[R-sig-Geo] credible interval for empirical Bayesian estimates of rates

[Roger Bivand]

On Fri, 24 Apr 2020, Dexter Locke wrote:

> Dear esteemed list,
>
> I'm using spdep::EBest with family = 'binomial' for counts of events within
> polygons that have an 'at risk' population. The resultant "estmm" is
> 'shrunk' compared to the raw rate (both given by EBest and calculated "by
> hand" rate. All good there.
>
> Using GeoDa version 1.14.0 24 August 2019 produces identical results for
> its Empirical Bayesian rate. This was confirmed by plotting the EBest
> output against GeoDa's rate and finding a perfect correlation along the 1
> to 1 line. All good there.

Please provide a reproducible example, as this may help with answers.

>
> Two questions:
> 1. How can credible intervals around these smoothed rate estimates be
> calculated?
> 2. The spdep documentation calls this a binomial family, but the identical
> results are obtained from GeoDa calls this "Poisson-Gamma" model here:
> https://geodacenter.github.io/workbook/3b_rates/lab3b.html#fnref11 , so
> what is actually being calculated? This question may help me answer the
> first question..

No, the default family is "poisson", with "binomial" available for 
non-rare conditions following Martuzzi, implemented by Olaf 
Berke, ?spdep::EBest.

The code in spdep is easily accessible, so can be read directly. Please 
also compare with code for the EB Moran test, and with analogous code in 
the DCluster package, empbaysmooth(). Cf. ASDAR 2nd ed., ch. 10, section 
10.2, pp. 322-328. The epitools::pois.exact() function is used for CIs. 
For code and data see https://asdar-book.org/bundles2ed/dismap_bundle.zip.

>
> Possibly the answers are addressed in the literature cited which I cannot
> access right now at home without institutional library access.
>

Most institutions do have proxy or VPN access, but the code will be as 
useful. In PySAL, the code would also guide you, but even though GeoDa is 
open source, the C++ is fairly dense.

Hope this helps,

Roger

> Thanks for your consideration,
> Dexter
> http://dexterlocke.com/
>
> 	[[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-Geo mailing list
> R-sig-Geo using r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>

-- 
Roger Bivand
Department of Economics, Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; e-mail: Roger.Bivand using nhh.no
https://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en