Heritability on the liability scale from the observed scale

The inverse of h2_observed(): h2_lat = h2_obs * p (1 - p) / z^2 (Dempster & Lerner 1950). This is the direction a user needs when a linear model was fit to a 0/1 trait and the estimate has to be reported on the scale the threshold literature uses.

Usage

h2_liability(h2, incidence)

Arguments

h2

heritability on the observed (0/1) scale, in [0, 1]

incidence

proportion of the "affected" category, strictly inside (0, 1); vectorized

Value

heritability on the liability scale. A warning fires when the pair implies a liability h2 above 1: the two numbers are then not consistent with the threshold model.

References

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

Examples

h2_liability(0.093, 0.234)   # back to ~0.178
#> [1] 0.1773568