MANOVA for Nested Designs with Unequal Cell Sizes and Unequal Cell Covariance Matrices
We propose and study parametric bootstrap (PB) tests for heteroscedastic two-factor MANOVA with nested designs. For the problem of testing “main effects” of both factors, we develop a flexible test based on a parametric bootstrap approach. The PB test is shown to be invariant under affine-transforma...
| Published in: | Journal of Applied Mathematics |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Online Access: | http://dx.doi.org/10.1155/2014/649202 |
| _version_ | 1849870619195211776 |
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| author | Li-Wen Xu |
| author_facet | Li-Wen Xu |
| author_sort | Li-Wen Xu |
| collection | DOAJ |
| container_title | Journal of Applied Mathematics |
| description | We propose and study parametric bootstrap (PB) tests for heteroscedastic two-factor MANOVA with nested designs. For the problem of testing “main effects” of both factors, we develop a flexible test based on a parametric bootstrap approach. The PB test is shown to be invariant under affine-transformations. Moreover, the PB test does not depend on the chosen weights used to define the parameters uniquely. The proposed test is compared with the approximate Hotelling T2 (AHT) test by the simulations. Simulation results indicate that the PB test performs
satisfactorily for various cell sizes and parameter configurations and generally outperforms the AHT test in terms of controlling the nominal size. For the heteroscedastic cases, the PB test outperforms the AHT test in terms of power. In addition, the PB test does not lose too much power when the homogeneity assumption is actually valid. |
| format | Article |
| id | doaj-art-0fdffa302ba24fbbaf6cc41d80eda878 |
| institution | Directory of Open Access Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| spelling | doaj-art-0fdffa302ba24fbbaf6cc41d80eda8782025-08-20T01:14:37ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/649202649202MANOVA for Nested Designs with Unequal Cell Sizes and Unequal Cell Covariance MatricesLi-Wen Xu0College of Sciences, North China University of Technology, Beijing 100144, ChinaWe propose and study parametric bootstrap (PB) tests for heteroscedastic two-factor MANOVA with nested designs. For the problem of testing “main effects” of both factors, we develop a flexible test based on a parametric bootstrap approach. The PB test is shown to be invariant under affine-transformations. Moreover, the PB test does not depend on the chosen weights used to define the parameters uniquely. The proposed test is compared with the approximate Hotelling T2 (AHT) test by the simulations. Simulation results indicate that the PB test performs satisfactorily for various cell sizes and parameter configurations and generally outperforms the AHT test in terms of controlling the nominal size. For the heteroscedastic cases, the PB test outperforms the AHT test in terms of power. In addition, the PB test does not lose too much power when the homogeneity assumption is actually valid.http://dx.doi.org/10.1155/2014/649202 |
| spellingShingle | Li-Wen Xu MANOVA for Nested Designs with Unequal Cell Sizes and Unequal Cell Covariance Matrices |
| title | MANOVA for Nested Designs with Unequal Cell Sizes and Unequal Cell Covariance Matrices |
| title_full | MANOVA for Nested Designs with Unequal Cell Sizes and Unequal Cell Covariance Matrices |
| title_fullStr | MANOVA for Nested Designs with Unequal Cell Sizes and Unequal Cell Covariance Matrices |
| title_full_unstemmed | MANOVA for Nested Designs with Unequal Cell Sizes and Unequal Cell Covariance Matrices |
| title_short | MANOVA for Nested Designs with Unequal Cell Sizes and Unequal Cell Covariance Matrices |
| title_sort | manova for nested designs with unequal cell sizes and unequal cell covariance matrices |
| url | http://dx.doi.org/10.1155/2014/649202 |
| work_keys_str_mv | AT liwenxu manovafornesteddesignswithunequalcellsizesandunequalcellcovariancematrices |