Empirically Corrected Rescaled Statistics for SEM with Small N and Large p.

Area of Science:

• Statistics
• Quantitative Psychology
• Econometrics

Background:

• Structural equation modeling (SEM) is widely used for analyzing complex survey data.
• The Trml statistic is commonly recommended for SEM with nonnormally distributed data.
• Existing Trml statistics are unreliable with small sample sizes (N) or large numbers of variables (p).

Purpose of the Study:

• To develop reliable test statistics for SEM under conditions of small N or large p, particularly with nonnormal data.
• To address the limitations of the Trml statistic in challenging data scenarios.
• To enhance the accuracy and control of Type I errors in SEM analyses.

Main Methods:

• The study applies the principle of Bartlett correction to develop empirical corrections for the Trml statistic.
• The proposed method aims to adjust the statistic so its mean approximates the degrees of freedom of the chi-square distribution.
• The performance of the corrected statistics is evaluated through simulations and a real data example.

Main Results:

• Empirically corrected statistics demonstrate reasonable control of Type I errors, even when N is smaller than 2p.
• The Trml statistic can lead to excessive Type I errors (up to 100% rejection) with small N or large p, even with normal data.
• The developed corrections provide a more reliable testing approach in previously problematic SEM scenarios.

Conclusions:

• Empirical corrections offer a robust solution for structural equation modeling with small sample sizes or numerous variables.
• The findings suggest that these corrected statistics are particularly valuable when dealing with nonnormally distributed survey data.
• This research provides a more dependable statistical tool for SEM practitioners facing common data limitations.