A general approach to causal mediation analysis.

Traditionally in the social sciences, causal mediation analysis has been formulated, understood, and implemented within the framework of linear structural equation models. We argue and demonstrate that this is problematic for 3 reasons: the lack of a general definition of causal mediation effects independent of a particular statistical model, the inability to specify the key identification assumption, and the difficulty of extending the framework to nonlinear models. In this article, we propose an alternative approach that overcomes these limitations. Our approach is general because it offers the definition, identification, estimation, and sensitivity analysis of causal mediation effects without reference to any specific statistical model. Further, our approach explicitly links these 4 elements closely together within a single framework. As a result, the proposed framework can accommodate linear and nonlinear relationships, parametric and nonparametric models, continuous and discrete mediators, and various types of outcome variables. The general definition and identification result also allow us to develop sensitivity analysis in the context of commonly used models, which enables applied researchers to formally assess the robustness of their empirical conclusions to violations of the key assumption. We illustrate our approach by applying it to the Job Search Intervention Study. We also offer easy-to-use software that implements all our proposed methods. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Assessing Psychological Change in Adulthood: An Overview of Methodological Issues.

This article reviews the current status of methods available for the analysis of psychological change in adulthood and aging. Enormous progress has been made in designing statistical models that can capture key aspects of intraindividual change, as reflected in techniques such as latent growth curve models and multilevel (random-effects) models. However, the rapid evolution of statistical innovations may have obscured the critical importance of addressing rival explanations for statistical outcomes, such as cohort differences or practice effects that could influence estimates of age-related change. Choice of modeling technique and implementation of a specific modeling approach should be grounded in and reflect both the theoretical nature of the developmental phenomenon and the features of the sampling design that selected persons, variables, and contexts for empirical observation. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Testing model nesting and equivalence.

When using existing technology, it can be hard or impossible to determine whether two structural equation models that are being considered may be nested. There is also no routine technology for evaluating whether two very different structural models may be equivalent. A simple nesting and equivalence testing (NET) procedure is proposed that uses random sample and model-reproduced moment matrices to evaluate both model nesting and equivalence. The analysis is “local” rather than “global” in nature, but its use with simulation or bootstrapping can imply global conclusions. Two standard applications of NET are to verify whether or not two proposed models are equivalent and whether a baseline model used in an incremental fit index is appropriately nested. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An overview of Markov chain methods for the study of stage-sequential developmental processes.

This article presents an overview of quantitative methodologies for the study of stage-sequential development based on extensions of Markov chain modeling. Four methods are presented that exemplify the flexibility of this approach: the manifest Markov model, the latent Markov model, latent transition analysis, and the mixture latent Markov model. A special case of the mixture latent Markov model, the so-called mover-stayer model, is used in this study. Unconditional and conditional models are estimated for the manifest Markov model and the latent Markov model, where the conditional models include a measure of poverty status. Issues of model specification, estimation, and testing using the Mplus software environment are briefly discussed, and the Mplus input syntax is provided. The author applies these 4 methods to a single example of stage-sequential development in reading competency in the early school years, using data from the Early Childhood Longitudinal Study--Kindergarten Cohort. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Estimating the nonlinear and interactive effects of latent variables.

Describes a procedure that enables researchers to estimate nonlinear and interactive effects of latent variables in structural equation models. Given that the latent variables are normally distributed, the parameters of such models can be estimated. To do this, products of the measured variables are used as indicators of latent product variables. Estimation must be done using a procedure that allows nonlinear constraints on parameters. The procedure is demonstrated in 3 examples. The 1st 2 examples use artificial data with known parameter values. These parameters are successfully recovered by the procedure. The final complex example uses national election survey data. (14 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The Integration of Continuous and Discrete Latent Variable Models: Potential Problems and Promising Opportunities.

