A Note on the Likelihood Ratio Test in High-Dimensional Exploratory Factor Analysis
The likelihood ratio test is widely used in exploratory factor analysis to assess the model fit and determine the number of latent factors. Despite its popularity and clear statistical rationale, researchers have found that when the dimension of the response data is large compared to the sample size...
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| Veröffentlicht in: | Psychometrika 2021-06, Vol.86 (2), p.442-463 |
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| description | The likelihood ratio test is widely used in exploratory factor analysis to assess the model fit and determine the number of latent factors. Despite its popularity and clear statistical rationale, researchers have found that when the dimension of the response data is large compared to the sample size, the classical Chi-square approximation of the likelihood ratio test statistic often fails. Theoretically, it has been an open problem when such a phenomenon happens as the dimension of data increases; practically, the effect of high dimensionality is less examined in exploratory factor analysis, and there lacks a clear statistical guideline on the validity of the conventional Chi-square approximation. To address this problem, we investigate the failure of the Chi-square approximation of the likelihood ratio test in high-dimensional exploratory factor analysis and derive the
necessary and sufficient
condition to ensure the validity of the Chi-square approximation. The results yield simple quantitative guidelines to check in practice and would also provide useful statistical insights into the practice of exploratory factor analysis. |
| doi_str_mv | 10.1007/s11336-021-09755-4 |
| format | Article |
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necessary and sufficient
condition to ensure the validity of the Chi-square approximation. The results yield simple quantitative guidelines to check in practice and would also provide useful statistical insights into the practice of exploratory factor analysis.</description><identifier>ISSN: 0033-3123</identifier><identifier>EISSN: 1860-0980</identifier><identifier>DOI: 10.1007/s11336-021-09755-4</identifier><identifier>PMID: 33770318</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Approximation ; Assessment ; Behavioral Science and Psychology ; Chi-square test ; Discriminant analysis ; Factor analysis ; Humanities ; Law ; Mathematical Methods In Social Sciences ; Mathematics ; Mathematics, Interdisciplinary Applications ; Physical Sciences ; Psychology ; Psychology, Mathematical ; Psychometrics ; Science & Technology ; Social Sciences ; Social Sciences, Mathematical Methods ; Statistical Theory and Methods ; Statistics ; Statistics for Social Sciences ; Testing and Evaluation ; Theory and Methods ; Theory and Methods (T&M) ; Validity</subject><ispartof>Psychometrika, 2021-06, Vol.86 (2), p.442-463</ispartof><rights>The Psychometric Society 2021</rights><rights>The Psychometric Society 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>true</woscitedreferencessubscribed><woscitedreferencescount>1</woscitedreferencescount><woscitedreferencesoriginalsourcerecordid>wos000633296100001</woscitedreferencesoriginalsourcerecordid><citedby>FETCH-LOGICAL-c375t-b6f3636207376d14c5534b43f0e3d25c426bd8f74b5847a39c24099faf345d923</citedby><cites>FETCH-LOGICAL-c375t-b6f3636207376d14c5534b43f0e3d25c426bd8f74b5847a39c24099faf345d923</cites><orcidid>0000-0003-4023-5413</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11336-021-09755-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11336-021-09755-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,27929,27930,39262,39263,41493,42562,51324</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/33770318$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>He, Yinqiu</creatorcontrib><creatorcontrib>Wang, Zi</creatorcontrib><creatorcontrib>Xu, Gongjun</creatorcontrib><title>A Note on the Likelihood Ratio Test in High-Dimensional Exploratory Factor Analysis</title><title>Psychometrika</title><addtitle>Psychometrika</addtitle><addtitle>PSYCHOMETRIKA</addtitle><addtitle>Psychometrika</addtitle><description>The likelihood ratio test is widely used in exploratory factor analysis to assess the model fit and determine the number of latent factors. Despite its popularity and clear statistical rationale, researchers have found that when the dimension of the response data is large compared to the sample size, the classical Chi-square approximation of the likelihood ratio test statistic often fails. Theoretically, it has been an open problem when such a phenomenon happens as the dimension of data increases; practically, the effect of high dimensionality is less examined in exploratory factor analysis, and there lacks a clear statistical guideline on the validity of the conventional Chi-square approximation. To address this problem, we investigate the failure of the Chi-square approximation of the likelihood ratio test in high-dimensional exploratory factor analysis and derive the
necessary and sufficient
condition to ensure the validity of the Chi-square approximation. 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necessary and sufficient
condition to ensure the validity of the Chi-square approximation. The results yield simple quantitative guidelines to check in practice and would also provide useful statistical insights into the practice of exploratory factor analysis.</abstract><cop>New York</cop><pub>Springer US</pub><pmid>33770318</pmid><doi>10.1007/s11336-021-09755-4</doi><tpages>22</tpages><orcidid>https://orcid.org/0000-0003-4023-5413</orcidid></addata></record> |
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| subjects | Approximation Assessment Behavioral Science and Psychology Chi-square test Discriminant analysis Factor analysis Humanities Law Mathematical Methods In Social Sciences Mathematics Mathematics, Interdisciplinary Applications Physical Sciences Psychology Psychology, Mathematical Psychometrics Science & Technology Social Sciences Social Sciences, Mathematical Methods Statistical Theory and Methods Statistics Statistics for Social Sciences Testing and Evaluation Theory and Methods Theory and Methods (T&M) Validity |
| title | A Note on the Likelihood Ratio Test in High-Dimensional Exploratory Factor Analysis |
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