Abstract
Linear regression and analysis of variance are widely used in applied psychological measurement to estimate group, condition, and covariate effects, yet statistical efficiency and conventional inference can be compromised when outcome variance changes across groups or covariate levels. This article introduces varGuid for R and varguid for Python, open-source implementations of variance-guided regression for linear models. The method estimates a covariate-dependent mean-variance relationship and uses it to iteratively reweight the original mean model. Ordinary analyses use iteratively reweighted least squares, whereas sparse analyses use an iteratively reweighted lasso. Because the original design matrix and outcome scale are retained, regression coefficients and ANOVA contrasts remain directly comparable with conventional effect estimates. Robustness here refers to relaxation of the homoscedasticity assumption rather than resistance to outliers. Under the conditions established for variance-guided regression, the estimator matches the homoscedastic baseline in population predictive quasi-risk when variance is constant and improves on that baseline when variance depends on covariates. The packages accept general linear-model design matrices, including ANOVA-style encodings, and provide baseline and variance-guided predictions, example data, and heteroscedasticity-consistent summaries for non-lasso fits. The Python implementation also supports NumPy and pandas inputs, Patsy formulas, model summaries, and a scikit-learn-compatible estimator. Both implementations are operating-system independent and require no unusual hardware. Source code, documentation, examples, and installable files are available through CRAN, PyPI, GitHub, and Zenodo. The packages provide accessible tools for applying variance-guided regression as a primary or companion analysis when homogeneity of variance is uncertain in routine measurement research and related quantitative applications.