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Model selection in covariance structures analysis and the "problem" of sample size: a clarification.
Psychological Bulletin
|May 1, 1991
Summary
The sample size problem in model selection means complex covariance matrix models are often chosen with large datasets. This study argues that large sample sizes influencing model selection are not necessarily undesirable for covariance matrix estimation.
Area of Science:
- Statistics
- Multivariate Analysis
- Psychometrics
Background:
- Complex models for covariance matrices involve many parameters, while simple models require fewer.
- Model selection often favors complex structures with large sample sizes, a phenomenon known as the sample size problem.
Purpose of the Study:
- To argue that the influence of sample size on model selection for covariance matrices is not inherently undesirable.
- To explore the relationships between population covariance matrices and their model-based estimates.
Main Methods:
- Evaluation of covariance matrix models with differing complexity using goodness of fit indices.
- Analysis of the relationships among population covariance matrices and two model-based estimates.
Main Results:
- Models with more parameters are more likely to be selected with larger sample sizes, irrespective of other utility considerations.
- The influence of sample size on model selection is examined in the context of covariance matrix estimation.
Conclusions:
- The sample size problem in covariance matrix model selection may not be a drawback.
- Understanding the relationships between population and estimated covariance matrices is key to practical implications.