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The use of item parcels in structural equation modelling: non-normal data and small sample sizes
1The Chinese University of Hong Kong, Shatin, N.T., Hong Kong. kthau@cuhk.edu.hk
The British Journal of Mathematical and Statistical Psychology
|October 30, 2004
Summary
Maximum likelihood estimation in confirmatory factor analysis (CFA) struggles with non-normal data and small samples. Alternative strategies, like asymptotically distribution-free methods and specific parceling techniques, show promise for improving parameter estimates and model fit under these conditions.
Area of Science:
- Psychometrics
- Statistical Modeling
- Quantitative Psychology
Background:
- Confirmatory Factor Analysis (CFA) using maximum likelihood estimation (MLE) typically requires large sample sizes and normally distributed data.
- These ideal conditions are frequently unmet in real-world research, posing challenges for accurate statistical inference.
- Non-normality and small sample sizes can lead to convergence issues, biased parameter estimates, and inaccurate model fit indices in CFA.
Purpose of the Study:
- To investigate alternative strategies for confirmatory factor analysis (CFA) when data are non-normal and sample sizes are small.
- To compare the performance of different indicator formation methods (items vs. parcels) and parcelling strategies.
- To evaluate the robustness of maximum likelihood (ML) versus asymptotically distribution-free (ADF) estimation methods under various non-normality and sample size conditions.
Main Methods:
- Two simulation studies were conducted, systematically varying the degree of non-normality, sample size (50–1000), indicator formation (items vs. parcels), parcelling strategy (uniform vs. counterbalanced skew/kurtosis), and estimation method (ML vs. ADF).
- Convergence behavior, parameter estimate bias and variability, and overall goodness of fit were assessed for each condition.
Main Results:
- The study identified specific parcelling strategies that effectively mitigate the negative impacts of non-normality.
- Asymptotically distribution-free (ADF) methods demonstrated better performance than maximum likelihood (ML) under severe non-normality, particularly with smaller sample sizes.
- The choice of indicator formation and parcelling strategy significantly influenced the convergence and accuracy of parameter estimates.
Conclusions:
- Alternative strategies, including carefully constructed parcels and asymptotically distribution-free (ADF) estimation, can improve the accuracy of confirmatory factor analysis (CFA) with non-normal and small sample data.
- Researchers should consider these alternatives when standard maximum likelihood (ML) assumptions are violated.
- The findings provide practical guidance for selecting appropriate methods in CFA to enhance the reliability of results.