Structural equation mixture modeling (SEMM) integrates continuous and discrete latent variable models. Drawing on prior research on the relationships between continuous and discrete latent variable models, the authors identify 3 conditions that may lead to the estimation of spurious latent classes in SEMM: misspecification of the structural model, nonnormal continuous measures, and nonlinear relationships among observed and/or latent variables. When the objective of a SEMM analysis is the identification of latent classes, these conditions should be considered as alternative hypotheses and results should be interpreted cautiously. However, armed with greater knowledge about the estimation of SEMMs in practice, researchers can exploit the flexibility of the model to gain a fuller understanding of the phenomenon under study. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A nonlinear mixed model framework for item response theory.

Mixed models take the dependency between observations based on the same cluster into account by introducing 1 or more random effects. Common item response theory (IRT) models introduce latent person variables to model the dependence between responses of the same participant. Assuming a distribution for the latent variables, these IRT models are formally equivalent with nonlinear mixed models. It is shown how a variety of IRT models can be formulated as particular instances of nonlinear mixed models. The unifying framework offers the advantage that relations between different IRT models become explicit and that it is rather straightforward to see how existing IRT models can be adapted and extended. The approach is illustrated with a self-report study on anger. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Inference in regression models of heavily skewed alcohol use data: A comparison of ordinary least squares, generalized linear models, and bootstrap resampling.

Analysis of alcohol use data and other low base rate risk behaviors using ordinary least squares regression models can be problematic. This article presents 2 alternative statistical approaches, generalized linear models and bootstrapping, that may be more appropriate for such data. First, the basic theory behind the approaches is presented. Then, using a data set of alcohol use behaviors and consequences, results based on these approaches are contrasted with the results from ordinary least squares regression. The less traditional approaches consistently demonstrated better fit with model assumptions, as demonstrated by graphical analysis of residuals, and identified more significant variables potentially resulting in theoretically different interpretations of the models of alcohol use. In conclusion, these models show significant promise for furthering the understanding of alcohol-related behaviors. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Mixture distribution latent state-trait analysis: Basic ideas and applications.

Extensions of latent state-trait models for continuous observed variables to mixture latent state-trait models with and without covariates of change are presented that can separate individuals differing in their occasion-specific variability. An empirical application to the repeated measurement of mood states (N = 501) revealed that a model with 2 latent classes fits the data well. The larger class (76%) consists of individuals whose mood is highly variable, whose general well-being is comparatively lower, and whose mood variability is influenced by daily hassles and uplifts. The smaller class (24%) represents individuals who are rather stable and happier and whose mood is influenced only by daily uplifts but not by daily hassles. A simulation study on the model without covariates with 5 sets of sample sizes and 5 sets of number of occasions revealed that the appropriateness of the parameter estimates of this model depends on number of observations (the higher the better) and number of occasions (the higher the better). Another simulation study estimated Type I and II errors of the Lo-Mendell-Rubin test. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

When constraints interact: A caution about reference variables, identification constraints and scale dependencies in structural equation modeling.

In traditional approaches to structural equations modeling, variances of latent endogenous variables cannot be specified or constrained directly and, consequently, are not identified, unless certain precautions are taken. The usual method for achieving identification has been to fix one factor loading for each endogenous latent variable at unity. An alternative approach is to fix variances using newer constrained estimation algorithms. This article examines the philosophy behind such constraints and shows how their appropriate use is neither as straightforward nor as noncontroversial as portrayed in textbooks and computer manuals. The constraints on latent variable variances can interact with other model constraints to interfere with the testing of certain kinds of hypotheses and can yield incorrect standardized solutions with some popular software. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The theoretical status of latent variables.

This article examines the theoretical status of latent variables as used in modern test theory models. First, it is argued that a consistent interpretation of such models requires a realist ontology for latent variables. Second, the relation between latent variables and their indicators is discussed. It is maintained that this relation can be interpreted as a causal one but that in measurement models for interindividual differences the relation does not apply to the level of the individual person. To substantiate intraindividual causal conclusions, one must explicitly represent individual level processes in the measurement model. Several research strategies that may be useful in this respect are discussed, and a typology of constructs is proposed on the basis of this analysis. The need to link individual processes to latent variable models for interindividual differences is emphasized. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Comparing the relative fit of categorical and dimensional latent variable models using consistency tests.

