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A new algorithm for fitting semi-parametric variance regression models

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  • Kristy P. Robledo

    (University of Sydney)

  • Ian C. Marschner

    (University of Sydney)

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.

Suggested Citation

  • Kristy P. Robledo & Ian C. Marschner, 2021. "A new algorithm for fitting semi-parametric variance regression models," Computational Statistics, Springer, vol. 36(4), pages 2313-2335, December.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:4:d:10.1007_s00180-021-01067-6
    DOI: 10.1007/s00180-021-01067-6
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    References listed on IDEAS

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    1. Shujie Ma, 2014. "A plug-in the number of knots selector for polynomial spline regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 489-507, September.
    2. Murray Aitkin, 1987. "Modelling Variance Heterogeneity in Normal Regression Using GLIM," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 332-339, November.
    3. Ravi Varadhan & Christophe Roland, 2008. "Simple and Globally Convergent Methods for Accelerating the Convergence of Any EM Algorithm," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 335-353, June.
    4. Clifford M. Hurvich & Jeffrey S. Simonoff & Chih‐Ling Tsai, 1998. "Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 271-293.
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