Path Analysis

Defining Path Analysis

Path analysis was invented by Sewall Wright as he developed his shifting balance theory (SBT) of population genetics. He needed a technique that could be used to track effects of forces on changes in one variable over time or the effect of different variables on each other. SBT posits that evolution occurs over three phases with species fitness as the key criterion variable. In path analysis, the direct effects of predictors on the criterion variable are estimated just like in multiple regression. Several decision rules exist for determining when direct effects belong in the model. For researchers who feel the need for dichotomous decision-making, a significance test can be conducted to determine the odds that a coefficient differs from zero. For researchers who prefer estimation to significance tests, a confidence interval can be placed around the coefficient to provide a sense of the range that the actual coefficient is likely to fall into. Alternatively, researchers can determine if deleting the effect from the model generates an error in the model that is significant by z test.

According to the product rule of path analysis, researchers can estimate the indirect effect of a cause on an effect by multiplying the direct effects along the paths from the beginning to the end of a causal chain of variables. The product rule assumes that each of the effects in the chain is linear and homoscedastic. Indirect effects of antecedent variables (i.e., variables that exert influence on other variables) on a consequent variable (i.e., a variable that is influenced by other variables) can be summed to determine the total effects on that criterion variable. Typically, researchers propose a structure that describes the causal flow from antecedent to consequent variables.

This structure allows the researcher to estimate the indirect effects in the proposed model. The predicted value of the indirect effect of an antecedent on a consequent variable is compared to the [Page 1194]obtained correlation between the two variables. The difference between the predicted and obtained values represents an error in the proposed structure.

Multiple regression examines one criterion variable at a time so it is not well suited to discovering how the criterion variables relate to one another. One important condition to recognize is that of a spurious relationship between criterion variables. As Sewall notes, a common causal antecedent (CCA) that causes two consequent variables will cause the two consequent variables to be correlated. The observed correlation between those two consequent variables may lead researchers to conclude that they are causally related to one another; in reality, the observed correlation may be merely due to the CCA. Path analysis can also uncover the suppression of antecedent effects on a consequent variable; this can occur when the effect of the antecedent on the consequent is mediated by two variables that have opposing effects on the consequent variable—producing a model of antagonistic impacts.

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