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Factor Scores in Small Samples: Recommendations and Solutions.

Christian L L Strauss¹

¹Vanderbilt University, Nashville, TN, USA.

Educational and Psychological Measurement

|May 18, 2026

Summary

This summary is machine-generated.

For small sample sizes in structural equation modeling (SEM), factor scores from essentially tau-equivalent models offer better convergence and stability than sum scores. These scores are a viable alternative when congeneric models fail.

Keywords:

factor scores measurement sum scores tau-equivalent

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Area of Science:

Psychometrics
Statistical Modeling

Background:

Simultaneous estimation in structural equation modeling (SEM) is challenging with small sample sizes (N).
Existing scoring recommendations are based on larger sample sizes (N > 200).
Factor scores and sum scores are common methods for obtaining reliable estimates in SEM.

Purpose of the Study:

Extend scoring recommendations for SEM to small sample sizes (N ≤ 200).
Compare the performance of factor scores and sum scores in small samples.
Introduce and evaluate factor scores from an essentially tau-equivalent model as an alternative scoring method.

Main Methods:

Simulated data with small sample sizes (N ≤ 200).
Direct comparison of factor scores and sum scores.
Introduction and analysis of factor scores derived from an essentially tau-equivalent factor model.

Main Results:

Factor scores from essentially tau-equivalent models demonstrate advantages in convergence and stability for small N.
These scores are obtainable even when congeneric factor models do not converge.
Factor scores from essentially tau-equivalent models show comparable correlations with true scores to traditional factor scores in small samples.

Conclusions:

Factor scores from essentially tau-equivalent models are recommended for SEM with small sample sizes.
This scoring method balances the benefits of sum and factor scores.
The utility of essentially tau-equivalent factor scores is robust to minor assumption violations.