# Latent variable model

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One-dimensional congeneric measurement model. T is the latent variable, X are the manifest variables, e are the (latent) error variables, λ are the factor loadings (i.e. the influence of the latent variable on the manifest variable)

A latent variable model describes the relationship between observable (or manifest) variables and the latent variables behind them. The factor analysis and structural equation modeling are the best known procedures to the latent variable models.

An example of a latent variable is intelligence . It cannot be measured directly, but one or more latent variables (intelligence) behind the test results can be extracted from a variety of test results (the observable variables).

## Latent variable

In the human and social sciences, a latent variable (also: construct) is a variable to be determined that is not accessible to direct measurement or observation and can only be made measurable through so-called operationalization . The measurable variables (called indicators or manifest variables) are clearly defined and measurable. It is assumed that the latent variable has a causal influence on the manifestation of the manifest variable.

For example, the answers to the questions Are you satisfied? and do you feel good? about manifest variables; the answers ( yes / no ) can be measured directly. However, mood , which is responsible for the cause of the responses, cannot be measured directly and is therefore the latent variable.

In contrast to manifest variables, latent variables are free of measurement errors, as can be seen in the figure. The expression of the manifest variables is causally influenced by two latent variables: the construct (T) and the respective specific error (e). Because of this property, latent variables are preferred to empirically verify the true (i.e., measurement error-adjusted) relationship between constructs (e.g., whether the personality traits conscientiousness and neuroticism are identical or different).

## Overview of latent variable models

In models with latent variables, a distinction is made between a measurement model and a structural model. The measurement model includes the relationships between the manifest variables and the latent variables, while the structural model is limited to the relationships between the latent variables (see structural equation model ).

The methods for analyzing the measurement model differ in terms of the scale level of the latent and manifest variables:

Manifest variables
Latent Variables Metric Categorically
Metric Factor analysis Probabilistic test theory
Categorically Latent profile analysis Latent class analysis

## Individual evidence

1. David J. Bartholomew, Fiona Steel, Irini Moustaki, Jane. I. Galbraith: The Analysis and Interpretation of Multivariate Data for Social Scientists . Chapman & Hall / CRC, 2002, ISBN 978-1-58488-295-4 , pp. 145 .