Behavior Genetics

, Volume 49, Issue 1, pp 99–111 | Cite as

Type I Error Rates and Parameter Bias in Multivariate Behavioral Genetic Models

  • Brad VerhulstEmail author
  • Elizabeth Prom-Wormley
  • Matthew Keller
  • Sarah Medland
  • Michael C. Neale
Original Research


For many multivariate twin models, the numerical Type I error rates are lower than theoretically expected rates using a likelihood ratio test (LRT), which implies that the significance threshold for statistical hypothesis tests is more conservative than most twin researchers realize. This makes the numerical Type II error rates higher than theoretically expected. Furthermore, the discrepancy between the observed and expected error rates increases as more variables are included in the analysis and can have profound implications for hypothesis testing and statistical inference. In two simulation studies, we examine the Type I error rates for the Cholesky decomposition and Correlated Factors models. Both show markedly lower than nominal Type I error rates under the null hypothesis, a discrepancy that increases with the number of variables in the model. In addition, we observe slightly biased parameter estimates for the Cholesky decomposition and Correlated Factors models. By contrast, if the variance–covariance matrices for variance components are estimated directly (without constraints), the numerical Type I error rates are consistent with theoretical expectations and there is no bias in the parameter estimates regardless of the number of variables analyzed. We call this the direct symmetric approach. It appears that each model-implied boundary, whether explicit or implicit, increases the discrepancy between the numerical and theoretical Type I error rates by truncating the sampling distributions of the variance components and inducing bias in the parameters. The direct symmetric approach has several advantages over other multivariate twin models as it corrects the Type I error rate and parameter bias issues, is easy to implement in current software, and has fewer optimization problems. Implications for past and future research, and potential limitations associated with direct estimation of genetic and environmental covariance matrices are discussed.


Twin models Type I error Cholesky decomposition Correlated factors model Direct symmetrical matrix 



An earlier draft of this paper was circulated to the faculty of the 2018 International Workshop on Statistical Genetic Methods for Human Complex Traits in Boulder, Colorado and was presented at the 48th meeting of the Behavioral Genetics Association in Boston Mass., June 20 to June 23, 2018. We would like to thank the workshop faculty and students, conference attendees for their suggestions to improve the paper.


This study was supported by NIDA Grants R01DA-018673 and R25DA-26119.

Compliance with ethical standards

Conflict of interest

Brad Verhulst, Elizabeth Prom-Wormley, Matthew C Keller, Sarah Medland, and Michael C. Neale declare that they have no conflict of interest.

Informed consent

For this type of study formal consent is not required.

Statement of human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PsychologyMichigan State UniversityEast LansingUSA
  2. 2.Family Medicine and Population HealthVirginia Commonwealth UniversityRichmondUSA
  3. 3.Department of Psychology and NeuroscienceUniversity of ColoradoBoulderUSA
  4. 4.Psychiatric Genetics LaboratoryQIMR Berghofer Medical Research InstituteBrisbaneAustralia
  5. 5.Department of Psychiatry and Human GeneticsVirginia Commonwealth UniversityRichmondUSA

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