Penalized Composite Link Model for Efficient Estimation of Smooth Distributions from Coarsely Binned Data

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This repository contains a versatile method for ungrouping histograms (binned count data) assuming that counts are Poisson distributed and that the underlying sequence on a fine grid to be estimated is smooth. The method is based on the composite link model and estimation is achieved by maximizing a penalized likelihood. Smooth detailed sequences of counts and rates are so estimated from the binned counts. 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; and the last interval is often wide and open-ended and, thus, covers a lot of information in the tail area. Age-at-death distributions grouped in age classes and abridged life tables are examples of binned data. Because of modest assumptions, the approach is suitable for many demographic and epidemiological applications. For a detailed description of the method and applications see Rizzi et al. (2015).


  1. Make sure you have the most recent version of R
  2. Run the following code in your R console

Updating to the latest version of ungroup package

You can track (and contribute to) the development of ungroup at To install it:

  1. Install the release version of devtools from CRAN with install.packages("devtools").

  2. Make sure you have a working development environment.
  3. Install the development version of ungroup.


Get started with ungroup by checking the vignette R browseVignettes(package = "ungroup")


This software is an academic project. We welcome any issues and pull requests. * If ungroup is malfunctioning, please report the case by submitting an issue on GitHub. * If you wish to contribute, please submit a pull request following the guidelines in


Rizzi S, Gampe J and Eilers PHC. 2015. Efficient Estimation of Smooth Distributions From Coarsely Grouped Data. American Journal of Epidemiology, Volume 182, Issue 2, Pages 138-147.

Eilers PHC. 2007. Ill-posed problems with counts, the composite link model and penalized likelihood. Statistical Modelling, Volume 7, Issue 3, Pages 239-254.