Latent variable model: Difference between revisions

Revision as of 11:44, 3 July 2018

Latest revision as of 13:48, 13 August 2025

(28 intermediate revisions by 16 users not shown)

Line 1:

{{Short description|Statistical model relating manifest and latent variables}}

{{Multiple issues|

{{refimprove|date=April 2011}}

Line 4 ⟶ 5:

}}

A '''latent variable model''' is a [[statistical model]] that relates 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|url-access=subscription }}</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>

A '''latent variable model''' is a [[statistical model]] that relates a set of [[observable variable]]s (so-called ''manifest variables'') to a set of [[latent variable]]s.

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]]).

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]]).

Different types of the latent variable models can be grouped according to whether the manifest and latent variables are categorical or continuous:<ref>{{cite book |first1=David J. |last1=Bartholomew, |authorlink=D. J. Bartholomew |first2=Fiona |last2=Steel, |authorlink2=Fiona Steele |first3=Irini |last3=Moustaki, |first4=Jane I. |last4=Galbraith (|year=2002), ''|title=The Analysis and Interpretation of Multivariate Data for Social Scientists'', |___location= |publisher=Chapman & Hall/CRC, p. |page=145 |isbn=1-58488-295-6 }}</ref>

Different types of the latent variable model can be grouped according to whether the manifest and

latent variables are categorical or continuous:<ref>David J. Bartholomew, Fiona Steel, Irini Moustaki, Jane I. Galbraith (2002), ''The Analysis and Interpretation of Multivariate Data for Social Scientists'', Chapman & Hall/CRC, p. 145</ref>

{| class="wikitable" style="margin: 1em auto;"

<center>

{| class="wikitable"

!

! colspan="2" | Manifest variables

Line 30 ⟶ 27:

| [[Latent class analysis]]

|}

</center>

The [[Rasch model]] represents the simplest form of item response theory. [[Mixture models]] are central to latent profile analysis.

In [[factor analysis]] and [[latent trait analysis]]{{refn|group=note|name=LTAandIRT| The terms "latent trait analysis" and "item response theory" are often used interchangeably.<ref>{{Cite web |first=John |last=Uebersax |title=Latent Trait Analysis and Item Response Theory (IRT) Models |url=http://www.john-uebersax.com/stat/lta.htm |url-status=live |archive-url=https://web.archive.org/web/20221101072029/http://www.john-uebersax.com/stat/lta.htm |archive-date=2022-11-01 |access-date=2022-11-01 |website=John-Uebersax.com |language=en-US}}</ref>}} the latent variables are treated as continuous [[normal distribution|normally distributed]] variables, and in latent profile analysis and latent class analysis as from a [[multinomial distribution]].<ref>{{cite book |last=Everitt |first=BS |title=An Introduction to Latent Variables Models |year=1984 |publisher=Chapman & Hall |isbn=9780-412-25310-94010895480 }}</ref> The manifest variables in factor analysis and latent profile analysis are continuous and in most cases, their conditional distribution given the latent variables is assumed to be normal. In latent trait analysis and latent class analysis, the manifest variables are discrete. These variables could be dichotomous, ordinal or nominal variables. Their conditional distributions are assumed to be binomial or multinomial.

Because the distribution of a continuous latent variable can be approximated by a discrete distribution, the distinction between continuous and discrete variables turns out not to be fundamental at all. Therefore, there may be a psychometrical latent variable, but not a [[psychology|psychological]] psychometric variable.

Recently DSDs and Latent Variable modeling were applied for the first time to the optimization of an extraction procedure in order to analyze target compounds present in wine samples. Latent Variable modeling can be a relevant tool for the optimization of analytical techniques, contributing to the implementation of rigorous, systematic and more efficient optimization protocols <ref>{{Cite web|url=https://www.sciencedirect.com/science/article/pii/S0169743918300947|title=Definitive Screening Designs and latent variable modelling for the optimization of solid phase microextraction (SPME): Case study - Quantification of volatile fatty acids in wines|website=www.sciencedirect.com|access-date=2018-07-03}}</ref>

==See also==

* [[Confirmatory factor analysis]]

* [[Hidden Markov model]]

* [[Partial least squares path modeling]]

* [[Partial least squares regression]]

* [[Structural equation modeling]]

== Notes ==

{{reflist|group=note}}

== References ==

{{Reflist}}

== Further reading ==

<references />

* {{cite book |first1=Anders |last1=Skrondal |first2=Sophia |last2=Rabe-Hesketh |authorlink2=Sophia Rabe-Hesketh |title=Generalized Latent Variable Modeling |___location= |publisher=Chapman & Hall |year=2004 |isbn=1-58488-000-7 }}

{{DEFAULTSORT:Latent Variable Model}}