Latent and observable variables: Difference between revisions

Revision as of 18:11, 19 January 2024

Revision as of 18:12, 19 January 2024

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In [[statistics]], '''latent variables''' (from [[Latin]]: [[present participle]] of ''lateo'', “lie hidden”) 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 [[political science]], [[demography]], [[engineering]], [[medicine]], [[ecology]], [[physics]], [[machine learning]]/[[artificial intelligence]], [[bioinformatics]], [[chemometrics]], [[natural language processing]], [[management]], [[psychology]] and the [[social sciences]].

{{quote|But the latent process of which we speak, is far from being obvious to men’s minds, beset as they now are. For we mean not the measures, symptoms, or degrees of any process which can be exhibited in the bodies themselves, but simply a continued process, which, for the most part, escapes the observation of the senses.|''Sir [[Francis Bacon]]'', ''[[Novum Organum]]''<ref>{{cite book|author-last=Bacon|author-first=Francis|title=Novum Organum|chapter=APHORISMS—BOOK II: ON THE INTERPRETATION OF NATURE, OR THE REIGN OF MAN|url=https://www.gutenberg.org/files/45988/45988-h/45988-h.htm}}</ref>

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===Economics===

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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. But 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===

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Latent-variable methodology is used in many branches of [[medicine]]. A class of problems that naturally lend themselves to latent variables approaches are [[longitudinal studies]] where the time scale (e.g. age of participant or time since study baseline) is not synchronized with the trait being studied. For such studies, an unobserved time scale that is synchronized with the trait being studied can be modeled as a transformation of the observed time scale using latent variables. Examples of this include [[Nonlinear_mixed-effects_model#Example: Disease progression modeling|disease progression modeling]] and [[Nonlinear_mixed-effects_model#Example: Growth analysis|modeling of growth]] (see box).

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===Bayesian algorithms and methods===

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[[Bayesian statistics]] is often used for inferring latent variables.