Causal Modelling and Path Analysis. Some Notes on Causal Modelling and Path Analysis.
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]
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.
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.
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-
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.
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.
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
E.g. for path #1 for X1 = pX2X1 * pX3X2 * px5x3
for path #2 for X1 = pX4X3 * pX5X4
3. For each X sum together the products from each path.
E.g., the indirect effect for X1 = product for path #1 + the
product for path #2 or
= (pX2X1 * pX3X2 * px5x3) + (pX4X3 * pX5X4)
For each X, add the direct effect if there is one (the path coefficient for the arrow between X1 and Y) to the indirect effect for X (see above).