Bias in correlations from selected samples of relatives: the effects of soft selection

Martin and Wilson (1982) describe two forms of sampling bias in twin studies. One is "hard selection," where individuals above a threshold participate, and those below do not. The second is "soft selection," where the probability of including a pair of relatives varies over the range of the character. We present an alternative model of soft selection which has strikingly different consequences for the resemblance between relatives. In general, the softer the threshold, the more the correlation resembles that in the underlying population. Results are presented where the probability of selection equals the cumulative distribution function of a normal distribution with 10% of the variance of the selected variable. In these circumstances, soft selection usually leads to less severely attenuated correlations than truncate selection.