A new SAS procedure for latent transition analysis: Transitions in dating and sexual risk behavior.

The set of statistical methods available to developmentalists is continually being expanded, allowing for questions about change over time to be addressed in new, informative ways. Indeed, new developments in methods to model change over time create the possibility for new research questions to be posed. Latent transition analysis, a longitudinal extension of latent class analysis, is a method that can be used to model development in discrete latent variables, for example, stage processes, over 2 or more times. The current article illustrates this approach using a new SAS procedure, PROC LTA, to model change over time in adolescent and young adult dating and sexual risk behavior. Gender differences are examined, and substance use behaviors are included as predictors of initial status in dating and sexual risk behavior and transitions over time. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Psychometric approaches for developing commensurate measures across independent studies: Traditional and new models.

[Correction Notice: An erratum for this article was reported in Vol 14(4) of Psychological Methods (see record 2009-22665-007). 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.] 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)     

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)     

Analysis of multivariate frequency data by graphical models and generalizations of the multidimensional row-column association model.

Models used to analyze cross-classifications of counts from psychological experiments must represent associations between multiple discrete variables and take into account attributes of stimuli, experimental conditions, or characteristics of subjects. The models must also lend themselves to psychological interpretations about underlying structures mediating the relationship between stimuli and responses. To meet these needs, the author extends the graphical latent variable models for nominal and/or ordinal data proposed by C. J. Anderson and J. K. Vermunt (2000) to situations in which dependencies between observed variables are not fully accounted for by the latent variables. The graphical models provide a unified framework for studying multivariate associations that include log-linear models and log-multiplicative association models as special cases. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The logic of interpreting evidence of developmental ordering: Strong inference and categorical measures.

Developmental ordering is a fundamental prediction of developmental theories and a central issue in developmental research. However, logically sound evidence of developmental ordering is difficult to obtain. This article analyzes the logical basis of testing developmental order hypotheses with categorical measures. Depending on whether saltatory (i.e., discrete) or continuous developmental changes are being assessed, the observed relationship between categorical measures yields very different types of information about developmental ordering. When change is continuous, the relationship between the measures does not confirm any one ordering hypothesis, but rather, disconfirms one or more hypotheses. Whether an underlying variable undergoes saltatory or continuous development has long been recognized as an important theoretical issue, but its impact on the interpretation of developmental ordering has not previously been explicated. (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)     

"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)     

A global odds ratio regression model for bivariate ordered categorical data from ophthalmologic studies

In typical clinical trials or epidemiologic studies of a bilateral eye disease, the primary outcome data consist of pairs of ordered categorical responses that tend to be highly correlated. In such studies, interest often centres in associating the outcome data with a grouping variable such as the treatment indicator or the exposure status and other person- and eye-specific covariates. In this paper, we propose a latent variable regression model to analyse such bivariate ordered categorical data. We use as a joint distribution for bivariate latent random variables the cross ratio distribution proposed by Plackett, which results in modelling the dependency between the fellow eyes with the global odds ratio. We illustrate the proposed model with data from the Wisconsin Epidemiologic Study of Diabetic Retinopathy, a study that seeks to identify risk factors among younger-onset diabetics.     

Parametric statistics and levels of measurement: Factorial designs and multiple regression.

Let Y be a continuous, ordinal measure of a latent variable Θ. In general, for factorial designs, an analysis of variance of the observed variable Y cannot be used to draw inferences about main effects and interactions on the latent variable Θ even when the standard normality and equality of variance assumptions hold. If Y is a continuous, ordinal measure of a latent variable Θ; X?,…, Xn are continuous, ordinal measures of latent variables Φ?,…, Φn; and the observed measures have a multivariate normal distribution, then a multiple regression analysis of the observed criterion measure Y and predictors X?,…, Xn can be used to test hypotheses about multivariate associations among the latent variables. Furthermore, the predicted values Y′ are unbiased estimates of quantities that are monotonically related to predicted values on the latent criterion variable Θ. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Testing hypotheses on specific environmental causal effects on behavior.

There have been strong critiques of the notion that environmental influences can have an important effect on psychological functioning. The substance of these criticisms is considered in order to infer the methodological challenges that have to be met. Concepts of cause and of the testing of causal effects are discussed with a particular focus on the need to consider sample selection and the value (and limitations) of longitudinal data. The designs that may be used to test hypotheses on specific environmental risk mechanisms for psychopathology are discussed in relation to a range of adoption strategies, twin designs, various types of "natural experiments," migration designs, the study of secular change, and intervention designs. In each case, consideration is given to the need for samples that "pull-apart" variables that ordinarily go together, specific hypotheses on possible causal processes, and the specification and testing of key assumptions. It is concluded that environmental risk hypotheses can be (and have been) put to the test but that it is usually necessary to use a combination of research strategies. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Profiling retirees in the retirement transition and adjustment process: Examining the longitudinal change patterns of retirees' psychological well-being.

The author used role theory, continuity theory, and the life course perspective to form hypotheses regarding the different retirement transition and adjustment patterns and how different individual and contextual variables related to those patterns. The longitudinal data of 2 samples (n? = 994; n? = 1,066) from the Health and Retirement Survey were used. Three latent growth curve patterns of retirees' psychological well-being were identified as coexisting in the retiree samples through growth mixture modeling (GMM) analysis. On the basis of the latent class membership derived from GMM, retiree subgroups directly linked to different growth curve patterns were profiled with individual (e.g., bridge job status) and contextual variables (e.g., spouse working status). By recognizing the existence of multiple retiree subgroups corresponding to different psychological well-being change patterns, this study suggests that retirees do not follow a uniform adjustment pattern during the retirement process, which reconciles inconsistent previous findings. A resource perspective is further introduced to provide a more integrated theory for the current findings. The practical implications of this study are also discussed at both individual level and policy level. (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)     

Measurement of psychological disorders using cognitive diagnosis models.

