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A Third Moment Adjusted Test Statistic for Small Sample Factor Analysis.

Johnny Lin¹, Peter M Bentler

¹University of California, Los Angeles.

Multivariate Behavioral Research

|November 13, 2012

Summary

This summary is machine-generated.

This study introduces a new statistical method for factor analysis, improving accuracy in small samples. The adjusted statistic enhances robustness and Type I error rates, outperforming existing methods in specific conditions.

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Area of Science:

Psychometrics
Statistical Modeling
Quantitative Psychology

Background:

Goodness of fit testing in factor analysis relies on asymptotic chi-square distribution, which can be unreliable in small samples.
Existing robust methods (e.g., Browne's ADF, Satorra-Bentler) primarily address non-normality, not skewness in normally distributed data.
Sampling error can induce high skewness in test statistics, even with normal population distributions.

Purpose of the Study:

To propose an extension of the Satorra-Bentler statistic that adjusts for the skewness of the test statistic.
To improve the robustness and accuracy of goodness of fit testing in factor analysis for small sample sizes.
To evaluate the performance of the proposed third moment adjusted statistic against existing methods.

Main Methods:

Development of a modified Satorra-Bentler statistic incorporating third moment adjustments (skewness) for degrees of freedom.
Conducting a simulation study to compare the proposed statistic with established methods under various sample sizes.
Application of the adjusted statistic to real-world data from a study on student abilities.

Main Results:

The third moment adjusted statistic demonstrates comparable asymptotic performance to existing methods.
At very small sample sizes, the proposed statistic shows superior Type I error rates under correctly specified models.
The real-world data analysis illustrates the practical utility of the adjusted statistic.

Conclusions:

The proposed extension enhances the robustness of factor analysis goodness of fit testing in small samples, particularly when skewness is present.
This method offers improved Type I error control, making it a valuable tool for researchers working with limited data.
The adjusted statistic provides a more reliable assessment of model fit in scenarios where traditional methods may falter.