Estimation of Heritability of Threshold Characters

Many traits of dairy cattle such as disease resistance and type breakdown scores may have an underlying distribution of values which are approximately normal but must be measured on a yes or no basis. Theory from literature suggests that heritability estimated from such binomial data is only z2/p(1-p) as large as heritability if it could be measured on the normal scale where z is the ordinate on the normal distribution at the threshold point corresponding to a fraction p of the population having the character. Data were generated from a pseudo-normal distribution to test this theory for estimates derived from parent-offspring correlation and paternal sib correlation. The adjustment from theory was quite satisfactory for the paternal sib correlation but would lead to substantial overestimates of heritability on the normal scale when p is small and normal heritability is actually large