In the past decade, moderated mediation analysis has been extensively and increasingly employed in social and behavioral sciences. With its widespread use, it is particularly important to ensure the moderated mediation analysis will not bring spurious results. Spurious effects have been studied in both mediation and moderation analysis, but this…

Recently there has been a renewed interest in formative measurement and its role in properly specified models. Formative measurement models are difficult to identify, and hence to estimate and test. Existing solutions to the identification problem are shown to not adequately represent the formative constructs of interest. We propose a new two-step…

A distinction is proposed between measures and predictors of latent variables. The discussion addresses the consequences of the distinction for the true-score model, the linear factor model, Structural Equation Models, longitudinal and multilevel models, and item-response models. A distribution-free treatment of calibration and…

Mediation analysis is a statistical approach used to examine how the effect of an independent variable on an outcome is transmitted through an intervening variable (mediator). In this article, we provide a gentle introduction to single-level and multilevel mediation analyses. Using single-level data, we demonstrate an application of structural…

This article shows that the mean and covariance structure of the predetermined autoregressive latent trajectory (ALT) model are very flexible. As a result, the shape of the modeled growth curve can be quite different from what one might expect at first glance. This is illustrated with several numerical examples that show that, for example, a…

The presence of suppression (and multicollinearity) in multiple regression analysis complicates interpretation of predictor-criterion relationships. The mathematical conditions that produce suppression in regression analysis have received considerable attention in the methodological literature but until now nothing in the way of an analytic…

Researchers in career and technical education often ignore more effective ways of reporting and treating missing data and instead implement traditional, but ineffective, missing data methods (Gemici, Rojewski, & Lee, 2012). The recent methodological, and even the non-methodological, literature has increasingly emphasized the importance of…

Components of the home environment are associated with children's academic functioning. The accumulation of risks in the home are expected to prove more detrimental to achievement than any one risk alone, but the processes accounting for this relation are unclear. Using an index of cumulative home risk (CHR) inclusive of protective factors, as…

Despite the common belief that information and communication technology (ICT) has the potential to support certain fundamental changes in learning, few have examined ICT implementation conceptually within a wider context of educational change. Methodologically, we are by and large limited to building simple models that accommodate only a single…

This article shows how nonlinear latent curve models may be fitted for simultaneous analysis of multiple variables measured longitudinally using Mx statistical software. Longitudinal studies often involve observation of several variables across time with interest in the associations between change characteristics of different variables measured…

Second-generation early intervention research typically involves the specification of multivariate relations between interventions, outcomes, and other variables. Moderation and mediation involve variables or sets of variables that influence relations between interventions and outcomes. Following the framework of Baron and Kenny's (1986) seminal…

Describes how a hierarchical regression analysis may be conducted in structural equation modeling. The main procedure is to perform a Cholesky or triangular decomposition of the intercorrelations among the latest predictors. Provides an example of a hierarchical regression analysis with latent variables. (SLD)

Participants were 360 (52.2% male) ethnically diverse and academically at-risk first-grade children attending one of three school districts in southeast and central Texas. Using latent variable structural equation modeling, we tested a theoretical model positing that the quality of the teacher-student relationship in first grade predicts…

Nonlinear relationships and latent variable assumptions can lead to serious specification errors in structural models. A quadratic relationship, described by a linear structural model with a latent variable, is shown to have less predictive validity than a simple manifest variable regression model. Advocates the use of simpler preliminary…

The article uses confirmatory factor analysis (CFA) as a template to explain didactically multilevel structural equation models (ML-SEM) and to demonstrate the equivalence of general mixed-effects models and ML-SEM. An intuitively appealing graphical representation of complex ML-SEMs is introduced that succinctly describes the underlying model and…