On the estimation of variance parameters in non-standard generalised linear mixed models: application to penalised smoothing

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dc.contributor.author Rodríguez Álvarez, María Xosé
dc.contributor.author Durbán Reguera, María Luz
dc.contributor.author Lee, Dae-Jin
dc.contributor.author Eilers, Paul H. C.
dc.date.accessioned 2021-03-22T11:07:52Z
dc.date.available 2021-03-22T11:07:52Z
dc.date.issued 2019-05-01
dc.identifier.bibliographicCitation Statistics and Computing, 2019, 29,483–500
dc.identifier.issn 0960-3174
dc.identifier.uri http://hdl.handle.net/10016/32195
dc.description.abstract We present a novel method for the estimation of variance parameters in generalised linear mixed models. The method has its roots in Harville (J Am Stat Assoc 72(358):320-338, 1977)'s work, but it is able to deal with models that have a precision matrix for the random effect vector that is linear in the inverse of the variance parameters (i.e., the precision parameters). We call the method SOP (separation of overlapping precision matrices). SOP is based on applying the method of successive approximations to easy-to-compute estimate updates of the variance parameters. These estimate updates have an appealing form: they are the ratio of a (weighted) sum of squares to a quantity related to effective degrees of freedom. We provide the sufficient and necessary conditions for these estimates to be strictly positive. An important application field of SOP is penalised regression estimation of models where multiple quadratic penalties act on the same regression coefficients. We discuss in detail two of those models: penalised splines for locally adaptive smoothness and for hierarchical curve data. Several data examples in these settings are presented.
dc.description.sponsorship This research was supported by the Basque Government through the BERC 2018-2021 program and by Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation SEV-2013-0323 and through projects MTM2017-82379-R funded by (AEI/FEDER, UE) and acronym “AFTERAM”, MTM2014-52184-P and MTM2014-55966-P. The MRI/DTI data were collected at Johns Hopkins University and the Kennedy-Krieger Institute. We are grateful to Pedro Caro and Iain Currie for useful discussions, to Martin Boer and Cajo ter Braak for the detailed reading of the paper and their many suggestions, and to Bas Engel for sharing with us his knowledge. We are also grateful to the two peer referees for their constructive comments of the paper.
dc.format.extent 18
dc.rights Copyright © 2018, Springer Science Business Media, LLC, part of Springer Nature
dc.subject.other Generalised Linear Mixed Models
dc.subject.other Generalised Additive Models
dc.subject.other Variance Parameters
dc.subject.other Smoothing Parameters
dc.subject.other Reml
dc.subject.other Effective Degrees Of Freedomm
dc.subject.other Restricted Maximum-Likelihood
dc.subject.other Animal-Models
dc.subject.other Selection
dc.subject.other Splines
dc.subject.other Components
dc.subject.other Penalties
dc.title On the estimation of variance parameters in non-standard generalised linear mixed models: application to penalised smoothing
dc.type article
dc.subject.eciencia Estadística
dc.identifier.doi 10.1007/s11222-018-9818-2
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2014-52184-P
dc.relation.projectID Gobierno de España. MTM2014-55966-P
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 483
dc.identifier.publicationissue 3
dc.identifier.publicationlastpage 500
dc.identifier.publicationtitle STATISTICS AND COMPUTING
dc.identifier.publicationvolume 29
dc.identifier.uxxi AR/0000023628
dc.contributor.funder Ministerio de Economía y Competitividad (España)
dc.affiliation.dpto UC3M. Departamento de Estadística
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