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dc.contributor.author | Millard, Sollie M.![]() |
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dc.contributor.author | Kanfer, Frans H.J.![]() |
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dc.date.accessioned | 2023-03-06T06:26:21Z | |
dc.date.available | 2023-03-06T06:26:21Z | |
dc.date.issued | 2022-02-18 | |
dc.description.abstract | The mixture of generalised linear models (MGLM) requires knowledge about each mixture component’s specific exponential family (EF) distribution. This assumption is relaxed and a mixture of semi-parametric generalised linear models (MSPGLM) approach is proposed, which allows for unknown distributions of the EF for each mixture component while much of the parametric structure of the traditional MGLM is retained. Such an approach inherently allows for both symmetric and non-symmetric component distributions, frequently leading to non-symmetrical response variable distributions. It is assumed that the random component of each mixture component follows an unknown distribution of the EF. The specific member can either be from the standard class of distributions or from the broader set of admissible distributions of the EF which is accessible through the semi-parametric procedure. Since the inverse link functions of the mixture components are unknown, the MSPGLM estimates each mixture component’s inverse link function using a kernel smoother. The MSPGLM algorithm alternates the estimation of the regression parameters with the estimation of the inverse link functions. The properties of the proposed MSPGLM are illustrated through a simulation study on the separable individual components. The MSPGLM procedure is also applied on two data sets. | en_US |
dc.description.department | Statistics | en_US |
dc.description.librarian | am2023 | en_US |
dc.description.sponsorship | STATOMET, the Bureau for Statistical and Survey Methodology at the University of Pretoria. | en_US |
dc.description.uri | https://www.mdpi.com/journal/symmetry | en_US |
dc.identifier.citation | Millard, S.M.; Kanfer, F.H.J. Mixtures of Semi-Parametric Generalised Linear Models. Symmetry 2022, 14, 409. https://DOI.org/10.3390/sym14020409. | en_US |
dc.identifier.issn | 2073-8994 (online) | |
dc.identifier.other | 10.3390/sym14020409 | |
dc.identifier.uri | https://repository.up.ac.za/handle/2263/89961 | |
dc.language.iso | en | en_US |
dc.publisher | MDPI | en_US |
dc.rights | © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license. | en_US |
dc.subject | Mixture regression | en_US |
dc.subject | Generalised linear models | en_US |
dc.subject | Semi-parametric modelling | en_US |
dc.subject | Unknown link function | en_US |
dc.subject | Flexible models | en_US |
dc.subject | Mixture of generalised linear models (MGLM) | en_US |
dc.subject | Exponential family distribution | en_US |
dc.subject | Mixture of semi-parametric generalised linear models (MSPGLM) | en_US |
dc.title | Mixtures of semi-parametric generalised linear models | en_US |
dc.type | Article | en_US |