A new algorithm for fitting semi-parametric variance regression models

Kristy P. Robledo () and Ian C. Marschner
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Kristy P. Robledo: University of Sydney
Ian C. Marschner: University of Sydney

Computational Statistics, 2021, vol. 36, issue 4, No 1, 2313-2335

Abstract: Abstract Variance regression allows for heterogeneous variance, or heteroscedasticity, by incorporating a regression model into the variance. This paper uses a variant of the expectation–maximisation algorithm to develop a new method for fitting additive variance regression models that allow for regression in both the mean and the variance. The algorithm is easily extended to allow for B-spline bases, thus allowing for the incorporation of a semi-parametric model in both the mean and variance. Although there are existing methods to fit these types of models, this new algorithm provides a reliable alternative approach that is not susceptible to numerical instability that can arise in this constrained estimation context. We utilise the developed algorithm with a series of simulation studies and analyse illustrative data. Various simulation studies show that the algorithm can recover the true model for a variety of scenarios. We also study automatic selection of model complexity based on information-based criteria, and show that the Akaike information criterion is useful for choosing the optimal number of knots in a B-spline model. An R package is available for implementing these methods.

Keywords: Variance regression; Semi-parametric regression; EM algorithm; B-splines (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00180-021-01067-6

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