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A Monte Carlo Investigation of Methods for Controlling Type I Errors with Specification Searches in Structural
Multivariate Behavioral Research
|January 20, 2016
Summary
The Bonferroni approach effectively controls Type 1 errors in structural equation modeling when conducting multiple Lagrange multiplier (LM) tests. This method offers better familywise error rate control than standard or simultaneous test procedures for factor analytic models.
Area of Science:
- Statistics
- Psychometrics
- Structural Equation Modeling
Background:
- Structural equation modeling (SEM) often involves post-hoc model modification using Lagrange multiplier (LM) tests.
- Controlling Type 1 errors across multiple LM tests is crucial to prevent the inclusion of spurious parameters.
Purpose of the Study:
- To evaluate the Type 1 error control of three methods for multiple LM tests in factor analytic models.
- To compare the standard approach, Bonferroni correction, and simultaneous test procedure (STP) under various conditions.
Main Methods:
- Simulated data for factor analytic models were generated.
- Three factors were manipulated: factor weights, sample size, and the number of parameters in the specification search.
- Type 1 error rates were assessed for the standard (.05 level), Bonferroni, and STP methods.
Main Results:
- The standard approach was overly liberal, and the STP was overly conservative in controlling familywise error rates.
- The Bonferroni approach demonstrated error rates closer to the nominal level.
- Bonferroni remained superior in controlling familywise error rates, especially when the alpha level was adjusted per step.
Conclusions:
- The Bonferroni method provides superior control over Type 1 errors in multiple LM tests for factor analytic models compared to standard or STP approaches.
- Adjusting the alpha level within the Bonferroni procedure enhances its effectiveness in controlling familywise error rates during model specification searches.
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