Causal Models and Probability

Abstract

Elementary probability statements are employed in causal inference models as an alternative to Blalock's correlation technique. By making use of certain simplifying assumptions, surplus equations become available for predictive use. Probability statements and predictions are shown for one-way causal models with causal chain, possibly spurious, and convergent patterns of relations. Fictitious data are used to illustrate the feasibility of probability models. Probability models thus provide another perspective for the kinds of causal models considered by Blalock. B lalock has extended and refined a technique for making causal inferences from correlational data based on earlier work by Simon.' This technique, in essence, requires explicit assumptions about the presence and direction of causal connections among a specific set of variables treated as a closed system. Zero-order and partial correlation coefficients-or beta coefficients-are computed for one or more specific models to help determine whether predicted relationships obtain. A particular model is retained as a possible causal explanation, if predictions are confirmed. Otherwise a model is rejected. This paper takes the position that probability statements may be used in causal inference models as an alternative to correlation or beta coefficients. If probability statements can serve as a substitute kind of measure, as the following discussion indicates, then we have a different set of analytic procedures for tackling problems of causal inference. Attention will be limited in this paper to (1) specifying the kinds of predictions that can be made for certain basic patterns of relationships among variables in threeand four-variable models, (2) illustrating the feasibility of causal probability models, and (3) noting similarities and differences between probability statements and correlation coefficients in causal models. A basic requirement in developing strategy and techniques for handling causal models is to establish prediction equations. In approaching this task we can briefly note some similarities between probability statements and correlation coefficients. First, in one-way causal models, statements of relationship must be asymmetric. This is accomplished by establishing a system of recursive equations in Blalock's approach and can be attained in a similar manner for probability models. Second, simplifying assumptions are necessary in order to have one or more excess equations for predictive purposes. Prediction equations become available partly as a result of assuming that certain variables in the model are unrelated. Thus a zero correlation can be predicted in using Blalock's technique as compared with a prediction of independence with the probability approach. Third, some predictions require controls for other variables in a model that may influence certain relations. In comparison with partial coefficients, conditional probability statements achieve this end in a slightly different manner, as subsequent discussion will show. Blalock's position on the concept of causality can be accepted as a working basis for the following discussion.2 In brief, this posi* Revised version of a paper presented at the annual meeting of the Southern Sociological Society, Atlanta, Georgia, April 1965. 1 See Hubert M. Blalock, Jr., Causal Inferences in Nonexperimental Research (Chapel Hill: The University of North Carolina Press, 1964), and Herbert A. Simon, Spurious Correlations: A Causal Interpretation, Journal of the American Statistical Association, 49 (September 1954), pp. 467479. 2 For a discussion of this position, see Hubert M. Blalock, Jr., Four-Variable Causal Models and Partial Correlations, American Journal of Sociology, 68 (September 1962), p. 183, and Blalock, op. cit., pp. 3-26. This content downloaded from 157.55.39.104 on Sun, 19 Jun 2016 05:53:26 UTC All use subject to http://about.jstor.org/terms