Multiple regression often raises as many questions as it answers. It examines data via correlations without establishing causation. Path analysis seeks causal pathways; in fact, it can be called causal pathway modeling.
(HATCO is a fictitious company.) HATCO's personnel department identified three employee attitudes they felt most important: job satisfaction, organizational commitment, and probability of employee turnover. They then modeled each of these as follows, in terms of
Make a path diagram for this situation.
| SEARS' PATH MODEL | ||
| Employee Attitudes | Customers | Financial Performance |
| about the job | customer retention | revenue growth |
| about the company | recommending Sears to others |
Executives' pay bonuses are now related not only to Financial Performance but also to Employee Attitudes and Customer Satisfaction generated by those who report to them.
So, to do a path analysis, the researcher begins with an assumed model, indicating the direction and sources of causality among the variables.
Path Analysis plays a role in causal analysis. It is not, however, by itself a method of discovering causal laws but rather a procedure for giving a quantitative interpretation to an assumed causal system. In the example, everything is relative to the relationships assumed and the corresponding diagram. E.g., in the example above, another modeler might have put in an arrow directly from Pay Level to Job Satisfaction. In the Sears example, Sears execs specified the model; the consulting firm of econometric statistician (Claes Fornel International/CFI, headquartered in Ann Arbor), "ran the numbers."
Consider the simplest case, one Y and two X's. In path analysis, the contribution from X1 and X2 is split into four components or "paths" which are
-- direct paths from X1 to Y and X2 to Y; and
-- indirect paths from X1 through X2 to Y and X2 through X1 to Y.
The four paths which are thus defined are as follows.
X1 --> Y X2 --> Y X1 --> X2 --> Y X2 --> X1 --> Y
X1 --> Y, X2 --> Y, X1 <--> X2
write down the path equations and their solution in terms of the three
correlation coefficients.
2. For the system
X --> Y, X --> T, T --> Y
write down the path equations and their solution in terms of the three
correlation coefficients.
3. For the system
F --> X1, F --> X2,
write down the path equations and their solution in terms of the three
correlation coefficients.
4. For the system
F --> X1, F --> X2, F --> X3,
write down the path equations and their solution in terms of the three
correlation coefficients.
Harvard Business School. "Sears, Roebuck and Company (A): Turnaround." Case #9-898-007. "Sears, Roebuck and Company (B): Transformation." Case #9-898-077. Rev. 3-February 3, 1998.
Rucci, Anthony J., Kirn, Steven P, and Quinn, Richard T. "The Employee-Customer-Profit Chain at Sears." Harvard Business Review, January-February 1998. Reprint 98109.
LISREL (Linear Structural RELations) was perhaps the first implementation. It is available with SPSS. LISREL is the implementation of SEM that is discussed in the book in the Appendix to Chapter 11.
At UIC, LISREL 7 can be run on the mainframe through the LISREL command in SPSS. PC software has been developed to implement path analysis; among such software, in addition to LISREL, is EQS and a package from Systat.
GEMINI is a UIC-developed mainframe program for Path Analysis which is user friendly. The manual is referenced above. (However, GEMINI ran on the old UIC mainframe under CMS which was de-activated from regular service on 31-December-1999.)
AMOS is a newer program for
SEM. It is available through SPSS. It is perhaps more user-friendly than
is LISREL.