Heritability on the observed scale from the liability scale

h2_obs = h2_lat * z^2 / (p (1 - p)), with p the incidence and z the normal density at the threshold qnorm(p). Dempster & Lerner (1950). The transformation is NOT in the 4th edition of Mrode & Pocrnic – chapter 15 works entirely on the liability scale – but it is what translates a liability h2 into the number a linear analysis of the 0/1 trait estimates. At the incidence of the book's Example 15.2 (0.234) the factor is 0.524: half the heritability disappears in the scale, before any modelling choice.

Usage

h2_observed(h2, incidence)

Arguments

h2

heritability on the liability scale, in [0, 1]

incidence

proportion of the "affected" category, strictly inside (0, 1); vectorized, so a whole column of incidences converts in one call

Value

heritability on the observed (0/1) scale

References

Dempster, E.R. & Lerner, I.M. (1950) Heritability of threshold characters. Genetics 35, 212-236.

Examples

h2_observed(0.1781, 0.234)   # the 0.178 of Example 15.2 publishes as 0.093
#> [1] 0.09338971