This book provides a comprehensive and unified approach to factor analysis and latent variable modeling and theory, providing a unified and coherent treatment from a statistical perspective. A general framework is presented to enable the derivation of the commonly used models. Updated numerical examples are provided as well as the software to carry them out. Written by leading experts in the field, Latent Variable Models and Factor Analysis: * Includes new topics such as, covariate effects and non-linear terms, multiple population analysis and univariate and bivariate margins. * Provides a new section on structural equation models (SEM) and Markov Chain Monte Carlo methods, along with illustrative examples. * Looks at estimation methods, goodness-of-fit, non-linear models, covariates, longitudinal data and multilevel modeling along with updated examples throughout. * Unifies many different streams of latent variable modeling and probability modeling. An introductory section is provided, which looks at the nature and interpretation of a latent variable, motivating discussions of closely related methods which make little or no explicit use of latent variables. Principal components are discussed in more depth, exploring its relationship to factor analysis in both historical and contemporary and theoretically and empirically. Furthermore, the book explores The Bonds' Model for abilities, a model which has a correlation structure which is identical to that of the factor model and hence cannot be distinguished from it and does not involve latent variables. No prior acquaintance with latent variable modeling is needed although a broad understanding of statistical theory is necessary.