Behavior Genetics

, Volume 25, Issue 3, pp 211–216 | Cite as

Approximate solutions for the maximum-likelihood estimates in models of univariate human twin data

  • U. W. L. Wijesiri
  • Christopher J. Williams
Article

Abstract

We present numerical results concerning the accuracy of approximate maximum-likelihood estimators of variance components for several models of univariate human twin data. The approximations are obtained via a spectral decomposition of the twin model covariance matrix. The results apply to likelihood functions for univariate twin data based on either the Wishart distribution or the bivariate normal distribution. For sample sizes of 100 twin pairs for each zygosity group, if the difference of the traces of the sample covariance matrices is 10% or less of the sum of the traces, the approximate solutions can be used as the maximum-likelihood estimators for some models.

Key Words

Eigenvalues human genetics Lagrange multiplier spectral decomposition 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Haseman, J. K., and Elston, R. C. (1970). The estimation of genetic variance from twin data.Behav. Genet. 1:11–19.Google Scholar
  2. Jöreskog, K. G., and Sörbom, D. (1986).Lisrel VI, Scientific Software, Morersville, IN.Google Scholar
  3. Lange, K., Westlake, J., and Spence, M. A. (1976). Extensions to pedigree analysis. II. Variance components by scoring method.Ann. Hum. Genet. 39:485–491.Google Scholar
  4. Lange, K. L., Weeks D., and Boehnke, M. (1988). Programs for pedigree analysis: MENDEL, FISHER, and dGENE.Genet. Epidemiol. 5:471–472.Google Scholar
  5. Nagoshi, C. T., and Johnson, R. C. (1993). Familial transmission of cognitive abilities in offspring tested in adolescence and adulthood: A longitudinal study.Behav. Genet. 23:279–285.Google Scholar
  6. Neale, M. C., and Cardon, L. R. (1992).Methodology for Genetic Studies of Twins and Families, Kluwer Academic, Amsterdam.Google Scholar
  7. Neale, M. C. (1991).Mx Statistical Modeling, Department of Human Genetics, Box 3 MCV, Richmond, VA.Google Scholar
  8. Sims, J., Boomsma, D. I., Carrol, D., Hewitt, J. K., and Turner, J. R. (1991). Genetics of Type A behavior in two European countries: Evidence for sibling interaction.Behav. Genet. 21:513–528.Google Scholar
  9. Thapar, A., Petrill, S. A., and Thompson, L. A. (1994). The heritability of memory in the Western Reserve Twin Project.Behav. Genet. 24:155–160.Google Scholar
  10. Wijesiri, U. W. L., and Williams, C. J. (1994). Likelihood equation solutions in models of twin data (submitted for publication).Google Scholar
  11. Williams, C. J. (1993). On the covariance between parameter estimates in models of twin data.Biometrics 49:557–568.Google Scholar
  12. Williams, C. J., Christian, J. C., and Norton, J. A., Jr. (1992a). Twinan90: A FORTRAN program for conducting ANOVA-based and likelihood-based analyses of twin data.Comput. Methods Prog. Biomed. 38:167–176.Google Scholar
  13. Williams, C. J., Viken, R., and Rose, R. J. (1992b). Likelihood-based longitudinal twin and family data: Experience with pedigree-based approaches.Behav. Genet. 22:215–223.Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • U. W. L. Wijesiri
    • 1
  • Christopher J. Williams
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of IdahoMoscow

Personalised recommendations