Disturbance Term Regression Test Procedures for Recursive and Nonrecursive Models: Solution From Intercorrelation...

Area of Science:

• Structural Equation Modeling
• Statistical Methods
• Psychometrics

Background:

• Structural models are crucial for understanding complex relationships.
• Assessing the logical consistency of these models is vital for valid inferences.
• Existing methods for evaluating model fit have limitations.

Purpose of the Study:

• To review the logic and procedures of disturbance term regression tests.
• To demonstrate the mathematical equivalence of this test to part correlation in specific cases.
• To provide practical procedures for applying these tests in research.

Main Methods:

• Review of disturbance term regression test principles.
• Mathematical analysis for recursive and nonrecursive designs.
• Demonstration of equivalence to part correlation in a three-variable mediational model.
• Outline of procedures using intercorrelation matrices.

Main Results:

• The disturbance term regression test is mathematically equivalent to part correlation in a simple, complete mediational case.
• Procedures are presented for conducting these tests using only intercorrelation matrices.
• Generalizable methods are provided for testing mediation and cross-effects.

Conclusions:

• Disturbance term regression offers a valuable tool for assessing structural model consistency.
• The outlined procedures facilitate the application of these tests in both recursive and nonrecursive models.
• This approach provides an alternative or complement to other model fit indices.