Cognitive diagnosis models are constrained (multiple classification) latent class models that characterize the relationship of questionnaire responses to a set of dichotomous latent variables. Having emanated from educational measurement, several aspects of such models seem well suited to use in psychological assessment and diagnosis. This article presents the development of a new cognitive diagnosis model for use in psychological assessment--the DINO (deterministic input; noisy "or" gate) model--which, as an illustrative example, is applied to evaluate and diagnose pathological gamblers. As part of this example, a demonstration of the estimates obtained by cognitive diagnosis models is provided. Such estimates include the probability an individual meets each of a set of dichotomous Diagnostic and Statistical Manual of Mental Disorders (text revision [DSM-IV-TR]; American Psychiatric Association, 2000) criteria, resulting in an estimate of the probability an individual meets the DSM-IV-TR definition for being a pathological gambler. Furthermore, a demonstration of how the hypothesized underlying factors contributing to pathological gambling can be measured with the DINO model is presented, through use of a covariance structure model for the tetrachoric correlation matrix of the dichotomous latent variables representing DSM-IV-TR criteria. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Influential factors in career orientation and career aspiration of early adolescent girls.

Two models of the career development of early adolescent girls were investigated. For each model, endogenous variables were adolescents' gender role attitudes and the mother–daughter relationship (psychological separation and attachment); exogenous variables were adolescents' grade point averages, agentic characteristics, and a latent variable, maternal characteristics. Career orientation (Model 1) and career aspirations (Model 2) were the final outcome variables. A sample of 276 girls drawn from 7th and 8th graders in the rural area of a southeastern state and their mothers participated. In both models, adolescents' agentic characteristics and maternal variables contributed significantly to adolescents' gender role attitudes. In addition, in Model 2, adolescents' agentic characteristics and the mother–daughter relationship contributed to the girls' career aspirations. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Information-theoretic latent distribution modeling: Distinguishing discrete and continuous latent variable models.

Distinguishing between discrete and continuous latent variable distributions has become increasingly important in numerous domains of behavioral science. Here, the authors explore an information-theoretic approach to latent distribution modeling, in which the ability of latent distribution models to represent statistical information in observed data is emphasized. The authors conclude that loss of statistical information with a decrease in the number of latent values provides an attractive basis for comparing discrete and continuous latent variable models. Theoretical considerations as well as the results of 2 Monte Carlo simulations indicate that information theory provides a sound basis for modeling latent distributions and distinguishing between discrete and continuous latent variable models in particular. (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)     

Assessing Interactive Causal Influence.

The discovery of conjunctive causes--factors that act in concert to produce or prevent an effect--has been explained by purely covariational theories. Such theories assume that concomitant variations in observable events directly license causal inferences, without postulating the existence of unobservable causal relations. This article discusses problems with these theories, proposes a causal-power theory that overcomes the problems, and reports empirical evidence favoring the new theory. Unlike earlier models, the new theory derives (a) the conditions under which covariation implies conjunctive causation and (b) functions relating observable events to unobservable conjunctive causal strength. This psychological theory, which concerns simple cases involving 2 binary candidate causes and a binary effect, raises questions about normative statistics for testing causal hypotheses regarding categorical data resulting from discrete variables. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Reciprocal influences in children's and families' adaptation to early childhood wheezing.

Objective: The objective of the present study was to demonstrate the reciprocal relationships between family adaptation to illness and children's medication use over time among children who presented with wheezing illness in infancy but have varying illness outcomes by age 4. Design: A longitudinal design and latent growth curve models (LGM) were used to predict change in family and caregiver adaptation to illness and children's medication use over three years among 140 infants with wheezing, among families from low socioeconomic, multi-ethnic backgrounds. Main Outcome Measures: One LGM predicted level and change (slope) of family adaptation to illness from children's baseline medication use. The second LGM predicted level and change (slope) of children's medication use from baseline family adjustment to illness. In both models, illness severity, caregivers' psychological resources, and emergency department use were covaried with the independent variable. Results: Two latent growth models were found to adequately fit the data and demonstrate full reciprocal relations between family adaptation to illness and children's medication use while accounting for baseline variables. Baseline measures of caregiver psychological functioning and illness severity were also significant predictors of family adaptation and children's medication use over time. The two models were not statistically different for children with and without active asthma at 4 years of age. Conclusion: Findings support the reciprocal effects model of child and family influences on pediatric illness and underscore the importance of early indicators of individual and family functioning. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Structural-equation models of current drug use: Are appropriate models so simple(x)?

The simplex and common-factor models of drug use were compared using maximum-likelihood estimation of latent variable structural models in two samples: a sample of 226 high school students, using ratio-scale measures of current drug use, and a sample of 310 industrial workers and 811 college students, using ordinal-scale measures of current drug use. Latent variables of alcohol, marihuana, enhancer hard drugs, and dampener hard drugs were specified in a series of structural models. Contrary to previous findings with cumulative drug-use data, the common-factor model provided a more acceptable representation of the observed current-use data than did the simplex model in both samples. In addition, the similarity of results across both of these samples supports recent contentions by Huba and Bentler (1982) that quantitatively measured variables are not necessarily superior to qualitative, ordinal indicators in latent variable models of drug use. (49 ref) (PsycINFO Database Record (c) 2010 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)