"Psychometric approaches for developing commensurate measures across independent studies: Traditional and new models": Clarification to Bauer and Hussong (2009).

Reports a clarification to "Psychometric approaches for developing commensurate measures across independent studies: Traditional and new models" by Daniel J. Bauer and Andrea M. Hussong (Psychological Methods, 2009[Jun], Vol 14[2], 101-125). In this article, the authors wrote, "To our knowledge, the multisample framework is the only available option within these [latent variable] programs that allows for the moderation of all types of parameters, and this approach requires a single categorical moderator variable to define the samples.” Bengt Muthén has clarified for the authors that some programs, including Mplus and Mx, can allow for continuous moderation through the implementation of nonlinear constraints involving observed variables, further enlarging the class of MNLFA models that can be fit with these programs. (The following abstract of the original article appeared in record 2009-08072-001.) When conducting an integrative analysis of data obtained from multiple independent studies, a fundamental problem is to establish commensurate measures for the constructs of interest. Fortunately, procedures for evaluating and establishing measurement equivalence across samples are well developed for the linear factor model and commonly used item response theory models. A newly proposed moderated nonlinear factor analysis model generalizes these models and procedures, allowing for items of different scale types (continuous or discrete) and differential item functioning across levels of categorical and/or continuous variables. The potential of this new model to resolve the problem of measurement in integrative data analysis is shown via an empirical example examining changes in alcohol involvement from ages 10 to 22 years across 2 longitudinal studies. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Item factor analysis: Current approaches and future directions.

The rationale underlying factor analysis applies to continuous and categorical variables alike; however, the models and estimation methods for continuous (i.e., interval or ratio scale) data are not appropriate for item-level data that are categorical in nature. The authors provide a targeted review and synthesis of the item factor analysis (IFA) estimation literature for ordered-categorical data (e.g., Likert-type response scales) with specific attention paid to the problems of estimating models with many items and many factors. Popular IFA models and estimation methods found in the structural equation modeling and item response theory literatures are presented. Following this presentation, recent developments in the estimation of IFA parameters (e.g., Markov chain Monte Carlo) are discussed. The authors conclude with considerations for future research on IFA, simulated examples, and advice for applied researchers. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Methods for integrating moderation and mediation: A general analytical framework using moderated path analysis.

Studies that combine moderation and mediation are prevalent in basic and applied psychology research. Typically, these studies are framed in terms of moderated mediation or mediated moderation, both of which involve similar analytical approaches. Unfortunately, these approaches have important shortcomings that conceal the nature of the moderated and the mediated effects under investigation. This article presents a general analytical framework for combining moderation and mediation that integrates moderated regression analysis and path analysis. This framework clarifies how moderator variables influence the paths that constitute the direct, indirect, and total effects of mediated models. The authors empirically illustrate this framework and give step-by-step instructions for estimation and interpretation. They summarize the advantages of their framework over current approaches, explain how it subsumes moderated mediation and mediated moderation, and describe how it can accommodate additional moderator and mediator variables, curvilinear relationships, and structural equation models with latent variables. (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)     

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)     

Nonlinear principal components analysis: Introduction and application.

The authors provide a didactic treatment of nonlinear (categorical) principal components analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated principal components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal variables and that it can handle and discover nonlinear relationships between variables. Also, nonlinear PCA can deal with variables at their appropriate measurement level; for example, it can treat Likert-type scales ordinally instead of numerically. Every observed value of a variable can be referred to as a category. While performing PCA, nonlinear PCA converts every category to a numeric value, in accordance with the variable's analysis level, using optimal quantification. The authors discuss how optimal quantification is carried out, what analysis levels are, which decisions have to be made when applying nonlinear PCA, and how the results can be interpreted. The strengths and limitations of the method are discussed. An example applying nonlinear PCA to empirical data using the program CATPCA (J. J. Meulman, W. J. Heiser, & SPSS, 2004) is provided. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Testing the degree of cross-sectional and longitudinal dependence between two discrete dynamic processes.

