1. Introduction to Path Analysis

2. Jargon Structural Equation Modeling (SEM) AKA:
Analysis of Covariance Structures; Causal Analysis; LISREL
Includes:
Latent variable SEM; CFA; Path Analysis
Path Analysis
Simplest form of SEM
Uses measured variables
Can be solved via MR

3. Correlations Among 3 Variables

4. A Causal Model

5. The Tracing Rule
The correlation between two variables X and Z is equal to the sum of the product of all paths from each possible tracing between X and Z [in Figure 2]. EXCEPT:
the same variable is not entered twice per tracing and
a variable is not both entered and exited through an arrowhead.

6. The Solved Model

7. Path Analysis with MR Regress Achievement on Ability and Motivation
Regress Motivation on Ability
See SPSS output

8. Regression Results
Paths to Achievement:
Path to Ability:

9. Disturbances = error = residuals = SQRT(1-R2)
A More Complete Model
Disturbances = error = residuals = SQRT(1-R2)

10. True or False? We should not infer causality from correlational data.
It is inappropriate to infer causality unless there has been active manipulation of the independent variable.
Smoking causes lung cancer in humans.
Divorce affects children’s subsequent achievement and behavior.
The earth’s gravity keeps the moon in orbit around the earth.
True or False?

11. Causal Inference from Correlations?
We find the old saw that “correlation does not mean causation,” although well intentioned, to be grossly misleading. Causation manifests itself in correlation, and its analysis can only proceed through the systematic analysis of correlation and regression.
from: Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum, p. 15.

12. Determining Causality
Causality = probabilistic statements
How to determine causality
Theory/Past Research
Time precedence
Logic

13. Recursive Model

14. Non-Recursive Model

15. Just-Identified Model
This model is “just” right: 3 correlations = 3 path coefficients

16. Under-Identified Model
Does c = d?
Not enough information: Have 3 correlations to estimate 4 path coefficients

17. Over-Identified Model
More than enough information: Paths can be estimated more than one way

18. Over-Identified Model
versus
and
versus

19. More Jargon

20. Steps: Path Analysis Develop the model
Check the identification status (just or overidentified)
Measure the variables
Estimate the model
Interpretation

21. More Complex Example

22. Paths to Achievement

23. Paths to Coursework

24. Paths to Motivation

25. Path to Ability

26. Standardized Coefficients

27. Calculating Indirect Effects

28. Direct, Indirect, & Total Effects
Variable
DIRECT
INDIRECT
TOTAL
Coursework a -
Motivation b
e*a
direct + indirect
Ability c
f*a+
h*b+
h*e*a+
Family Background d
g*a+
i*b+
i*e*a+
j*c+
j*f*a+
j*h*b+
j*h*e*a+

29. Direct, Indirect, and Total Effects
Variable
Direct Effect
Indirect Effect
Total Effect
Academic Coursework
0.310 -
Motivation
0.013
0.083
0.096
Ability
0.551
0.131
0.682
Family Background
0.069
0.348
0.417

30. Calculating Effects the Easy Way
Indirect effect = Total - Direct
SEM programs will do the calculations for you!

31. Non-causal Effects Variable Direct Indirect Total Non-causal
Original correlation
Non-causal
Academic Coursework
0.310 -
0.615
0.305
Motivation
0.013
0.083
0.096
0.255
0.159
Ability
0.551
0.131
0.682
0.737
.055
(j*d)
Family Background
0.069
0.348
0.417

32. Idea for Final Project
Develop and test a path model using a dataset of your own choice. Make sure you address the following issues in your write up:
How did you determine causality in your model? What theory or past research (or logic) guided the specification of your model?
Is your model just-identified or over-identified? Why?
Calculate the total, indirect, and direct effects of all paths (you can display this in a table or graphic format)
Calculate the disturbances
Interpret your model – what do the results suggest?