The Cross-Cultural Speech Act Realization Project (Blum-Kulka, House, & Kasper, 1989a) has identified five components of an "apology speech act set": five strategies that speakers use to apologize. This study examines the effects of four of those strategies (illocutionary force indicating device, expression of responsibility, promise of forebearance, and offer of repair) on the judgments made by hearers about the speaker and about the apology. Each of the strategies is shown to have an independent effect in improving reactions to the speaker. Further, the magnitude of these effects appear to be roughly similar for each of the strategies. The things people say to apologize do seem to be effective in accomplishing the self-presentational goals of apologizers.
Scher, Steven J. and Darley, John M., "How effective are the things people say to apologize? Effects of the realization of the apology speech act." (1997). Faculty Research and Creative Activity. 26.