A number of recent studies have used Meehl’s (1995) taxometric method to determine empirically whether one should model assessment-related constructs as categories or dimensions. The taxometric method includes multiple data-analytic procedures designed to check the consistency of results. The goal is to differentiate between strong evidence of categorical structure, strong evidence of dimensional structure, and ambiguous evidence that suggests withholding judgment. Many taxometric consistency tests have been proposed, but their use has not been operationalized and studied rigorously. What tests should be performed, how should results be combined, and what thresholds should be applied? We present an approach to consistency testing that builds on prior work demonstrating that parallel analyses of categorical and dimensional comparison data provide an accurate index of the relative fit of competing structural models. Using a large simulation study spanning a wide range of data conditions, we examine many critical elements of this approach. The results provide empirical support for what marks the first rigorous operationalization of consistency testing. We discuss and empirically illustrate guidelines for implementing this approach and suggest avenues for future research to extend the practice of consistency testing to other techniques for modeling latent variables in the realm of psychological assessment. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Mediation in dyadic data at the level of the dyads: A structural equation modeling approach.

An extended version of the Common Fate Model (CFM) is presented to estimate and test mediation in dyadic data. The model can be used for distinguishable dyad members (e.g., heterosexual couples) or indistinguishable dyad members (e.g., homosexual couples) if (a) the variables measure characteristics of the dyadic relationship or shared external influences that affect both partners; if (b) the causal associations between the variables should be analyzed at the dyadic level; and if (c) the measured variables are reliable indicators of the latent variables. To assess mediation using Structural Equation Modeling, a general three-step procedure is suggested. The first is a selection of a good fitting model, the second a test of the direct effects, and the third a test of the mediating effect by means of bootstrapping. The application of the model along with the procedure for assessing mediation is illustrated using data from 184 couples on marital problems, communication, and marital quality. Differences with the Actor-Partner Interdependence Model and the analysis of longitudinal mediation by using the CFM are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Testing Mediational Models With Longitudinal Data: Questions and Tips in the Use of Structural Equation Modeling.

R. M. Baron and D. A. Kenny (1986; see record 1987-13085-001) provided clarion conceptual and methodological guidelines for testing mediational models with cross-sectional data. Graduating from cross-sectional to longitudinal designs enables researchers to make more rigorous inferences about the causal relations implied by such models. In this transition, misconceptions and erroneous assumptions are the norm. First, we describe some of the questions that arise (and misconceptions that sometimes emerge) in longitudinal tests of mediational models. We also provide a collection of tips for structural equation modeling (SEM) of mediational processes. Finally, we suggest a series of 5 steps when using SEM to test mediational processes in longitudinal designs: testing the measurement model, testing for added components, testing for omitted paths, testing the stationarity assumption, and estimating the mediational effects. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints.

The authors show how the use of inequality constraints on parameters in structural equation models may affect the distribution of the likelihood ratio test. Inequality constraints are implicitly used in the testing of commonly applied structural equation models, such as the common factor model, the autoregressive model, and the latent growth curve model, although this is not commonly acknowledged. Such constraints are the result of the null hypothesis in which the parameter value or values are placed on the boundary of the parameter space. For instance, this occurs in testing whether the variance of a growth parameter is significantly different from 0. It is shown that in these cases, the asymptotic distribution of the chi-square difference cannot be treated as that of a central chi-square-distributed random variable with degrees of freedom equal to the number of constraints. The correct distribution for testing 1 or a few parameters at a time is inferred for the 3 structural equation models mentioned above. Subsequently, the authors describe and illustrate the steps that one should take to obtain this distribution. An important message is that using the correct distribution may lead to appreciably greater statistical power. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On measures of explained variance in nonrecursive structural equation models.

