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I'm currently working with a data set that consists of a monthly case count for several sites, along with a number of site-specific covariates. We're trying to estimate the effect of one of them on the case-load (either in terms of numbers or a percent). At the moment, I've been using Peng and Dominici's Statistical Methods for Environmental Epidemiology with R as a reference for the approach I'm considering using.

For a single site, the idea is to fit a Poisson model with roughly the following form:

$$\log ({\mu _t}) = \alpha + \beta {x_t} + \eta {z_t} + f(t) + {\varepsilon _t}$$

Where mu is the monthly case count, beta is the log-relative increase in cases due to a one unit increase in the variable of interest, eta is the vector of other measured covariates and f(t) is some sort of smoothed spline over time.

So far, I'm comfortable enough with this. My problem is implementing a hierarchical model that gives an estimate of the effect pulling from information from each site. Is there a particularly good way to approach this in R? A well-documented package for example? Is it sufficient to essentially treat this as a meta-analysis with each site as a "study" and use something like metafor? And is there a way to do it while modeling a site-specific covariate? The authors seem to be pushing for the use of a Bayesian hierarchical model, but the implementation of something like that is admittedly a bit of unexplored territory for me.

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  • $\begingroup$ I can't offer a complete answer, but there is a book devoted to hierarchical models. Checkout Gelman, Hill stat.columbia.edu/~gelman/arm $\endgroup$
    – Robert Kubrick
    Commented Apr 10, 2012 at 12:43
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    $\begingroup$ If time series problems like endogeneity, unit roots and etc are not an issue, i.e. you have repeated measures data, I would try to use something like glmer from package lme4. $\endgroup$
    – mpiktas
    Commented Apr 10, 2012 at 14:10
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    $\begingroup$ @RobertKubrick my recollection is that Gelman's book does not have much of a focus on approaches to hierarchical time series. Can you recommend some resources that deal with the subject in more detail? $\endgroup$
    – John
    Commented Oct 1, 2013 at 21:29
  • $\begingroup$ It's been a while, but I'm currently dealing with a very similar problem, where I would like to model time series data with a Bayesian structural time series where I also consider both fixed and mixed effects in the regression part. $\endgroup$
    – Tommaso Guerrini
    Commented Mar 30, 2017 at 19:16

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