Latent Variable Modelling: A Survey

• Published in: Scandinavian journal of statistics Vol. 34; no. 4; pp. 712 - 745
• Main Authors: SKRONDAL, ANDERS, RABE-HESKETH, SOPHIA
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.12.2007; Blackwell Publishing; Blackwell; Danish Society for Theoretical Statistics
• Series: Scandinavian Journal of Statistics
• Subjects: Economic models; Exact sciences and technology; Factor analysis; General topics; GLLAMM; item-response theory; latent class; latent trait; latent variable; Mathematical independent variables; Mathematical models; Mathematics; measurement error; mixed effects model; Modeling; multilevel model; Multilevel models; Observational research; Parametric models; Probability and statistics; Probability theory and stochastic processes; Psychometrics; random effect; School dropouts; Sciences and techniques of general use; Statistical analysis; Statistics; Stochastic analysis; structural equation model; Structural equation models; Scandinavia; GLLAMM; multilevel model; Error estimation; Response model; Covariate; Random effect; Integral; Mathematical model; Sample survey; Measurement error; Latent class model; latent variable; Stochastic equation; structural equation model; Factor model; Latent variable model; Mixed equation; mixed effects model; Statistical method; factor analysis; latent class; Mixed model; Non linear model; Structural model; Application; latent trait; item-response theory
• ISSN: 0303-6898; 1467-9469
• DOI: 10.1111/j.1467-9469.2007.00573.x

Latent variable modelling has gradually become an integral part of mainstream statistics and is currently used for a multitude of applications in different subject areas. Examples of 'traditional' latent variable models include latent class models, item—response models, common factor models, structural equation models, mixed or random effects models and covariate measurement error models. Although latent variables have widely different interpretations in different settings, the models have a very similar mathematical structure. This has been the impetus for the formulation of general modelling frameworks which accommodate a wide range of models. Recent developments include multilevel structural equation models with both continuous and discrete latent variables, multiprocess models and nonlinear latent variable models.