Exploring the Role of Variance Stabilizing Transformations in Improving Statistical Model Performance

Posted: Jan 28, 2000

• Kylie Rogers
• Layla Evans
• Leo Stewart

Abstract

Statistical modeling forms the backbone of empirical research across scientific disciplines, yet the preprocessing steps that precede model fitting often receive insufficient methodological attention. Traditional approaches to data preparation typically emphasize normalization, standardization, or simple logarithmic transformations without systematic consideration of variance structure. Variance stabilizing transformations (VSTs) represent a class of mathematical operations designed specifically to address heteroscedasticity—the phenomenon where variability in data changes with the mean level. While VSTs have established applications in specialized contexts such as Poisson count data or proportional measurements, their potential as a general-purpose preprocessing framework remains largely unexplored. The conventional wisdom in statistical modeling prioritizes linearity and normality assumptions, often overlooking the fundamental importance of variance homogeneity. This research challenges that paradigm by proposing that variance stabilization should precede, or at least complement, traditional normalization procedures. The theoretical foundation of VSTs rests on the delta method, which provides approximate variance expressions for transformed random variables. When properly selected, VSTs can render the variance approximately constant across the range of data values, thereby satisfying a key assumption of many statistical models and improving estimation efficiency. Our investigation addresses three primary research questions that have received limited attention in the literature. First, to what extent can systematic application of VSTs improve predictive performance across diverse statistical models and data types? Second, what criteria should guide the selection of appropriate transformations for different data distribution characteristics? Third, how do VSTs interact with modern machine learning algorithms that may not explicitly assume homoscedasticity? By answering these questions, we aim to establish VSTs as a fundamental component of the data preprocessing pipeline rather than a specialized tool for particular data types. The novelty of our approach lies in its comprehensive treatment of VSTs as a universal preprocessing framework.