Behavior Genetics

, Volume 46, Issue 2, pp 252–268 | Cite as

Applying Multivariate Discrete Distributions to Genetically Informative Count Data

  • Robert M. Kirkpatrick
  • Michael C. Neale
Original Research


We present a novel method of conducting biometric analysis of twin data when the phenotypes are integer-valued counts, which often show an L-shaped distribution. Monte Carlo simulation is used to compare five likelihood-based approaches to modeling: our multivariate discrete method, when its distributional assumptions are correct, when they are incorrect, and three other methods in common use. With data simulated from a skewed discrete distribution, recovery of twin correlations and proportions of additive genetic and common environment variance was generally poor for the Normal, Lognormal and Ordinal models, but good for the two discrete models. Sex-separate applications to substance-use data from twins in the Minnesota Twin Family Study showed superior performance of two discrete models. The new methods are implemented using R and OpenMx and are freely available.


Count variables Twin study Biometric variance components Multivariate discrete distributions Substance use Lagrangian probability distributions 



The authors were supported by U.S. Public Health Service grant DA026119. William G. Iacono and Matt McGue provided the MTFS dataset, which was supported by U.S. Public Health Service Grants DA05147, AA009367, and DA013240. The first author gives his special thanks to Matt McGue, Niels G. Waller, and Hermine H. Maes for their comments on drafts of the paper.

Compliance with Ethical Standards

Conflict of Interest

Robert M. Kirkpatrick and Michael C. Neale declare that they have no conflict of interest.

Human and animal rights and informed consent

The MTFS was reviewed and approved by the Institutional Review Board at the University of Minnesota. Written informed assent or consent was obtained from all participants, with parents providing written consent for their minor children.

Supplementary material

10519_2015_9757_MOESM1_ESM.pdf (150 kb)
Online Resource 1: Supplementary Appendices. Supplementary material 1 (pdf 150 kb) (16 kb)
Online Resource 2: 3 text files: a README file for the other two, an example R script from the Monte Carlo simulation, and an R script for producing graphs and summary statistics from the raw simulation data (read in over the web). Supplementary material 2 (zip 15 kb)


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Virginia Institute for Psychiatric & Behavioral GeneticsVirginia Commonwealth UniversityRichmondUSA

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