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Modeling multiplicative interaction effects in Gaussian structured additive regression models

Author

Listed:
  • Philipp Aschersleben

  • Julian Granna

  • Thomas Kneib

  • Stefan Lang

  • Nikolaus Umlauf

  • Winfried Steiner

Abstract

Gaussian Structured Additive Regression provides a flexible framework for additive decomposition of the expected value with nonlinear covariate effects and time trends, unit- or cluster-specific heterogeneity, spatial heterogeneity, and complex interactions between covariates of different types. Within this framework, we present a simultaneous estimation approach for highly complex multiplicative interaction effects. In particular, a possibly nonlinear function f(z) of a covariate z may be scaled by a multiplicative effect of the form exp(̃η), where ̃η is another possibly structured additive predictor. Inference is fully Bayesian and based on highly efficient Markov Chain Monte Carlo (MCMC) algorithms. We investigate the statistical properties of our approach inextensive simulation experiments. Furthermore, we apply and illustrate themethodology to an analysis of asking prices for 200000 dwellings in Germany.

Suggested Citation

  • Philipp Aschersleben & Julian Granna & Thomas Kneib & Stefan Lang & Nikolaus Umlauf & Winfried Steiner, 2024. "Modeling multiplicative interaction effects in Gaussian structured additive regression models," Working Papers 2024-01, Faculty of Economics and Statistics, Universität Innsbruck.
    • Handle: RePEc:inn:wpaper:2024-01
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    References listed on IDEAS

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    1. W. Brunauer & S. Lang & P. Wechselberger & S. Bienert, 2010. "Additive Hedonic Regression Models with Spatial Scaling Factors: An Application for Rents in Vienna," The Journal of Real Estate Finance and Economics, Springer, vol. 41(4), pages 390-411, November.
    2. Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.
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