Whereas measures of explained variance in a regression and an equation of a recursive structural equation model can be simply summarized by a standard R2 measure, this is not possible in nonrecursive models in which there are reciprocal interdependencies among variables. This article provides a general approach to defining variance explained in latent dependent variables of nonrecursive linear structural equation models. A new method of its estimation, easily implemented in EQS or LISREL and available in EQS 6, is described and illustrated. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Multivariate Polynomial Time-Series Models and Importance Ratios to Qualify Fecal Coliform Sources

Sensitivity analysis using importance ratios was applied to multivariate polynomial regression (MPR) models to make inferences about the nature and magnitude of fecal coliform (FC) sources in a combined sewer overflow-impacted stretch of the Passaic River at Paterson, New Jersey. The predictor variables in this study were temperature, discharge, precipitation, and upstream concentrations. The MPR models are applicable only for the current conditions with respect to pollutant sources. New models should be developed in case of any change in pollutant sources, by location or magnitude. This is a limitation that MPR models have in common with any empirical modeling approach, including multilinear regression or artificial neural networks. The performance of the MPR models using R2 was significantly better than simple linear models using the same variables. The importance ratio, a dimensionless measure of model sensitivity, was used for comparison of the effects of different variables. Because model sensitivities, and therefore importance ratios, are not constant in nonlinear models, this work examines their distributions and relates them to system behavior, for example by showing under what conditions dilution does or does not affect FC concentrations in the stream. The analysis showed that MPR models and importance ratios can be used to provide significant information to better understand pollutant sources at a site and the relative importance of various predictor variables in explaining the variability in the FC concentrations.     

Longitudinal tests of competing factor structures for the Rosenberg Self-Esteem Scale: Traits, ephemeral artifacts, and stable response styles.

Self-esteem, typically measured by the Rosenberg Self-Esteem Scale (RSE), is one of the most widely studied constructs in psychology. Nevertheless, there is broad agreement that a simple unidimensional factor model, consistent with the original design and typical application in applied research, does not provide an adequate explanation of RSE responses. However, there is no clear agreement about what alternative model is most appropriate—or even a clear rationale for how to test competing interpretations. Three alternative interpretations exist: (a) 2 substantively important trait factors (positive and negative self-esteem), (b) 1 trait factor and ephemeral method artifacts associated with positively or negatively worded items, or (c) 1 trait factor and stable response-style method factors associated with item wording. We have posited 8 alternative models and structural equation model tests based on longitudinal data (4 waves of data across 8 years with a large, representative sample of adolescents). Longitudinal models provide no support for the unidimensional model, undermine support for the 2-factor model, and clearly refute claims that wording effects are ephemeral, but they provide good support for models positing 1 substantive (self-esteem) factor and response-style method factors that are stable over time. This longitudinal methodological approach has not only resolved these long-standing issues in self-esteem research but also has broad applicability to most psychological assessments based on self-reports with a mix of positively and negatively worded items. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Generalized full-information item bifactor analysis.

Full-information item bifactor analysis is an important statistical method in psychological and educational measurement. Current methods are limited to single-group analysis and inflexible in the types of item response models supported. We propose a flexible multiple-group item bifactor analysis framework that supports a variety of multidimensional item response theory models for an arbitrary mixing of dichotomous, ordinal, and nominal items. The extended item bifactor model also enables the estimation of latent variable means and variances when data from more than 1 group are present. Generalized user-defined parameter restrictions are permitted within or across groups. We derive an efficient full-information maximum marginal likelihood estimator. Our estimation method achieves substantial computational savings by extending Gibbons and Hedeker's (1992) bifactor dimension reduction method so that the optimization of the marginal log-likelihood requires only 2-dimensional integration regardless of the dimensionality of the latent variables. We use simulation studies to demonstrate the flexibility and accuracy of the proposed methods. We apply the model to study cross-country differences, including differential item functioning, using data from a large international education survey on mathematics literacy. (PsycINFO Database Record (c) 2011 APA, all rights reserved)