Is the relationship between self-esteem and physical aggression necessarily U-shaped?

Recent research by Perez, Vohs, and Joiner [Perez, M., Vohs, K. D., & Joiner, T. E., Jr. (2005). Discrepancies between self- and other-esteem as correlates of aggression. Journal of Social and Clinical Psychology, 24, 607–620] has supported a U-shaped curvilinear relationship between self-esteem and physical aggression in a sample of 140 undergraduates. The present study attempted to replicate this effect with a sample size more than 12 times larger. Thus, 1781 undergraduates completed items from Rosenberg’s [Rosenberg, M. (1965). Society and adolescent self-image. Princeton, NJ: Princeton University] Self-Esteem Scale and from the Physical Aggression subscale of Buss and Perry’s [Buss, A. H., & Perry, M. (1992). The Aggression Questionnaire. Journal of Personality and Social Psychology, 63, 452–459] Aggression Questionnaire. The results did not support a U-shaped relationship between self-esteem and physical aggression; if anything, they supported an inverted U-shaped one, such that the simple relationship between self-esteem and physical aggression became more negative and as self-esteem increased. Controlling for gender strengthened these effects, consistent with a pattern of mutual suppression between gender and self-esteem.