A Novel Wavelet-Based Approach for ANOVA in Longitudinal Data Analysis Using the First Derivative of the Laplace Function
DOI:
https://doi.org/10.62933/92g47m85Keywords:
Wavelet ANOVA, Longitudinal data analysis, , Laplace Function, Repeated Measures, Dimension ReductionAbstract
Longitudinal data, characterized by repeated observations on the same subjects over time, present significant challenges for traditional statistical Analysis of Variance (ANOVA) methods, such as Repeated Measures ANOVA due to inherent intra-subject correlation and high dimensionality. This study introduced a novel wavelet-based ANOVA approach using the first derivative of the Laplace distribution to transform high-dimensional repeated measures data into a simplified Completely Randomized Design (CRD) structure, thereby facilitating classical ANOVA. The mathematical formulation and key properties (admissibility and energy localization) of this wavelet function are detailed. We rigorously proved that this wavelet satisfies the fundamental conditions required for signal analysis. Through a comprehensive simulation study, we demonstrated its effectiveness in preserving treatment differences, controlling Type I error rate, maintaining acceptable statistical power, and showing robustness to variations in the number of time points. The results validated the Laplace derivative wavelet as a powerful and reliable tool for dimensionality reduction and valid inference in longitudinal data analysis, offering a robust alternative to conventional repeated measures techniques.
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Copyright (c) 2026 Naziru Isah Muhammad, Musa Tasi'u, Yakubu Aliyu, Umar Kabir Abdullahi (Author)
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