Behavior Genetics

, Volume 24, Issue 3, pp 259–262 | Cite as

A simple algebraic demonstration of the validity of DeFries-Fulker analysis in unselected samples with multiple kinship levels

  • Joseph Lee Rodgers
  • Matt McGue


DeFries and Fulker's (Behav. Genet.15, 467–473, 1985) regression procedure (DF analysis) to estimatec2 andh2 was originally applied to selected twin data. Since then, DF analysis has been applied more broadly in unselected data and with multiple (nontwin) kinship levels. Theoretical work based on the matrix algebra of variance-covariance matrices has shown that estimates ofc2 andh2 are unbiased in selected two-group settings. In this article, a simple proof is presented supporting the validity of DF analysis in broader settings. We use scalar algebra to show that parameter estimates ofh2 andc2 are unbiased in unselected settings with multiple (more than two) kinship levels. Caveats are offered, and other DF analysis problems are identified.

Key words

DeFries-Fulker regression procedure heritability common-environmental influences multiple kinship levels algebra DF analysis unbiased estimates 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bouchard, T., and McGue, M. (1981). Familial studies of intelligence: A review.Science 250:223–238.Google Scholar
  2. Cherny, S. S., Cardon, L. R., Fulker, D. W., and DeFries, J. C. (1992a). Differential heritability across levels of cognitive ability.Behav. Genet.,22:153–162.Google Scholar
  3. Cherny, S. S., DeFries, J. C., and Fulker D. W. (1992b). Multiple regression of twin data: A model-fitting approach.Behav. Genet. 22:489–497.Google Scholar
  4. Cyphers, L. H., Phillips, K., Fulker, D. W., and Mrazek, D. A. (1990). Twin temperament during the transition from infancy to early childhood.J. Am. Acad. Child Adolesc. Psychiat. 29 (3):392–397.Google Scholar
  5. DeFries, J. C., and Fulker, D. W. (1985). Multiple regression analysis of twin data.Behav. Genet. 15:467–473.Google Scholar
  6. Detterman, D. K., Thompson, L. A., and Plomin, R. (1990). Differences in heritability across groups differing in ability.Behav. Genet. 20:369–384.Google Scholar
  7. Falconer, D. S. (1981).Introduction to Quantitative Genetics, Longman, New York.Google Scholar
  8. Galton, F. (1885). Regression towards mediocrity in hereditary stature.J. Anthropol. Inst. 15:246–263.Google Scholar
  9. Haggard, E. A. (1958).Intraclass Correlation and the Analysis of Variance, Dryden Press, New York.Google Scholar
  10. LaBuda, M. C., DeFries, J. C., and Fulker, D. W. (1986). Multiple regression analysis of twin data obtained from selected samples.Genet. Epidemiol.,3:425–433.Google Scholar
  11. Loehlin, J. C. (1989). Partitioning environmental and genetic contributions to behavioral development.Am. Psychol. 44:1285–1292.Google Scholar
  12. Plomin, R., and Rende, R. (1991). Human behavioral genetics. In Rosenzweig, M. R., and Porter, L. W. (eds.)Annual Review of Psychology, Annual Reviews, Palo Alto, CA.Google Scholar
  13. Rodgers, J. L., and Rowe, D. C., and Li, C. (1994). Beyond nature vs. nurture: DF Analysis of nonshared influences on problem behaviors.Dev. Psychol. 30:374–384.Google Scholar
  14. Zieleniewski, A. M., Fulker, D. W., DeFries, J. C., and LaBuda, M. C. (1987). Multiple regression analysis of twin and sibling data.Personal. Indiv. Diff. 8:787–791.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Joseph Lee Rodgers
    • 1
  • Matt McGue
    • 2
  1. 1.Department of PsychologyUniversity of OklahomaNorman
  2. 2.Department of PsychologyUniversity of MinnesotaMinneapolis

Personalised recommendations