Latent and observable variables

Source: Wikipedia, the free encyclopedia.
For similar uses, see Hidden variable (disambiguation).

In

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 Sir Francis Bacon's classic polemic the Novum Organum, itself a challenge to the more traditional logic expressed in Aristotle's Organon.

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[2]

In this situation, the term hidden variables is commonly used (reflecting the fact that the variables are meaningful, but not observable). Other latent variables correspond to abstract concepts, like categories, behavioral or mental states, or data structures. The terms hypothetical variables or hypothetical constructs may be used in these situations.

The use of latent variables can serve to

sub-symbolic
" data in the real world to symbolic data in the modeled world.

Examples

Estimation of a mean height curve (black) for boys from the Berkeley Growth Study with and without warping. The warping is based on latent variables that maps age to a synchronized biological age using a nonlinear mixed-effects model.[3]

Psychology

Latent variables, as created by factor analytic methods, generally represent "shared" variance, or the degree to which variables "move" together. Variables that have no correlation cannot result in a latent construct based on the common factor model.[4]

Economics

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

Latent-variable methodology is used in many branches of

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 disease progression modeling and modeling of growth
(see box).

Inferring latent variables

There exists a range of different model classes and methodology that make use of latent variables and allow inference in the presence of latent variables. Models include:

Analysis and inference methods include:

Bayesian algorithms and methods

Bayesian statistics is often used for inferring latent variables.

See also

References

  1. ISBN 0-19-920613-9
  2. ^ Bacon, Francis. "APHORISMS—BOOK II: ON THE INTERPRETATION OF NATURE, OR THE REIGN OF MAN". Novum Organum.
  3. doi:10.1016/j.patrec.2013.10.018
    .
  4. ISBN 978-0-321-05677-1.[page needed
    ]
  5. ^
    PMID 12747522. Archived from the original
    (PDF) on 2013-01-20. Retrieved 2008-04-08.
  6. PMID 19711618
    .
  7. JSTOR 1412107
    .
  8. ^ Kelly, Bryan T. and Pruitt, Seth and Su, Yinan, Instrumented Principal Component Analysis (December 17, 2020). Available at SSRN: https://ssrn.com/abstract=2983919 or http://dx.doi.org/10.2139/ssrn.2983919

Further reading

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