Mutual Suppression: Comment on Paulhus et al. (2004)

Abstract

Paulhus, Robins, Trzesniewski, and Tracy (Multivariate Behavioral Research, 2004, 39, 305–328) suggested that the three types of two-predictor suppression situations—classical suppression, cooperative suppression, and net suppression—-can all be considered special cases of mutual suppression, in that the magnitude of each of the two standardized partial regression coefficients exceeds the magnitude of its corresponding standardized bivariate regression coefficient. Classical suppression and cooperative suppression can be considered mutual suppression, but net suppression cannot. Hypothetical and empirical examples of net suppression in which the magnitude of the standardized partial regression coefficient for the suppressor variable is greater than, equal to, and less than the magnitude of its standardized bivariate regression coefficient are provided. The empirical examples were drawn from the social psychology literature relating psychological well-being outcomes to life aspirations.

Notes

¹ β _{YX 1} and β _{YX 2} are equivalent to the correlation coefficients r _{YX 1} and r _{YX 2} , respectively. Paulhus et al. (2004) also used “validity” (or “validity coefficient”) as a synonym for the correlation coefficient. However, a validity is the absolute value of a correlation coefficient (Lord & Novick, 1968, p. 61).

^a In Paulhus et al.'s (2004) two sets of empirical examples, X ₁ and X ₂ have been exchanged, so that β _{YX 2} (rather than β _{YX 1} ) is positive and β _{YX 1} (rather than β _{YX 2} ) is allowed to be zero, negative, or positive.

^b This might also be considered an example of net suppression because β _{YX 1} is not exactly zero.

^a The five empirical examples of net suppression were taken from a set of studies of the predictors of psychological well-being (Kasser & Ryan, 1993; p. 414, Table 2, self-actualization/financial success chances; p. 414, Table 2, vitality/financial success chances; p. 416, Table 5, depression/financial success chances, signs reversed; p. 414, Table 2, self-actualization/affiliation chances; p. 416, Table 5, vitality/affiliation importance). Only three of the five statistics were reported by Kasser and Ryan; the other two were computed from the three reported as described in the Appendix.

² This method is a variant of classic semi-ipsatization in which a mean score is subtracted from each individual score. It is not an optimal method of operationalizing relative importance or relative chances. Consider two persons, one of whom has five aspiration importance scores of 3, 3, 3, 3, and 3, the other of whom has five aspiration importance scores of 3, 1, 1, 5, and 5; the first score is for the importance of the aspiration for financial success. For both persons the mean aspiration importance score equals 3, and the importance score for the aspiration for financial success equals 3. To the regression for financial success importance, these persons appear identical, although it is clear from the aspiration importance scores themselves that the importance of the aspiration for financial success relative to the importance of the other four aspirations differs for the two persons. The problem is that this method considers only the location (mean) and not the scale (variance) of the aspiration scores.

³ Kasser and Ryan (1993) variously referred to their regression coefficients as “partial correlations” (p. 413, 1st paragraph, ll. 4–5), “semipartial correlations” (p. 413, 1st whole paragraph, l. 1; Tables 2, 5, and 8, titles and notes), and “betas” (p. 413, 1st whole paragraph, l. 1; Tables 2, 5, and 8, column headings), “beta” referring to the symbol β frequently used for the standardized regression coefficient. Their coefficients appear to be standardized regression coefficients.

⁴ “Approximately” because close examination of the results reported by Kasser and Ryan (1993) indicates that there must be computational and/or reporting errors for some of their sets of regressions. Unfortunately, I have not been able to obtain the raw data.