Causal Modelling and Path Analysis

Some Notes on Causal Modelling and Path Analysis. “Path analysis is... superior to ordinary regression analysis since it allows us to move beyond the estimation of direct effects, the basic output of regression. Rather, path analysis allows one to examine the causal processes underlying the observed relationships and to estimate the relative importance of alternative paths of influence. The model testing permitted by path analysis further encourages a more explicitly causal approach in the search for explanations of the phenomena under investigation.” (Asher 1983, pp )

Some criteria for establishing the existence of a causal relationship: 1. Covariation (joint variation or association between a pair of variables) 2. Time Order (changes in the independent variables must precede changes in the dependnet variable). 3. Non-spuriousness (covariation between and independent and dependent variable is not due to the effects of a third variable). [B&K p. 411]

Some Key Concepts for Causal Modelling and Path Analysis: Causal Diagram: a visual representation of the cause-and-effect relationships amongst variables, using keyword names and directed arrows. Exogenous Variable: a predetermined variable whose causes remain unexplained, and outside the scope of a model. Endogenous Variable: A variable who cause(s) of variation are represented in a model. Direct Effect: a connecting path in a causal model between two variables without an intervening third variable. Indirect Effect: a compound path connecting two variables in a causal model through an intervening third variable.

Some Key Concepts for Causal Modelling and Path Analysis (Continued): Residual Variable: an unmeasured variable in a path model that is posited as causing the unexplained part of an observed variable. Recursive Model: a model in which all the causal influences are assumed to be asymmetric (one-way) Nonrecursive Model: a model in which causal influences between dependent variable may occur in both directions. Path Analysis: a statistical method for analyzing quantitative data that provides empirical estimates fo the effects of variables in an hypothesized causal system. Path Coefficient: a numerical estimate of the causal relationships between two variables in a path analysis.

Rules for Constructing Causal Diagrams. 1. Variables names are represented either by short key words or letters. 2. Variables placed to the left in a diagram are assumed to be causally prior to those on the right. 3. Causal relationships between variables are represented by single- headed arrows. 4. Variables assumed to be correlated but not causally related are linked by a curved double-headed arrow. 5. Variables assumed to be correlated but not causally related should be at the same point on the horizontal axis of the causal diagram. 6. The causal effect presumed between two variables is indicated by placing + or - signs along the causal arrows to show how increases or decreases in one variable affect the other.

Some Rules for Identifying Paths: 1. No path may pass through the same variable more than once. 2. No path may go backward on (against the direction of) an arrow after the path has gone forward on a different arrow. 3. No path may pass through a double-headed curved arrow (representing an unanalyzed correlation between exogenous variables) more than once in any single path.

Calculating a Residual Path Coefficient:

Some Notes on Direct, Indirect, and Total Effects: Asher (1983) p. 36 states: In general, once the direct and indirect effects of one variable on another are determined, one can then calculate the total effect, which is simply the sum of the direct and indirect effects. It is possible that the direct effect will be a positive quantity and the indirect one negative (or vice versa). It is also possible that the indirect effect will exceed the direct effect in magnitude. Finally, in comparing the effects of two variables on some other variables, it is possible that one variable will have a larger direct effect than the second, but that the second will have the greater total effect.”

Calculating Indirect Effects: 1. For each X, identify all of the unique paths between X and Y. 2. For each path (for a given X), multiply the path coefficients by one another E.g. for path #1 for X 1 = p X2X1 * p X3X2 * p x5x3 for path #2 for X 1 = p X4X3 * p X5X4 3. For each X sum together the products from each path. E.g., the indirect effect for X 1 = product for path #1 + the product for path #2 or = (p X2X1 * p X3X2 * p x5x3 ) + (p X4X3 * p X5X4 )

Calculating Total Effects: For each X, add the direct effect if there is one (the path coefficient for the arrow between X 1 and Y) to the indirect effect for X (see above).