Transcript Causal Modelling and Path Analysis

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. 36-37)
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 singleheaded 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:
1 R
2
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 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)
Calculating Total Effects:
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).