Latent and observable variables: Difference between revisions

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{{For|similar uses|Hidden variable (disambiguation){{!}}Hidden variable}}

In [[statistics]], '''latent variables''' (from [[Latin]]: [[present participle]] of ''{{wikt-lang|la|lateo'',}} “lie hidden”<ref>{{cite web gloss|lie url=https://en.wiktionary.org/wiki/latent hidden}}{{cn| title=Latent | date=30 August 2024April 2025}}</ref>) are [[Variable (mathematics)|variables]] that can only be [[Statistical inference|inferred]] indirectly through a [[mathematical model]] from other '''observable variables''' that can be directly [[observation|observed]] or [[measurement|measured]].<ref>Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. {{isbn|0-19-920613-9}}</ref> Such ''[[latent variable model]]s'' are used in many disciplines, including [[engineering]], [[medicine]], [[ecology]], [[physics]], [[machine learning]]/[[artificial intelligence]], [[natural language processing]], [[bioinformatics]], [[chemometrics]], [[demography]], [[economics]], [[management]], [[political science]], [[psychology]] and the [[social sciences]].

Latent variables may correspond to aspects of physical reality. These could in principle be measured, but may not be for practical reasons. Among the earliest expressions of this idea is [[Francis Bacon]]'s [[polemic]] the ''[[Novum Organum]]'', itself a challenge to the more traditional logic expressed in [[Aristotle]]'s [[Organon]]:

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* extraversion<ref name="status">{{cite journal |last1=Borsboom |first1=D. |author2-link=Gideon J. Mellenbergh |last2=Mellenbergh, G.J. |last3=van Heerden |first3=J. |title=The Theoretical Status of Latent Variables |journal=Psychological Review |volume=110 |issue=2 |pages=203–219 |year=2003 |doi=10.1037/0033-295X.110.2.203 |pmid=12747522 |url=http://rhowell.ba.ttu.edu/BorsboomLatentvars2003.pdf |citeseerx=10.1.1.134.9704 |access-date=2008-04-08 |archive-url=https://web.archive.org/web/20130120044039/http://rhowell.ba.ttu.edu/BorsboomLatentvars2003.pdf |archive-date=2013-01-20 |url-status=dead }}</ref>

* spatial ability<ref name="status"/>

* wisdom: “Two of the more predominant means of assessing wisdom include wisdom-related performance and latent variable measures.”<ref name="wisdom">{{cite journal |last1=Greene |first1=Jeffrey A. |last2=Brown |first2=Scott C. |title=The Wisdom Development Scale: Further Validity Investigations |journal=International Journal of Aging and Human Development |volume=68 |issue=4 |pages=289–320 (at p. 291) |year=2009 |pmid=19711618 |doi=10.2190/AG.68.4.b }}</ref>

* [[Spearman's g]], or the [[g factor (psychometrics)|general intelligence factor]] in [[psychometrics]]<ref>{{Cite journal | last1 = Spearman | first1 = C. | author-link = Charles Spearman| title = "General Intelligence," Objectively Determined and Measured | journal = The American Journal of Psychology | volume = 15 | issue = 2 | pages = 201–292 | doi = 10.2307/1412107 | year = 1904 | jstor = 1412107 }}</ref>

===Economics===

{{unreferenced section|date=January 2024}}

Examples of latent variables from the field of [[economics]] include [[quality of life]], business confidence, morale, happiness and conservatism: these are all variables which cannot be measured directly. ButHowever, by linking these latent variables to other, observable variables, the values of the latent variables can be inferred from measurements of the observable variables. Quality of life is a latent variable which cannot be measured directly, so observable variables are used to infer quality of life. Observable variables to measure quality of life include wealth, employment, environment, physical and mental health, education, recreation and leisure time, and social belonging.

===Medicine===