On the Model-Based Bootstrap With Missing Data: Obtaining a P-Value for a Test of Exact Fit

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Evaluating structural equation model (SEM) fit using bootstrap methods typically requires data transformation for exact null hypothesis testing.
• Existing transformations for complete data (Beran & Srivastava, 1985; Bollen & Stine, 1992) have approximate extensions for missing data (Enders, 2002).

Purpose of the Study:

• To develop and evaluate exact bootstrap procedures for SEM with incomplete data.
• To address the limitations of approximate methods for handling missing data in SEM fit evaluation.

Main Methods:

• Developed an explicit solution for cases with invertible sample covariance matrices within missing data patterns.
• Proposed two iterative algorithms for obtaining exact solutions in general missing data scenarios.
• Conducted a Monte Carlo study to assess the performance of the new procedures using bootstrapped likelihood ratio statistics.

Main Results:

• The model-based bootstrap with incomplete data demonstrated robust performance across diverse distributional conditions, missing data mechanisms, and proportions of missing data.
• The newly developed procedures provide an exact solution for structural equation modeling fit evaluation with missing data.

Conclusions:

• The proposed exact bootstrap methods are effective for structural equation modeling with incomplete data.
• These methods offer a reliable approach for assessing model fit, improving upon existing approximate techniques.