A second strength of the re-parameterized equation is the potential for modifying an equation to test additional, specific hypotheses regarding parameters describing the interaction. For example, consider a dichotomous variable S (i.e., a dummy variable for Sex, coded 1 = male, 0 = female). Equation 10 could be modified in the following fashion: (19)Y=(A0+A0sS)+(B1+B1sS)(X1−(C+CsS))+(B3+B3sS)((X1−(C+CsS))·X2)+E where A0 is the intercept for females, A0s the intercept difference for males, B1 is the slope of X1 for females, B1s the difference in X1 slope for males, C is the cross-over point for females, Cs the difference in cross-over points for males, B3 is the slope coefficient for the product term for females, and B3s the difference in product term slope for males. One could test lower-order and interactive effects of Sex by altering Equations 1 or 2 (see Cohen et al., 2003, for details). The resulting equation would have 8 free parameters, just as Equation 19 does, and sex differences in the interaction would be embodied in coefficients. But, point estimates of the cross-over points for males and females still would not have
