Consistent with Aiken and West (1991), we derived a point estimator for the cross-over point as follows: Select two values for X2 (e.g., 0 and 1), insert one value for X2 into the right side of Equation 1, insert the other value for X2 into the right side of Equation 1, set the two equations to equality, and solve for X1: (3)B0+B1X1+B2(0)+B3(X1·0)=B0+B1X1+B2(1)+B3(X1·1) which, after a little algebra, yields: (4)X1=−B2B3=C where C is a symbol for the cross-over point, and other symbols were defined above. An analog of Equation 4 can be obtained using mean-centered predictors. This solution is: (5)X1*=−B2*B3*=C* which yields the cross-over point C* in a mean-centered metric. To calculate the cross-over point in the raw metric of X1, one must add X̄1 to each side of Equation 5, leading to: (6)X1=−B2*B3*+X¯1=C where symbols in Equations 3–6 were defined previously (see Aiken & West, 1991, for details).
