Latent and observable variables

In statistics, latent variables (as opposed to observable variables), are variables that are not directly observed but are rather inferred (through a mathematical model) from other variables that are observed and directly measured. They are also sometimes known as hidden variables, model parameters, hypothetical variables or hypothetical constructs. The use of latent variables is common in social sciences, robotics, and to an extent economics, but the exact definition of a latent variable varies in these fields. 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. However, given an economic model linking these latent variables to other, observable variables (such as GDP), the values of the latent variables can be inferred from measurements of the observable variables.

One advantage of using latent variables is that it reduces the dimensionality of data. A large number of observable variables can be aggregated in a model to represent an underlying concept, making it easier for humans to understand the data. In this sense, they serve the same function as theories in general do in science. At the same time, latent variables link observable ("sub-symbolic") data in the real world, to symbolic data in the modelled world.

Common methods for inferring latent variables

• Factor analysis
• Principal component analysis
• Latent semantic analysis and Probabilistic latent semantic analysis
• EM algorithm

Bayesian algorithms and methods

Bayesian statistics is often used for inferring latent variables.

• Latent Dirichlet Allocation
• The Chinese Restaurant Process is often used to provide a prior distribution over assignments of objects to latent categories.
• The Indian Buffet Process is often used to provide a prior distribution over assignments of latent binary features to objects.

Examples of latent variables

Psychology

• The "Big Five personality traits" have been inferred using factor analysis.
• extraversion ^[1]
• spatial ability ^[1]
• intelligence

See also

• Latent variable model
• Hidden Markov model
• Item response theory
• Rasch model

References

1. Borsboom, Mellenbergh, van Heerden (2003) The Theoretical Status of Latent Variables Psychological Review Vol 110, No 2 http://rhowell.ba.ttu.edu/BorsboomLatentvars2003.pdf