The measurement of consistency and occasion specificity with latent class models: A new model and its application to the measurement of affect.

After a short overview of different latent variable models for analyzing interindividual differences in intraindividual change, a latent class variability model is introduced. The model makes it possible to estimate the consistency of interindividual differences across naturally occurring situations. In addition, the contribution of latent trait variables and occasion-specific latent variables in predicting manifest responses can be analyzed, and the precision of predicting states by traits and occasion-specific effects can be assessed. The model is illustrated by an application to the measurement of positive affects. Finally, the model and its application are discussed with respect to conditional trait concepts in personality psychology and other potential areas of application. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On the meaning of formative measurement and how it differs from reflective measurement: Comment on Howell, Breivik, and Wilcox (2007).

D. Howell, E. Breivik, and J. B. Wilcox (2007; see record 2007-07830-006) have presented an important and interesting analysis of formative measurement and have recommended that researchers abandon such an approach in favor of reflective measurement. The author agrees with their recommendations but disagrees with some of the bases for their conclusions. He suggests that although latent variables refer to mental states or mental events that have objective reality, to gain knowledge of the existence of these states or events requires that emphasis be placed on the nature and interpretation of the relationship between latent and manifest variables. This relationship is not a causal one but rather a kind of correspondence rule that contains theoretical, empirical, operational, and logical meanings as part of its content and structure. Implications of the above views are discussed for formative and reflective measurement. (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)     

Latent curve modeling of internalizing behaviors and interpersonal skills through elementary school.

The trajectories of internalizing and interpersonal behaviors from kindergarten through fifth grade were studied using univariate and bivariate latent curve models. Internalizing behaviors demonstrated a small, yet statistically significant, linear increase over time, while interpersonal behaviors showed a small, yet statistically significant, linear decrease. There were individual differences in trajectories, and predictor variables accounted for some of this variation. In kindergarten, girls had more interpersonal behaviors than did boys. Children from higher SES families or with higher initial levels of externalizing behaviors had more internalizing behaviors and fewer interpersonal skills. One key finding from this study was that interpersonal and internalizing trajectories demonstrated a strong association. Increasing internalizing slopes were associated with decreasing interpersonal slopes. Establishing this empirical relation is necessary for understanding the developmental trajectory of these related behaviors, as well as important individual differences over time. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Issues in intraindividual variability: Individual differences in equilibria and dynamics over multiple time scales.

This article addresses three issues germane to experimental design and statistical analysis of intraindividual variability such as the articles contained within this special section. First, the time scale of the measurement of a process can have profound effects on the outcome of analyses of the resulting time series. Measurement in time poses special problems in the design of experiments: the time scale of the measurements must be appropriate for the time scale of the process. Second, deterministic and stochastic models should be fit at the individual level and only at a second level should individual differences in parameters be modeled. Third, one must consider the possibility that nomothetic relations may be exposed by the invariance of covariance between latent variables rather than within a factor analytic measurement model. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On the power of multivariate latent growth curve models to detect correlated change.

We evaluated the statistical power of single-indicator latent growth curve models (LGCMs) to detect correlated change between two variables (covariance of slopes) as a function of sample size, number of longitudinal measurement occasions, and reliability (measurement error variance). Power approximations following the method of Satorra and Saris (1985) were used to evaluate the power to detect slope covariances. Even with large samples (N=500) and several longitudinal occasions (4 or 5), statistical power to detect covariance of slopes was moderate to low unless growth curve reliability at study onset was above .90. Studies using LGCMs may fail to detect slope correlations because of low power rather than a lack of relationship of change between variables. The present findings allow researchers to make more informed design decisions when planning a longitudinal study and aid in interpreting LGCM results regarding correlated interindividual differences in rates of development. (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)     

Decomposing Person and Occasion-Specific Effects: An Extension of Latent State-Trait (LSI) Theory to Hierarchical LST Models.

An extension of latent state-trait (LST) theory to hierarchical LST models is presented. In hierarchical LST models, the covariances between 2 or more latent traits are explained by a general 3rd-order factor, and the covariances between latent state residuals pertaining to different traits measured on the same measurement occasion are explained by 2nd-order latent occasion-specific factors. Analogous to recent developments in multitrait-multimethod methodology, all factors are interpreted in relation to factors taken as comparison standards. An empirical example from test anxiety research illustrates how estimates of additive variance components due to general trait, specific trait, occasion, state residual, method, and measurement error can be obtained using confirmatory factor analysis. Advantages and limitations of these models are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Does resting electroencephalograph asymmetry reflect a trait? An application of latent state-trait theory.

Recent research on brain asymmetry and emotion treated measures of resting electroencephalograph (EEG) asymmetry as genuine trait variables, but inconsistency in reported findings and modest retest correlations of baseline asymmetry are not consistent with this practice. The present study examined the alternative hypothesis that resting EEG asymmetry represents a superimposition of a trait like activation asymmetry with substantial state-dependent fluctuations. Resting EEG was collected from 59 participants on 4 occasions of measurement, and data were analyzed in terms of latent state-trait theory. For most scalp regions, about 60% of the variance of the asymmetry measure was due to individual differences on a temporally stable latent trait, and 40% of the variance was due to occasion-specific fluctuations, but measurement errors were negligible. Further analyses indicated that these fluctuations might be efficiently reduced by aggregation across several occasions. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The use of causal indicators in covariance structure models: Some practical issues.

