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Likelihood Models for Multivariate Traits in Human Genetics 1
Author(s) -
Bonney George E.,
Elston Robert C.
Publication year - 1985
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710270511
Subject(s) - multivariate statistics , pedigree chart , trait , simple (philosophy) , mathematics , multivariate analysis , statistics , random variate , computer science , random variable , biology , genetics , gene , philosophy , epistemology , programming language
The formulation of likelihood functions for multivariate genetic traits in humans is discussed, and exact computing formulas presented for families and simple pedigrees. The model described incorporates all the features of the original ELSTON and STEWART (1971) formulation and that of LANGE et al. (1976, 1983); the integration of the two models is achieved through the introduction of quantities we call “relatedness coefficients.” These are subsequently used to define “status indices,” which turn out to be the key to the computational problem, for the polygenic and mixed models of genetic transmission. The highest order of matrices that enter into the calculation is pXp for a p ‐variate trait, instead of npXnp , where n is the size of the pedigree. The expressions that are presented can be extended to complex pedigree structures.