Abstract
Mixtures of regressions play a prominent role in regression analysis when it is known the population of interest is divided into homogeneous and disjoint groups. This typically consists in partitioning the observational space into several regions through particular hypersurfaces called decision boundaries. A geometrical analysis of these surfaces allows to highlight properties of the used classifier. In particular, a geometrical classification of decision boundaries for the three most used mixtures of regressions (with fixed covariates, with concomitant variables and random covariates) was provided in case of one and two covariates, under Gaussian assumptions and in presence of only one real response variable. This work aims to extend these results to a more complex setting where three independent variables are considered.
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References
DeSarbo, W. S., Cron, W. L.: A maximum likelihood methodology for clusterwise linear regression. J. Classif. 5, 249–282 (1988)
Grun, B., Leisch, F.: FlexMix version 2: finite mixtures with concomitant variables and varying and constant parameters. J. Stat. Softw. 28, 1–35 (2008)
Hennig, C.: Identifiablity of models for clusterwise linear regression. J. Classif. 17, 273–296 (2000)
Ingrassia, S., Minotti, S. C., Vittadini, G.: Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions. J. Classif. 29, 363-401 (2012)
Ingrassia, S., Punzo, A.: Decision boundaries for mixtures of regressions. J. Korean Stat. Soc. 45, 295-306 (2016)
Wedel, M.: Concomitant variables in finite mixture models. Stat. Neerl. 56, 362–375 (2002)
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Antonazzo, F., Ingrassia, S. (2023). A Trivariate Geometric Classification of Decision Boundaries for Mixtures of Regressions. In: Brito, P., Dias, J.G., Lausen, B., Montanari, A., Nugent, R. (eds) Classification and Data Science in the Digital Age. IFCS 2022. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-031-09034-9_3
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DOI: https://doi.org/10.1007/978-3-031-09034-9_3
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