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# PATH ANALYSIS

Path analysis is a particular application of multiple regression. In multiple regression, we know (1) which independent variables help to predict some dependent variable and (2) how much variance in the dependent variable is explained by each independent variable. But multiple regression is an inductive technique: It does not tell us which are the antecedent variables, which are the intervening variables, and so on.

Path analysis is the application of multiple regression for testing conceptual models of multivariate relations—that is, for testing specific theories about how the independent variables in a multiple regression equation may be influencing each other—and how this ultimately leads to the dependent variable outcome.

The method was developed by the geneticist Sewall Wright in 1921 and became very popular in the social sciences in the 1960s (see Duncan 1966). It fell out of favor for a while (isn’t it nice to know that even in statistics there are fads and fashions?), but it’s making a strong comeback as full-featured statistics packages become more widely available.

I rather like the method because it depends crucially on the researcher’s best guess about how a system of variables really works. It is, in other words, a nice combination of quantitative and qualitative methods. Here’s an example.

Thomas (1981) studied leadership in Niwan Witz, a Mayan village. He was interested in understanding what causes some people to emerge as leaders, while others remain followers. From existing theory, Thomas thought that there should be a relation among leadership, material wealth, and social resources. He measured these complex variables for all the household heads in Niwan Witz (using well-established methods) and tested his hypothesis using Pearson’s r. Pearson correlations showed that, indeed, in Niwan Witz leadership is strongly and positively related to material wealth and control of social resources.

Because the initial hypothesis was supported, Thomas used multiple regression to look at the relation of leadership to both types of resources. He found that 56% of the variance in leadership was explained by just three variables in his survey: wealth (accounting for 46%), family size (accounting for 6%), and number of close friends (accounting for 4%). But, since multiple regression does not, as Thomas said, ‘‘specify the causal structure among the independent variables’’ (1981:132), he turned to path analysis.

From prior literature, Thomas conceptualized the relation among these three variables as shown in figure 22.2. He felt that leadership, L, was caused by all three of the independent variables he had tested, that family size (fs) influenced both wealth (w) and the size of one’s friendship network (fr), and that wealth was a factor in determining the number of one’s friends.

The path coefficients in figure 22.2 are standardized values: They show the influence of the independent variables on the dependent variables in terms of standard deviations. The path coefficients in figure 22.2, then, show that ‘‘a one standard deviation increase in wealth produces a .662 standard deviation increase in leadership; a one standard deviation increase in family size results in a .468 standard deviation increase in leadership; and so on’’ (Thomas 1981:133). (For details about how path coefficients are determined, consult a textbook in multivariate analysis, like Kelloway 1998.)

Four things are clear from figure 22.2: (1) Among the variables tested, wealth is the most important cause of leadership in individuals. (2) Family size has a moderate causal

FIGURE 22.2.

Path analysis of effects of wealth, friendship, and family size on leadership in Niwan Witz. SOURCE: J. S. Thomas, ''The Socioeconomic Determinants of Leadership in a Tojalabal Maya Community.'' American Ethnologist, Vol. 8, pp. 127-38, 1981. Reproduced by permission of the American Anthropological Association. Not for further reproduction.

influence on wealth (making wealth a dependent, as well as an independent variable in this system). (3) The size of a person’s friendship network is only weakly related to either family size or wealth. (4) The combined direct and indirect effects of family size, wealth, and friendship network on leadership account for 56.5% (1 — .435) of the variance in leadership scores for the household heads of Niwan Witz.

Thomas concludes from this descriptive analysis that if you want to become a leader in the Mayan village of Niwan Witz, you need wealth, and the best way to get that is to start by having a large family.

Path analysis lets you test a particular theory about the relations among a system of variables, but it doesn’t produce the theory,that’s your job. In the case of Niwan Witz, for example, Thomas specified that he wanted his path analysis to test a particular model in which wealth causes leadership. The results were strong, leading Thomas to reject the null hypothesis that there really is no causal relation between wealth and leadership. But even the strong results that Thomas got don’t prove anything. In fact, Thomas noted that an alternative theory is plausible. It might be that leadership in individuals (wherever they get it from) causes them to get wealthy rather than the other way around.

Path analysis often serves as reality therapy for social scientists. It’s fun to build conceptual models—to think through a problem and hypothesize how variables are linked to each other—but our models are often much more complicated than they need to be. Path analysis can help us out of this fix. We can test several plausible theories and see which is most powerful. But in the end, you’re left out there, all by yourself, defending your theory on the basis of whatever data are available right now.

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