[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-160251-en":3,"doc-seo-160251-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},160251,5909887256941,"Mason","https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc",8,"Research & Report","Estimating the construct validity of Principal Components Analysis","In many scientific disciplines, key features cannot be directly observed and must be inferred from measured behaviour. Latent variable methods increasingly support this inverse inference, with Principal Components Analysis (PCA) being among the simplest and most widely used. This study tests how assumptions about the latent variable system shape whether PCA components capture true variance sources. Results show strong performance in ideal conditions, robustness to plausible measurement noise, yet fragility under violations of linearity and orthogonality plus additional subtle assumptions.","Title: Estimating the construct validity of Principal Components Analysis  \nAuthors: Thomas M. H. Hope 1,2, Cathy J. Price 1, Ajay Halai 3, Carola Salvi 2, Jenny Crinion 4, Merel Keijsers 2, Christoph Sperber 5, Howard Bowman 6  \n[1] Department of Imaging Neuroscience, Institute of Neurology, University College London, 12 Queen Square, London, WC1N 3AR, United Kingdom  \n[2] Department of Psychology and Social Sciences, John Cabot University, 00165 Rome, Italy  \n[3] MRC Cognition and Brain Sciences Unit, University of Cambridge, Cambridge CB2 7EF, UK  \n[4] Institute of Cognitive Science, Department of Experimental Psychology, University College London, London, WC1N 3AR, UK  \n[4] Universitätsklinik für Neurologie Inselspital, Freiburgstr. 16, 3010 Bern, Switzerland  \n[6] School of Psychology, University of Birmingham, Birmingham B15 2TT, UK  \nCorresponding author: Thomas Hope, [t.hope@ucl.ac.uk](t.hope@ucl.ac.uk)  \nAbstract  \nIn many scientific disciplines, the features of interest cannot be observed directly, so must instead be inferred from observed behaviour. Latent variable analyses are increasingly employed to systematise these inferences, and Principal Components Analysis (PCA) is perhaps the simplest and most popular of these methods. Here, we examine how the assumptions that we are prepared to entertain, about the latent variable system, mediate the likelihood that PCA-derived components will capture the true sources of variance underlying data. As expected, we find that this likelihood is excellent in the best case, and robust to empirically reasonable levels of measurement noise, but best-case performance is also: (a) not robust to violations of the method’s more prominent assumptions, of linearity and orthogonality; and also (b) requires that other subtler assumptions be made, such as that the latent variables should have varying importance, and that weights relating latent variables to observed data have zero mean. Neither variance explained, nor replication in independent samples, could reliably predict which (if any) PCA-derived components will capture true sources of variance in data. We conclude by describing a procedure to fit these inferences more directly to empirical data, and use it to find that components derived via PCA from two different empirical neuropsychological datasets, are less likely to have meaningful referents in the brain than we hoped.  \nKeywords: stroke, PCA, cognition, latent variables  \n1. Introduction  \nIn many scientific disciplines, the features of interest cannot be observed directly, so must instead be inferred from observed behaviour. In the study of the brain, for example, those‘features of interest’ might be the function of dissociable cognitive sub-systems, and the‘observed behaviour’might be accuracies and / or reaction times recorded in behavioural tasks that are thought to employ these subsystems. In this and many other fields, researchers commonly use latent variable analyses to systematise the inverse inference from observed data to features of interest 1-9. Principal Components Analysis (PCA) is one of the simplest and most popular of these methods. Here, we examine the likelihood that this inverse inference will succeed: i.e., that PCA-derived components will capture the true sources of variance underlying observed data. As expected, we find that this likelihood – what we call the construct validity of PCA-derived components – is excellent in the best case. But this excellence is more sensitive to subtler assumptions, about the latent variable system, than we thought – including assumptions that might be counter-intuitive in empirical practice. We also find that natural proxies for construct validity, including the variance that PCA-derived components explain, and the likelihood that they will replicate in independent samples, are unreliable. Finally, we propose a procedure to make more targeted inferences about empirical PCA-derived components – and use it to show that thei","cbCaih9oIQ5zT72f","https://ap.wps.com/l/cbCaih9oIQ5zT72f","pdf",666363,1,25,"English","en",105,"# Introduction\n## Principal Components Analysis overview\n## Construct validity and assumptions\n## Limitations of variance explained and replication\n## A more direct empirical inference procedure","[{\"question\":\"What is the main research focus regarding PCA in this paper?\",\"answer\":\"The paper examines how assumptions about the latent variable system affect the likelihood that PCA-derived components capture true sources of variance in data.\"},{\"question\":\"Which PCA assumptions most strongly affect construct validity?\",\"answer\":\"Performance is robust to reasonable measurement noise, but best-case results are not robust to violations of prominent assumptions such as linearity and orthogonality.\"},{\"question\":\"Why are variance explained and replication unreliable indicators here?\",\"answer\":\"Neither variance explained nor replication in independent samples reliably predicts which PCA-derived components will capture true variance sources.\"}]","Estimating the construct validity of Principal Components Analysis | 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is the main research focus regarding PCA in this paper?","Question",{"text":75,"@type":76},"The paper examines how assumptions about the latent variable system affect the likelihood that PCA-derived components capture true sources of variance in data.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which PCA assumptions most strongly affect construct validity?",{"text":80,"@type":76},"Performance is robust to reasonable measurement noise, but best-case results are not robust to violations of prominent assumptions such as linearity and orthogonality.",{"name":82,"@type":73,"acceptedAnswer":83},"Why are variance explained and replication unreliable indicators here?",{"text":84,"@type":76},"Neither variance explained nor replication in independent samples reliably predicts which PCA-derived components will capture true variance 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