On Likelihood Ratio Tests for Dimensionality Selection
On Likelihood Ratio Tests for Dimensionality Selection
Many multivariate statistical models have dimensional structures. Such models typically require judicious choice of dimensionality. Likelihood ratio tests are often used for dimensionality selection. However, to this day there is still a great deal of confusion about the asymptotic distributional properties of the log-likelihood ratio (LR) statistics in some areas of psychometrics. Although in many cases the asymptotic distribution of the LR statistic representing the difference between the correct model (of specific dimensionality) and the saturated model is guaranteed to be chi-square, that of the LR statistic representing the difference between the correct model and the one with one dimension higher than the correct model is not likely to be chi-square due to a violation of one of regularity conditions. In this paper, we attempt to clarify the misunderstanding that the latter is also assured to be asymptotically chi-square. This common misunderstanding has occurred repeatedly in various fields, although in some areas it has been corrected.
219-241
Takane, Yoshio
47f0fb15-0a43-4fef-9878-4caec66b2ff1
Van Der Heijden, Peter G. M.
85157917-3b33-4683-81be-713f987fd612
17 August 2023
Takane, Yoshio
47f0fb15-0a43-4fef-9878-4caec66b2ff1
Van Der Heijden, Peter G. M.
85157917-3b33-4683-81be-713f987fd612
Takane, Yoshio and Van Der Heijden, Peter G. M.
(2023)
On Likelihood Ratio Tests for Dimensionality Selection.
In,
Okada, A., Shigemasu, K., Yoshino, R. and Yokoyama, S.
(eds.)
Facets of Behaviormetrics: quantitative approaches to human behaviorThe 50th Anniversary of the Behaviormetric Society. Behaviormetrics:.
(Facets of Behaviormetrics, 4)
Singapore.
Springer Singapore, .
(doi:10.1007/978-981-99-2240-6_10).
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Abstract
Many multivariate statistical models have dimensional structures. Such models typically require judicious choice of dimensionality. Likelihood ratio tests are often used for dimensionality selection. However, to this day there is still a great deal of confusion about the asymptotic distributional properties of the log-likelihood ratio (LR) statistics in some areas of psychometrics. Although in many cases the asymptotic distribution of the LR statistic representing the difference between the correct model (of specific dimensionality) and the saturated model is guaranteed to be chi-square, that of the LR statistic representing the difference between the correct model and the one with one dimension higher than the correct model is not likely to be chi-square due to a violation of one of regularity conditions. In this paper, we attempt to clarify the misunderstanding that the latter is also assured to be asymptotically chi-square. This common misunderstanding has occurred repeatedly in various fields, although in some areas it has been corrected.
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Takane and van der Heijden (2023)
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Published date: 17 August 2023
Identifiers
Local EPrints ID: 481341
URI: http://eprints.soton.ac.uk/id/eprint/481341
ISSN: 2524-4027
PURE UUID: 600e66cd-c86a-471b-a26f-61687aee0151
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Date deposited: 23 Aug 2023 16:59
Last modified: 18 Mar 2024 03:25
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Contributors
Author:
Yoshio Takane
Editor:
A. Okada
Editor:
K. Shigemasu
Editor:
R. Yoshino
Editor:
S. Yokoyama
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