The Effects of Sampling Error and Model Characteristics on Parameter Estimation for Maximum Likelihood Confirmatory...

Area of Science:

• Psychometrics
• Statistical Modeling
• Quantitative Psychology

Background:

• Maximum likelihood confirmatory factor analysis (ML-CFA) is widely used for structural equation modeling.
• Understanding the impact of sampling error and model characteristics on parameter estimates is crucial for reliable analysis.
• Previous research has highlighted potential biases and variability in CFA parameter estimates under various conditions.

Purpose of the Study:

• To systematically investigate the effects of sampling error and model characteristics on parameter estimates and standard errors in ML-CFA.
• To evaluate how variations in sample size, number of indicators, factor correlations, and indicator reliability influence CFA results.
• To provide insights into the robustness of ML-CFA under different methodological conditions.

Main Methods:

• Employed Monte Carlo simulation methods to generate data under controlled conditions.
• Varied key parameters including sample size (50-300), number of indicators per factor, number of factors, factor correlations, and indicator reliabilities.
• Analyzed parameter estimates and their standard errors derived from ML-CFA models.

Main Results:

• Measurement and structural parameter estimates were generally found to be unbiased.
• An exception was noted for structural parameters linking factors defined by only two indicators, which showed bias.
• Significant sampling variability was observed, particularly with smaller sample sizes, fewer indicators per factor, and lower indicator reliabilities.

Conclusions:

• While ML-CFA parameter estimates are largely unbiased, sampling variability poses a considerable challenge.
• Model characteristics such as sample size, indicator count, and reliability critically influence the precision of estimates.
• Estimated standard errors adequately adjusted for sampling variability, offering a degree of correction for observed fluctuations.