A general latent trait model for response processes

The purpose of the current paper is to propose a general multicomponent latent trait model (GLTM) for response processes. The proposed model combines the linear logistic latent trait (LLTM) with the multicomponent latent trait model (MLTM). As with both LLTM and MLTM, the general multicomponent latent trait model can be used to (1) test hypotheses about the theoretical variables that underlie response difficulty and (2) estimate parameters that describe test items by basic substantive properties. However, GLTM contains both component outcomes and complexity factors in a single model and may be applied to data that neither LLTM nor MLTM can handle. Joint maximum likelihood estimators are presented for the parameters of GLTM and an application to cognitive test items is described.This research was partially supported by the National Institute of Education grant number NIE-6-7-0156 to Susan Embretson (Whitely), principal investigator. However the optinions expressed herein do not necessarily reflect the position or policy of the National Institute of Education, and no official endorsement by the National Institute of Education should be inferred.     

A comparison of latent trait and latent class analyses of Likert-type data

This paper brings together and compares two developments in the analysis of Likert attitude scales. The first is the generalization of latent class models to ordered response categories. The second is the introduction of latent trait models with multiplicative parameter structures for the analysis of rating scales. Key similarities and differences between these two methods are described and illustrated by applying a latent trait model and a latent class model to the analysis of a set of life satisfaction data. The way in which the latent trait model defines a unit of measurement, takes into account the order of the response categories, and scales the latent classes, is discussed. While the latent class model provides better fit to these data, this is achieved at the cost of a logically inconsistent assignment of individuals to latent classes.The author wishes to thank Clifford C. Clogg, Otis Dudley Duncan and Benjamin D. Wright for their helpful comments on an earlier version of this paper.     

Beyond IQ: A latent state-trait analysis of general intelligence, dynamic decision making, and implicit learning

The present study investigated cognitive performance measures beyond IQ. In particular, we investigated the psychometric properties of dynamic decision making variables and implicit learning variables and their relation with general intelligence and professional success. N = 173 employees from different companies and occupational groups completed two standard intelligence tests, two dynamic decision making tasks, and two implicit learning tasks at two measurement occasions each. We used structural equation models to test latent state-trait measurement models and the relation between constructs. The results suggest that dynamic decision making and implicit learning are substantially related with general intelligence. Furthermore, general intelligence is the best predictor for income, social status, and educational attainment. Dynamic decision making can predict supervisor ratings even beyond general intelligence.     

The relationship between anxiety sensitivity and latent symptoms of emotional problems: A structural equation modeling approach

A large body of research suggests that common and specific psychopathology dimensions underlie the symptoms that occur within mood and anxiety disorders. As of yet, it is unclear precisely how the facets of Anxiety Sensitivity (AS), or fear of the symptoms of fear and anxiety, relate to these latent factors. Using data from 606 adolescents participating in the baseline phase of a longitudinal study on risk factors for emotional disorders, we modeled the facets of AS as measured by the Anxiety Sensitivity Index-Expanded Form (ASI-X) and related these facets to a hierarchical model of latent symptoms of psychological distress. Results suggest that one facet of AS is associated with a broad General Distress factor underlying symptoms of most emotional disorders while others relate to intermediate-level and conceptually-meaningful narrow factors representing aspects of psychological distress specific to particular emotional disorders.     

Symptom-positive and symptom-negative items in the state-trait anxiety inventory: A comparison and replication

Substantially higher mean scores on symptom-negatively versus symptom-positively worded items have consistently been reported in the literature for the balanced Stait-Trait Anxiety Inventory. In this study we aimed at replicating and comparing these findings for the Dutch adaptation of the inventory. Results indicated significantly higher mean subscale scores for symptom-negative as opposed to symptompositive items of both the Trait and State version, across sexes and age groups as well as across different levels of distress in students, policemen and psychiatric out-patients. Positive-negative mean difference scores were consistently larger for the State than for the Trait version. State and Trait mean difference scores were found to be mainly confined to symptom-positive subscales. Scale intercorrelations were lowest between symptom-positive and symptom-negative subscales both within and across measures. Factor analyzing the combined versions identified separate symptom-negative and symptom-positive factors, tentatively labeled “absence of positive affect” and “presence of negative affect”. