Latent variable model: Difference between revisions

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A '''latent variable model''' is a [[statistical model]] that relates a set of [[observable variable]]s (also called ''manifest variables'' or ''indicators'')<ref>{{Cite web |title=Latent Variable Models |url=https://www.statistics.com/glossary/latent-variable-models/ |url-status=live |archive-url=https://web.archive.org/web/20221101060559/https://www.statistics.com/glossary/latent-variable-models/ |archive-date=2022-11-01 |access-date=2022-11-01 |website=Statistics.com: Data Science, Analytics & Statistics Courses |language=en-US}}</ref> to a set of [[latent variable]]s. Latent variable models are applied across a wide range of fields such as biology, computer science, and social science.<ref>{{Cite journal |last=Blei |first=David M. |date=2014-01-03 |title=Build, Compute, Critique, Repeat: Data Analysis with Latent Variable Models |url=https://www.annualreviews.org/doi/10.1146/annurev-statistics-022513-115657 |journal=Annual Review of Statistics and Its Application |language=en |volume=1 |issue=1 |pages=203–232 |doi=10.1146/annurev-statistics-022513-115657 |bibcode=2014AnRSA...1..203B |issn=2326-8298}}</ref>. Common use cases for latent variable models include applications in [[psychometrics]] (e.g., summarizing responses to a set of survey questions with a [[factor analysis]] model positing a smaller number of psychological attributes, such as the trait [[Extraversion and introversion|extraversion]], that are presumed to cause the survey question responses),<ref>{{Cite journal |last1=Borsboom |first1=Denny |last2=Mellenbergh |first2=Gideon J. |last3=van Heerden |first3=Jaap |date=April 2003 |title=The theoretical status of latent variables. |url=https://doi.apa.org/doi/10.1037/0033-295X.110.2.203 |journal=Psychological Review |language=en |volume=110 |issue=2 |pages=203–219 |doi=10.1037/0033-295X.110.2.203 |pmid=12747522 |issn=1939-1471}}</ref> and [[natural language processing]] (e.g., a [[topic model]] summarizing a corpus of texts with a number of "topics").<ref>{{Cite journal |last1=Blei |first1=David M. |last2=Ng |first2=Andrew Y. |last3=Jordan |first3=Michael I. |date=2003 |title=Latent dirichlet allocation |url=https://dl.acm.org/doi/10.5555/944919.944937 |journal=J. Mach. Learn. Res. |volume=3 |issue=3/1/2003 |pages=993–1022 |issn=1532-4435}}</ref>.

It is assumed that the responses on the indicators or manifest variables are the result of an individual's position on the latent variable(s), and that the manifest variables have nothing in common after controlling for the latent variable ([[local independence]]).