Threshold Characters

ABSTRACT A random phenotype is defined as a probability distribution over any given set of phenotypes. This includes as special cases the kinds of phenotypes usually considered (qualitative, quantitative, and threshold characters) and all others. Correspondingly general methods are indicated for analyzing data of all forms in terms of the classical Mendelian factor concept (as distinct from the biometrical methods usually applied to measurement and graded data, associated with the effective factor concept). These are applied in a new analysis of the data of E. L. Green (1951, 1954, 1962) on skeletal variation in the mouse. The adequacies of various classical one-factor and several-factor models are considered. Indications of an underlying scale are found from this new standpoint. The results are compared with those obtained by Green using the scaling approach. An illustrative application is also made to some of Bruell's (1962) continuous behavioural data on mice. This work was substantially completed in 1959 but not previously prepared for publication. The same approach was originated and developed independently by R. L. Collins who has treated a wider range of theoretical problems (cf. Collins 1967, 1968a, 1969b, 1970c) and a wider range of applications (cf. Collins and Fuller 1968; Collins 1968b, 1969a, 1970a). A less general independent development is that of Mode and Gasser 1972.

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SCALING THRESHOLD CHARACTERS

Genetics ◽

10.1093/genetics/99.2.357 ◽

1981 ◽

Vol 99 (2) ◽

pp. 357-364 ◽

Cited By ~ 1

Author(s):

Daniel Gianola ◽

H W Norton

Keyword(s):

Prediction Error ◽

Joint Distribution ◽

Mean Square ◽

Scaling Method ◽

Simple Method ◽

Normal Variable ◽

Mean Square Prediction Error ◽

Genetic Value ◽

Ordered Categorical ◽

Threshold Characters

ABSTRACT A simple method of scaling ordered categorical responses having a joint distribution with an underlying normal variable is presented. Scores are developed that maximize heritability of the observed variate and that in the class of scores based on polychotomies: (1) maximize the correlation between score and the underlying genetic value to be predicted, and (2) minimize mean-square prediction error. Several examples suggest little is lost, in terms of heritability, by using equally spaced scores. The proposed scaling method discriminates among candidates for selection that would be tied if equally spaced scores are used and sometimes yields different rankings of candidates.

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