joss/paper.md

In mpascariu/ungroup: Penalized Composite Link Model for Efficient Estimation of Smooth Distributions from Coarsely Binned Data

title: 'ungroup: An R package for efficient estimation of smooth distributions from coarsely binned data' tags: - composite link model - GLM - histogram - binned data - smoothing authors: - name: Marius D. Pascariu affiliation: 1 email: [e-mail] orcid: 0000-0002-2568-6489 - name: Maciej J. Dańko affiliation: 3 orcid: 0000-0002-7924-9022 - name: Jonas Schöley affiliation: 1 orcid: 0000-0002-3340-8518 - name: Silvia Rizzi affiliation: 2 affiliations: - name: Institute of Public Health, Center on Population Dynamics, University of Southern Denmark, Odense, Denmark index: 1 - name: Institute of Public Health, Unit of Epidemiology Biostatistics and Biodemography, University of Southern Denmark, Odense, Denmark index: 2 - name: Max Planck Institute for Demographic Research, Rostock, Germany index: 3 date: "19 September 2018" bibliography: paper.bib

Summary

ungroup is an open source software library written in the R programming language [@team2018r] that introduces a versatile method for ungrouping histograms (binned count data) assuming that counts are Poisson distributed and that the underlying sequence over a fine grid to be estimated is smooth. The method is based on the composite link model [@thompson1981] and estimation is achieved by maximizing a penalized likelihood [@eilers2007], which extends standard generalized linear models. The penalized composite link model (PCLM) implements the idea that observed counts, interpreted as realizations from Poisson distributions, are indirect observations of a finer (ungrouped) but latent sequence. This latent sequence represents the distribution of expected means on a fine resolution and has to be estimated from the aggregated data. Estimates are obtained by maximizing a penalized likelihood. This maximization is performed efficiently by a version of the iteratively re-weighted least-squares algorithm. Optimal values of the smoothing parameter are chosen by minimizing Bayesian or Akaike's Information Criterion [@hastie1990].

Ungrouping binned data can be desirable for many reasons: Bins can be too coarse to allow for accurate analysis; comparisons can be hindered when different grouping approaches are used in different histograms; the last interval may be wide and open-ended masking the tail behaviour of the underlying distribution. Age-at-death distributions grouped into age classes and abridged life tables are examples of binned data which can be ungrouped with the package ungroup. The modest assumptions of the methodology underpinning the PCLM method make it suitable for many demographic and epidemiological applications. For a detailed description of the method and applications see @rizzi2015 and @rizzi2016.

The penalized composite link model can be extended to a two-dimensional regression problem [@rizzi2018]. The two-dimensional regression analysis combines two approaches: the PCLM for ungrouping in one dimension and two-dimensional smoothing with P-splines [@currie2004]. As an example one can ungroup age-specific distributions from the coarsely grouped data and smooth across adjacent calendar years to estimate both detailed age-at-death distributions and mortality time trends.

Acknowledgments

We thank Paul H.C. Eilers who provided insight and expertise that greatly supported the creation of this R package; and Catalina Torres and Tim Riffe for testing and offering feedback on the early versions of the software.

The authors are grateful to the following institutions for their support:

• University of Southern Denmark;
• Max Planck Institute for Demographic Research;
• The SCOR Corporate Foundation for Science.

References

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