In conventional representations of covariance structure models, indicators are defined as linear functions of latent variables, plus error. In an alternative representation, constructs can be defined as linear functions of their indicators, called causal indicators, plus an error term. Such constructs are not latent variables but composite variables, and they have no indicators in the conventional sense. The presence of composite variables in a model can, in some situations, result in problems with identification of model parameters. Also, the use of causal indicators can produce models that imply zero correlation among many measured variables, a problem resolved only by the inclusion of a potentially large number of additional parameters. These phenomena are demonstrated with an example, and general principles underlying them are discussed. Remedies are described so as to allow for the evaluation of models that contain causal indicators. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A Latent Markov Model for the Analysis of Longitudinal Data Collected in Continuous Time: States, Durations, and Transitions.

Markov models provide a general framework for analyzing and interpreting time dependencies in psychological applications. Recent work extended Markov models to the case of latent states because frequently psychological states are not directly observable and subject to measurement error. This article presents a further generalization of latent Markov models to allow for the analysis of rating data that are collected at arbitrary points in time. This extension offers new ways of investigating change processes by focusing explicitly on the durations that are spent in latent states. In an experience sampling application the author shows that such duration analyses can provide valuable insights about chronometric features of emotions. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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)     

Testing Main Effects and Interactions in Latent Curve Analysis.

A key strength of latent curve analysis (LCA) is the ability to model individual variability in rates of change as a function of 1 or more explanatory variables. The measurement of time plays a critical role because the explanatory variables multiplicatively interact with time in the prediction of the repeated measures. However, this interaction is not typically capitalized on in LCA because the measure of time is rather subtly incorporated via the factor loading matrix. The authors' goal is to demonstrate both analytically and empirically that classic techniques for probing interactions in multiple regression can be generalized to LCA. A worked example is presented, and the use of these techniques is recommended whenever estimating conditional LCAs in practice. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Three Cs in measurement models: Causal indicators, composite indicators, and covariates.

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. (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)     

Using the longitudinal Guttman simplex as a basis for measuring growth.

Many difficulties inherent in the measurement of growth stem from the use of traditional measurement methodologies. The longitudinal Guttman simplex (LGS), an alternative approach based on a model of growth, is discussed in this article. The LGS has several advantages over traditional methodology. First, interindividual differences in developmental rates are a part of the model. Second, the LGS procedure can easily handle any number of occasions of measurement. Third, the LGS is suited to nonlinear as well as linear monotonic growth. Fourth, a consistency index associated with the LGS methodology, CL, indicates the extent to which cumulative, unitary development characterizes a particular latent variable. Finally, and perhaps most important, because a model of the growth undergone by the latent variable being measured is incorporated in the LGS model the resulting instruments enjoy a high level of construct validity. The LGS is limited to cumulative, unitary development; additional measurement theories are needed for other kinds of development. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Measurement invariance versus selection invariance: Is fair selection possible?

This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement instrument is used and group differences are present in the location but not in the variance of the latent distribution, sensitivity and positive predictive value will be higher in the group at the higher end of the latent dimension, whereas specificity and negative predictive value will be higher in the group at the lower end of the latent dimension. When latent variances are unequal, the differences in these quantities depend on the size of group differences in variances relative to the size of group differences in means. The effect originates as a special case of Simpson's paradox, which arises because the observed score distribution is collapsed into an accept-reject dichotomy. Simulations show the effect can be substantial in realistic situations. It is suggested that the effect may be partly responsible for overprediction in minority groups as typically found in empirical studies on differential academic performance. A methodological solution to the problem is suggested, and social policy implications are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Causal inference and related statistical methods

Statistical approaches for evaluating causal effects and for discovering causal networks are discussed in this paper.A causal relation between two variables is different from an association or correlation between them.An association measurement between two variables and may be changed dramatically from positive to negative by omitting a third variable,which is called Yule-Simpson paradox.We shall discuss how to evaluate the causal effect of a treatment or exposure on an outcome to avoid the phenomena of Yule-Simpson paradox. Surrogates and intermediate variables are often used to reduce measurement costs or duration when measurement of endpoint variables is expensive,inconvenient,infeasible or unobservable in practice.There have been many criteria for surrogates.However,it is possible that for a surrogate satisfying these criteria,a treatment has a positive effect on the surrogate,which in turn has a positive effect on the outcome,but the treatment has a negative effect on the outcome,which is called the surrogate paradox.We shall discuss criteria for surrogates to avoid the phenomena of the surrogate paradox. Causal networks which describe the causal relationships among a large number of variables have been applied to many research fields.It is important to discover structures of causal networks from observed data.We propose a recursive approach for discovering a causal network in which a structural learning of a large network is decomposed recursively into learning of small networks.Further to discover causal relationships,we present an active learning approach in terms of external interventions on some variables.When we focus on the causes of an interest outcome, instead of discovering a whole network,we propose a local learning approach to discover these causes that affect the outcome.     

Predicting group-level outcome variables from variables measured at the individual level: A latent variable multilevel model.

In multilevel modeling, one often distinguishes between macro-micro and micro-macro situations. In a macro-micro multilevel situation, a dependent variable measured at the lower level is predicted or explained by variables measured at that lower or a higher level. In a micro-macro multilevel situation, a dependent variable defined at the higher group level is predicted or explained on the basis of independent variables measured at the lower individual level. Up until now, multilevel methodology has mainly focused on macro-micro multilevel situations. In this article, a latent variable model is proposed for analyzing data from micro-macro situations. It is shown that regression analyses carried out at the aggregated level result in biased parameter estimates. A method that uses the best linear unbiased predictors of the group means is shown to yield unbiased estimates of the parameters. (PsycINFO Database Record (c) 2010 APA, all rights reserved)