Developmental research often involves studying change across 2 or more processes or constructs simultaneously. A natural question in this work is whether change in these 2 processes is related or independent. Associative latent transition analysis (ALTA) was designed to test hypotheses about the degree to which change in 2 discrete latent variables is related. The ALTA model is a type of latent class model, which is a categorical latent variable model based on categorical indicators. In the ALTA approach, level and change on 1 variable is predicted by level and change in another. Two types of hypotheses are discussed: (a) broad hypotheses of dependence between the 2 discrete latent variables and (b) targeted hypotheses comparing specific patterns of change between levels of the discrete variables. Both types of hypotheses are tested via nested model comparisons. Analyses of relations between psychological state and substance use illustrate the model. Recent psychological state and recent substance use were found to be associated cross-sectionally and longitudinally, implying that change in recent substance use was related to change in recent psychological state. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables.

Uncorrectable skew and heteroscedasticity are among the "lemons" of psychological data, yet many important variables naturally exhibit these properties. For scales with a lower and upper bound, a suitable candidate for models is the beta distribution, which is very flexible and models skew quite well. The authors present maximum-likelihood regression models assuming that the dependent variable is conditionally beta distributed rather than Gaussian. The approach models both means (location) and variances (dispersion) with their own distinct sets of predictors (continuous and/or categorical), thereby modeling heteroscedasticity. The location submodel link function is the logit and thereby analogous to logistic regression, whereas the dispersion submodel is log linear. Real examples show that these models handle the independent observations case readily. The article discusses comparisons between beta regression and alternative techniques, model selection and interpretation, practical estimation, and software. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Using comparison data to differentiate categorical and dimensional data by examining factor score distributions: Resolving the mode problem.

Factor-analytic research is common in the study of constructs and measures in psychological assessment. Latent factors can represent traits as continuous underlying dimensions or as discrete categories. When examining the distributions of estimated scores on latent factors, one would expect unimodal distributions for dimensional data and bimodal or multimodal distributions for categorical data. Unfortunately, identifying modes is subjective, and the operationalization of counting local maxima has not performed very well. Rather than locating and counting modes, the authors propose performing parallel analyses of categorical and dimensional comparison data and calculating an index of the relative fit of these competing structural models. In an extensive Monte Carlo study, the authors replicated prior results for mode counting and found that trimming distributions' tails helped. However, parallel analyses of comparison data achieved much greater accuracy, improved base rate estimation, and afforded consistency checks with other taxometric procedures. Two additional studies apply this approach to empirical data either known to be categorical or presumed to be dimensional. Each study supports this new method for factor-analytic research on the latent structure of constructs and measures in psychological assessment. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Confirmatory factor analysis and item response theory: Two approaches for exploring measurement invariance.

Investigated the utility of confirmatory factor analysis (CFA) and item response theory (IRT) models for testing the comparability of psychological measurements. Both procedures were used to investigate whether mood ratings collected in Minnesota and China were comparable. Several issues were addressed. The 1st issue was that of establishing a common measurement scale across groups, which involves full or partial measurement invariance of trait indicators. It is shown that using CFA or IRT models, test items that function differentially as trait indicators across groups need not interfere with comparing examinees on the same trait dimension. Second, the issue of model fit was addressed. It is proposed that person-fit statistics be used to judge the practical fit of IRT models. Finally, topics for future research are suggested. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Regression models: calculating the confidence interval of effects in the presence of interactions

The main goal of regression analysis (multiple, logistic, Cox) is to assess the relationship of one or more exposure variables to a response variable, in the presence of confounding and interaction. The confidence interval for the regression coefficient of the exposure variable, obtained through the use of a computer statistical package, quantify these relationships for models without interaction. Relationships between variables that present interactions are represented by two or more terms, and the corresponding confidence intervals can be calculated 'manually' from the covariance matrix. This paper suggests an easy procedure for obtaining confidence intervals from any statistical package. This procedure is applicable for modifying variables which are continuous as well as categorical.     

