Principles and practice of scaled difference chi-square testing

We highlight critical conceptual and statistical issues and how to resolve them in conducting Satorra–Bentler (SB) scaled difference chi-square tests. Concerning the original (Satorra & Bentler, 2001) and new (Satorra & Bentler, 2010) scaled difference tests, a fundamental difference...

ver descrição completa

Detalhes bibliográficos
Autores: Bryant, Fred B., Satorra, Albert
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2012
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10230/46110
Acesso em linha:http://hdl.handle.net/10230/46110
http://dx.doi.org/10.1080/10705511.2012.687671
Access Level:acceso abierto
Palavra-chave:Chi-square difference test statistic
Goodness-of-fit test
Moment structures
Nonnormality
Scaled chi-square
id ES_6b6fe809a00a669a94d959c17bc4dc42
oai_identifier_str oai:recercat.cat:10230/46110
network_acronym_str ES
network_name_str España
repository_id_str
spelling Principles and practice of scaled difference chi-square testingBryant, Fred B.Satorra, AlbertChi-square difference test statisticGoodness-of-fit testMoment structuresNonnormalityScaled chi-squareWe highlight critical conceptual and statistical issues and how to resolve them in conducting Satorra–Bentler (SB) scaled difference chi-square tests. Concerning the original (Satorra & Bentler, 2001) and new (Satorra & Bentler, 2010) scaled difference tests, a fundamental difference exists in how to compute properly a model's scaling correction factor (c), depending on the particular structural equation modeling software used. Because of how LISREL 8 defines the SB scaled chi-square, LISREL users should compute c for each model by dividing the model's normal theory weighted least-squares (NTWLS) chi-square by its SB chi-square, to recover c accurately with both tests. EQS and Mplus users, in contrast, should divide the model's maximum likelihood (ML) chi-square by its SB chi-square to recover c. Because ML estimation does not minimize the NTWLS chi-square, however, it can produce a negative difference in nested NTWLS chi-square values. Thus, we recommend the standard practice of testing the scaled difference in ML chi-square values for models M 1 and M 0 (after properly recovering c for each model), to avoid an inadmissible test numerator. We illustrate the difference in computations across software programs for the original and new scaled tests and provide LISREL, EQS, and Mplus syntax in both single- and multiple-group form for specifying the model M 10 that is involved in the new test.This research was supported in part by a grant SEJ2006-13537 from the Spanish Ministry of Science and Technology (to Albert Satorra).Taylor & Francis202020202012info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/46110http://dx.doi.org/10.1080/10705511.2012.687671reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésStructural Equation Modeling. 2012 Jul 31;19(3):372-98info:eu-repo/grantAgreement/ES/2PN/SEJ2006-13537© This is an Accepted Manuscript of an article published by Taylor & Francis in Structural Equation Modeling on 2012 Jul 31, available online: http://www.tandfonline.com/10.1080/10705511.2012.687671info:eu-repo/semantics/openAccessoai:recercat.cat:10230/461102026-05-29T05:05:01Z
dc.title.none.fl_str_mv Principles and practice of scaled difference chi-square testing
title Principles and practice of scaled difference chi-square testing
spellingShingle Principles and practice of scaled difference chi-square testing
Bryant, Fred B.
Chi-square difference test statistic
Goodness-of-fit test
Moment structures
Nonnormality
Scaled chi-square
title_short Principles and practice of scaled difference chi-square testing
title_full Principles and practice of scaled difference chi-square testing
title_fullStr Principles and practice of scaled difference chi-square testing
title_full_unstemmed Principles and practice of scaled difference chi-square testing
title_sort Principles and practice of scaled difference chi-square testing
dc.creator.none.fl_str_mv Bryant, Fred B.
Satorra, Albert
author Bryant, Fred B.
author_facet Bryant, Fred B.
Satorra, Albert
author_role author
author2 Satorra, Albert
author2_role author
dc.subject.none.fl_str_mv Chi-square difference test statistic
Goodness-of-fit test
Moment structures
Nonnormality
Scaled chi-square
topic Chi-square difference test statistic
Goodness-of-fit test
Moment structures
Nonnormality
Scaled chi-square
description We highlight critical conceptual and statistical issues and how to resolve them in conducting Satorra–Bentler (SB) scaled difference chi-square tests. Concerning the original (Satorra & Bentler, 2001) and new (Satorra & Bentler, 2010) scaled difference tests, a fundamental difference exists in how to compute properly a model's scaling correction factor (c), depending on the particular structural equation modeling software used. Because of how LISREL 8 defines the SB scaled chi-square, LISREL users should compute c for each model by dividing the model's normal theory weighted least-squares (NTWLS) chi-square by its SB chi-square, to recover c accurately with both tests. EQS and Mplus users, in contrast, should divide the model's maximum likelihood (ML) chi-square by its SB chi-square to recover c. Because ML estimation does not minimize the NTWLS chi-square, however, it can produce a negative difference in nested NTWLS chi-square values. Thus, we recommend the standard practice of testing the scaled difference in ML chi-square values for models M 1 and M 0 (after properly recovering c for each model), to avoid an inadmissible test numerator. We illustrate the difference in computations across software programs for the original and new scaled tests and provide LISREL, EQS, and Mplus syntax in both single- and multiple-group form for specifying the model M 10 that is involved in the new test.
publishDate 2012
dc.date.none.fl_str_mv 2012
2020
2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10230/46110
http://dx.doi.org/10.1080/10705511.2012.687671
url http://hdl.handle.net/10230/46110
http://dx.doi.org/10.1080/10705511.2012.687671
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Structural Equation Modeling. 2012 Jul 31;19(3):372-98
info:eu-repo/grantAgreement/ES/2PN/SEJ2006-13537
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869410196051197953
score 15.81155

Registos relacionados