Using difference scores to avoid the regression paradox: An example with fathers’ level of education and respondents’ wages and intelligence

The regression paradox, also called the reverse regression problem, is a phenomenon where the effect of X on Y when adjusting for Z and the effect of X on Z when adjusting for Y can suggest diametrically different circumstances. In data from the National Longitudinal Study of Youth (NLSY) 1979 (N = 12,686) and 1997 (N = 8984), we demonstrate the regression paradox and show that respondents’ fathers’ level of education had a positive effect on the respondents’ wages when adjusting for their intelligence. This could be seen to indicate favoritism of the highborn and discrimination against the lowborn. However, the same data revealed a positive effect of fathers’ education on respondents’ intelligence when adjusting for their wages, suggesting, paradoxically, discrimination against the highborn and favoritism of the lowborn. As fathers’ education had a stronger correlation with the respondents’ intelligence than with their wages, we also found a positive effect of fathers’ education on the respondents’ wage - intelligence difference score, suggesting that the highborn had not fully capitalized on their high intelligence. We propose that estimating effects on difference scores can be used to avoid the regression paradox and to scrutinize adjusted regression effects.