University of Illinois at Chicago
College of Business Administration
Department of Information & Decision Sciences
MBA                   Statistics for Management

Instructor             Stan Sclove
Notes on Path Analysis

These notes Copyright © 2000   Stanley Louis Sclove

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

Exogenous variables:--
X1: Coworker Attitude
X2: Work Environment
X3: Pay Level
Intermediate-level dependent variables:--
Y1, Job Satisfaction = f(Coworker Attitude, Work Environment)
Y2, Organizational commitment = f(Job satisfaction, Pay Level)
Final level dependent variable:--
Y3, Probability of employee turnover = f(Job Satisfaction, Organizational commitment)


Make a path diagram for this situation.

Competing Models

Others may feel a different path diagram, with fewer or more or just different paths, is better.  It is possible to test these competing models against one another.

5.2. Sears Case

We add another example here (although it is not a particularly "simple" example). This is an example of the use of Path Analysis at Sears, Roebuck & Co. This effort was overseen by Tony Rucci, former Dean of the CBA at UIC.   (See the Additional References at the end of these notes.)   The Sears' model is not unlike the HATCO example, except that, very importantly, it takes things a step further and relates employee and customer satisfaction to financial performance. Financial Performance in quarter t is modelled with Customer Satisfaction in quarter t-1 and Employee Satisfaction in quarter t-2. This yields a predictive model for Financial Performance. Data on the other variables are obtained by such devices as a note on randomly selected cash-register receipts which tells the customers that if they will dial the given 800 number and respond by telephone push buttons to a few questions, they will receive five dollars.
 
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

Each of these may or may not be in the diagram used by the researcher to model a given situation. (What would be all the possible paths with three X's and one Y?)
 

    Exercises (optional--not required)

1. For the system

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.


References

Sears, Roebuck Case

FORTUNE Magazine. "Bringing Sears into the New World." Smart Managing Section. 13-Oct-1997. Stratford Sherman interviews Anthony Rucci. On line

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.

Software

Wolfle, Lee M., and Ethington, Corinna A.   GEMINI: Program for Analysis of Structural Equations with Standard Errors of Indirect Effects. USER'S MANUAL. Manuscript, Dept. of Educational Psychology, College of Education, UIC.

APPENDIX: Software

Here we mention some implementations of SEM.

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.


Created 9 Mar 1999     Updated 6 Dec 2000