to write a loop, and compute each element 'by hand', as described above.

Best Answer

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Solved – JAGS: posterior predictive distribution

Solved – Vector multiplication in BUGS and JAGS

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