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Tests of homoscedasticity, normality, and missing completely at random for incomplete multivariate data
Mortaza Jamshidian1, Siavash Jalal
1Department of Mathematics, California State University, Fullerton, CA 92834 mori@fullerton.edu.
Psychometrika
|July 2, 2011
Summary
This study introduces improved statistical tests for homogeneity of covariances, enhancing the detection of missing completely at random (MCAR) data. The new methods offer better performance and power, especially with non-normal or incomplete datasets.
Area of Science:
- Statistics
- Statistical Analysis
- Data Science
Background:
- Homogeneity of covariances (homoscedasticity) testing is crucial in statistical analysis.
- Existing tests for homoscedasticity in incomplete data, particularly for missing completely at random (MCAR) data, often require large sample sizes and fail with non-normal data.
- Hawkins' (1981) test for multivariate normality and homoscedasticity is exact for small complete datasets but has limitations.
Purpose of the Study:
- To propose a modified Hawkins' test for improved performance on complete data.
- To extend the test's application for homoscedasticity and MCAR testing with multivariate normal and incomplete data.
- To develop a nonparametric test for homoscedasticity applicable to both normal and non-normal data.
Main Methods:
- Modification of Hawkins' test for enhanced performance on complete data.
- Extension of the modified Hawkins' test for homoscedasticity and MCAR in multivariate normal incomplete data.
- Development of a nonparametric homoscedasticity test by combining the Hawkins' test statistic with a k-sample test.
- Application of multiple imputation techniques for handling missing data.
Main Results:
- Simulation studies indicate the proposed tests outperform existing methods in Type I error rejection rates.
- The new tests demonstrate good statistical power.
- Multiple imputation methods confirmed results obtained using single imputation.
- The proposed methods successfully identified groups with differing covariance matrices using multiple imputation.
Conclusions:
- The modified Hawkins' test and the combined normal-theory/nonparametric approach provide robust methods for testing homoscedasticity, MCAR, and multivariate normality.
- These methods are effective even with non-normal and incomplete data.
- Multiple imputation is a valuable tool for identifying covariance matrix differences in incomplete datasets.
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