Measurement equivalence: A comparison of methods based on confirmatory factor analysis and item response theory.

Current interest in the assessment of measurement equivalence emphasizes 2 major methods of analysis. The authors offer a comparison of a linear method (confirmatory factor analysis) and a nonlinear method (differential item and test functioning using item response theory) with an emphasis on their methodological similarities and differences. The 2 approaches test for the equality of true scores (or expected raw scores) across 2 populations when the latent (or factor) score is held constant. Both approaches can provide information about when measurrment nonequivalence exists and the extent to which it is a problem. An empirical example is used to illustrate the 2 approaches. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The structure of late-life depressive symptoms across a 20-year span: A taxometric investigation.

Past studies of the underlying structure of depressive symptoms have yielded mixed results, with some studies supporting a continuous conceptualization and others supporting a categorical one. However, no study has examined this research question with an exclusively older adult sample, despite the potential uniqueness of late-life depressive symptoms. In the present study, the underlying structure of late-life depressive symptoms was examined among a sample of 1,289 individuals across 3 waves of data collection spanning 20 years. The authors employed a taxometric methodology using indicators of depression derived from the Research Diagnostic Criteria (R. L. Spitzer, J. Endicott, & E. Robins, 1978). Maximum eigenvalue analyses and inchworm consistency tests generally supported a categorical conceptualization and identified a group that was primarily characterized by thoughts about death and suicide. However, compared to a categorical depression variable, depressive symptoms treated continuously were generally better predictors of relevant criterion variables. These findings suggest that thoughts of death and suicide may characterize a specific type of late-life depression, yet a continuous conceptualization still typically maximizes the predictive utility of late-life depressive symptoms. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Data analysis using item response theory.

The purpose of this article is to illustrate the power of item response theory (IRT) for the item analysis of measurement instruments in psychology. Through illustration, we show that IRT latent variable models fit data from a wide variety of sources and that interpretation of the features of these fitted models leads to interesting insights into the psychology underlying the data. The illustrations involve personality and attitude measurement as well as the evaluation of cognitive proficiency. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

New approaches to studying problem behaviors: A comparison of methods for modeling longitudinal, categorical adolescent drinking data.

Analyzing problem-behavior trajectories can be difficult. The data are generally categorical and often quite skewed, violating distributional assumptions of standard normal-theory statistical models. In this article, the authors present several currently available modeling options, all of which make appropriate distributional assumptions for the observed categorical data. Three are based on the generalized linear model: a hierarchical generalized linear model, a growth mixture model, and a latent class growth analysis. They also describe a longitudinal latent class analysis, which requires fewer assumptions than the first 3. Finally, they illustrate all of the models using actual longitudinal adolescent alcohol-use data. They guide the reader through the model-selection process, comparing the results in terms of convergence properties, fit and residuals, parsimony, and interpretability. Advances in computing and statistical software have made the tools for these types of analyses readily accessible to most researchers. Using appropriate models for categorical data will lead to more accurate and reliable results, and their application in real data settings could contribute to substantive advancements in the field of development and the science of prevention. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Latent structure of the alexithymia construct: A taxometric investigation.

Despite a wealth of research on the validity of alexithymia and its association with a number of common medical and psychiatric disorders, the fundamental question of whether alexithymia is best conceptualized as a dimensional or categorical construct remains unresolved. In the current investigation, taxometric analysis is used to examine the nature of the latent structure of alexithymia. Several nonredundant taxometric procedures were performed with item sets from the 20-item Toronto Alexithymia Scale (R. M. Bagby, J. D. A. Parker, & G. J. Taylor, 1994) as indicators. These procedures were applied separately in large community (n = 1,933) and undergraduate (n = 1,948) samples and in a smaller sample of psychiatric outpatients (n = 302). The results across various taxometric procedures and the different samples provide strong support that alexithymia is a dimensional construct. Some theoretical implications of these findings for research on the alexithymia construct are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An Empirical Evaluation of Alternative Methods of Estimation for Confirmatory Factor Analysis With Ordinal Data.

