Better Rules for Better Decisions

About a decade ago, after David Grusky and I had suffered endlessly over the choices among alternative models in our comparative analyses of social mobility (Grusky and Hauser 1984), our satisfaction with the product of those analyses was temporarily shattered by the news that Adrian Raftery (1986) would publish a methodological comment on the work. What would he have to say? And could we defend our work? Would we take the standard defensive posture of sociologists whose work was under criticism? In actuality, Raftery's brief and elegant comment turned out not to require a defense at all. Rather, it outlined a superior way to think about the decisions that we had faced-namely, how to choose among alternative models in a sample so large that standard inferential methods would lead us to reject all but a saturated model. Raftery's proposal to use the Bayesian information criterion (BIC) relieved, rather than increased our discomfort at having ignored standard rules of statistical inference, and it even supported some-though not all-of the decisions that we had made.1 Pleased as I was that some parts of the Grusky-Hauser analysis survived Raftery's scrutiny, I am happier yet that our efforts prompted the introduction of a simple and defensible rule of thumb that could be used to improve decisions in discrete multivariate analysis and structural equation models (Raftery 1993). For the past several years, I have routinely used BIC as a guide in model selection (Hauser and Wong 1989; Wong and Hauser 1992; Hout and Hauser 1992; Hauser 1993; Hauser and Phang 1993; Kuo and Hauser 1995a, 1995b), sometimes without showing the details of inferential procedures in the text.