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Generative Models for Simulating Non-Normal Multivariate Data for Robust MANOVA Testing

Multivariate Analysis of Variance (MANOVA) is a foundational statistical method used to detect group differences across multiple correlated outcome variables. Classical MANOVA test statistics, including Wilk’s Lambda, Pillai’s Trace, and Roy’s Root, are optimal under multivariate normality and homogeneity of covariance matrices. However, their performances can deteriorate under non-normality or small sample sizes. This study builds upon the truncated MANOVA statistics (W3, P3, R3) which demonstrated improved robustness under specific non-Gaussian conditions. Here, we introduce a generative modeling framework using Variational Autoencoders (VAE), Generative Adversarial Networks (GAN), and Conditional Variational Autoencoders (CVAE) to simulate multivariate data with complex, realistic non-normal structures. We benchmark the power and Type I error control of classical, truncated, and permutation-based MANOVA statistics on these generative datasets. Results show that P3 and R3 maintain competitive robustness across all conditions, while W3 remains sensitive to effect size and distributional form. Permutation MANOVA shows strong power under multimodal and heavy-tailed distributions. Our work highlights the utility of generative models as simulation engines for statistical robustness research.

Author(s)
S. O. AGHAMIE
J. C. EHIWARIO
R. N. NWAKA,
G. C. EBOH
Volume
2
Keyword(s)
Multivariate Analysis
Generative Adversarial Networks
Generative Models
Variational Autoencoders
Conditional Variational Autoencoders
Year
2025
Page Number
233-243
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BJPS 2(1) Paper 16.pdf (875.91 KB)
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