▪ Abstract The paper discusses the use of latent variables in psychology and social science research. Local independence, expected value true scores, and nondeterministic functions of observed variables are three types of definitions for latent variables. These definitions are reviewed and an alternative “sample realizations” definition is presented. Another section briefly describes identification, latent variable indeterminancy, and other properties common to models with latent variables. The paper then reviews the role of latent variables in multiple regression, probit and logistic regression, factor analysis, latent curve models, item response theory, latent class analysis, and structural equation models. Though these application areas are diverse, the paper highlights the similarities as well as the differences in the manner in which the latent variables are defined and used. It concludes with an evaluation of the different definitions of latent variables and their properties.

In the last 2 decades attention to causal (and formative) indicators has grown. Accompanying this growth has been the belief that one can classify indicators into 2 categories: effect (reflective) indicators and causal (formative) indicators. We argue that the dichotomous view is too simple. Instead, there are effect indicators and 3 types of variables on which a latent variable depends: causal indicators, composite (formative) indicators, and covariates (the "Three Cs"). Causal indicators have conceptual unity, and their effects on latent variables are structural. Covariates are not concept measures, but are variables to control to avoid bias in estimating the relations between measures and latent variables. Composite (formative) indicators form exact linear combinations of variables that need not share a concept. Their coefficients are weights rather than structural effects, and composites are a matter of convenience. The failure to distinguish the Three Cs has led to confusion and questions, such as, Are causal and formative indicators different names for the same indicator type? Should an equation with causal or formative indicators have an error term? Are the coefficients of causal indicators less stable than effect indicators? Distinguishing between causal and composite indicators and covariates goes a long way toward eliminating this confusion. We emphasize the key role that subject matter expertise plays in making these distinctions. We provide new guidelines for working with these variable types, including identification of models, scaling latent variables, parameter estimation, and validity assessment. A running empirical example on self-perceived health illustrates our major points.

Causal-formative indicators directly affect their corresponding latent variable. They run counter to the predominant view that indicators depend on latent variables and are thus often controversial. If present, such indicators have serious implications for factor analysis, reliability theory, item response theory, structural equation models, and most measurement approaches that are based on reflective or effect indicators. Psychological Methods has published a number of influential articles on causal and formative indicators as well as launching the first major backlash against them. This article examines 7 common criticisms of these indicators distilled from the literature: (a) A construct measured with "formative" indicators does not exist independently of its indicators; (b) Such indicators are causes rather than measures; (c) They imply multiple dimensions to a construct and this is a liability; (d) They are assumed to be error-free, which is unrealistic; (e) They are inherently subject to interpretational confounding; (f) They fail proportionality constraints; and (g) Their coefficients should be set in advance and not estimated. We summarize each of these criticisms and point out the flaws in the logic and evidence marshaled in their support. The most common problems are not distinguishing between what we call causal-formative and composite-formative indicators, tautological fallacies, and highlighting issues that are common to all indicators, but presenting them as special problems of causal-formative indicators. We conclude that measurement theory needs (a) to incorporate these types of indicators, and (b) to better understand their similarities to and differences from traditional indicators. (PsycINFO Database Record

The Maximum-likelihood estimator dominates the estimation of general structural equation models. Noniterative, equation-by-equation estimators for factor analysis have received some attention, but little has been done on such estimators for latent variable equations. I propose an alternative 2SLS estimator of the parameters in LISREL type models and contrast it with the existing ones. The new 2SLS estimator allows observed and latent variables to originate from nonnormal distributions, is consistent, has a known asymptotic covariance matrix, and is estimable with standard statistical software. Diagnostics for evaluating instrumental variables are described. An empirical example illustrates the estimator.

Fixed- and random-effects models for longitudinal data are common in sociology. Their primary advantage is that they control for time-invariant omitte