Confirmatory factor analysis (CFA) is widely used for examining hypothesized relations among ordinal variables (e.g., Likert-type items). A theoretically appropriate method fits the CFA model to polychoric correlations using either weighted least squares (WLS) or robust WLS. Importantly, this approach assumes that a continuous, normal latent process determines each observed variable. The extent to which violations of this assumption undermine CFA estimation is not well-known. In this article, the authors empirically study this issue using a computer simulation study. The results suggest that estimation of polychoric correlations is robust to modest violations of underlying normality. Further, WLS performed adequately only at the largest sample size but led to substantial estimation difficulties with smaller samples. Finally, robust WLS performed well across all conditions. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

La prévention de la dépression: l'état actuel des connaissances.

Suggests that even if many authors underscore the importance of working to prevent depression, some practical and theoretical confusions still plague this field of research: What is depression? How to define prevention? What should be the theoretical basis of a program to prevent depression? Is it possible to prevent depression? It is with the objective to shed some light on these topics that the present article was written. First, the authors expose some evidence in favor of a continuous definition of depression. Second, the authors propose a definition of prevention that is compatible with a continuous definition of depression. Third, the authors formulate the main parts of an integrative biopsychosocial model of depression. Finally, the authors review the principal selective and universal depression prevention programs. On the basis of this review, it is concluded that it is possible to prevent depression selectively and universally. However, it seems that, to be effective, these programs should not take a traditional therapeutic orientation but should follow the principles of organizational change (universal prevention programs) and try to improve the fit between an individual and his/her environment (selective prevention program). (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On the nature of nicotine addiction: A taxometric analysis.

Taxometric procedures were used to determine whether nicotine addiction is best conceptualized as a dimensional or a categorical (i.e., taxonic) phenomenon. Using data from the 2003 National Survey on Drug Use and Health (NSDUH; N = 12,467), results from MAMBAC, MAXEIG, and LMODE taxometric analyses provided strong evidence that nicotine addiction has a taxonic latent structure. Members of the addiction taxon, which constituted approximately 48% of those who reported smoking in the past 30 days, consumed a higher number of cigarettes per day, had stronger craving, higher levels of nicotine tolerance, more inflexible smoking patterns, and shorter latencies to smoking their first cigarette on waking compared with nontaxon members. These findings of a distinct addiction taxonic structure were replicated using a 2002 NSDUH sample (N = 12,224). Finally, the predictive validity of the taxon variable was compared with a continuous indicator sum. The taxon accounted for most of the predictive variance in the indicator sum, but the latter generally showed significant predictive power even after controlling for the former. Thus, these smoking variables may have both a categorical and a dimensional structure. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Examining the structural validity of the Strengths and Difficulties Questionnaire (SDQ) in a U.S. sample of custodial grandmothers.

The authors examined the structural validity of the parent informant version of the Strengths and Difficulties Questionnaire (SDQ) with a sample of 733 custodial grandparents. Three models of the SDQ's factor structure were evaluated with confirmatory factor analysis based on the item covariance matrix. Although indices of fit were good across all 3 models, a model that included a newly hypothesized positive construal method factor in addition to the 4 symptom factors (Emotional Symptoms, Conduct Problems, Hyperactivity-Inattention, Peer Problems) and the single Prosocial Behavior factor originally intended for the SDQ provided the best representation of this instrument's latent structure. Structural validity was further evidenced by measurement invariance across grandparent race and grandchild gender and age, a conceptually meaningful pattern of cross-scale correlations, and the acceptable internal reliability estimates found for each subscale. Measurement and clinical implications of the results are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)