Path Analysis

Key Components

In a path analysis model, an observed variable is presented within a square or rectangle. An observed variable is either exogenous (X1 and X2) or endogenous (Y1, Y2, and Y3), which corresponds to a predictor or outcome variable, respectively, in a regression model. The cause of an exogenous variable is not included in the model, whereas the cause of an endogenous variable is explicitly specified. The causal relationship is indicated by a single-headed arrow (e.g., X1 → Y1 in Figure 1), with the variable at the tail of the arrow being the cause and the variable at the head of the arrow being the effect. The direct effect from one variable to another is quantified by the path coefficient, similar to the slope in regression analysis. In a path analysis model, exogenous variables may also affect endogenous variables through some intermediate variables (X1 → Y1 → Y3). The intermediate variables are sometimes called mediators, and the mediating effect is called the indirect effect. The double-headed curved arrow at the top of an exogenous variable indicates the variance of the exogenous variable (φ11, φ22), and the double-headed curved arrow connecting two exogenous variables is the covariance between the two variables (φ12). Each endogenous variable has an unobserved disturbance (D1, D2, and D3), represented within a circle or oval. A disturbance contains two [Page 1223]confounded components: the measurement error of the endogenous variable and all the causes of the endogenous variable that are not explicitly specified in the model. If it is known that a pair of endogenous variables share some common missing causes, their disturbances can be correlated. The path coefficient from a disturbance to its endogenous variable is typically fixed at 1 to assign a metric to the disturbance.

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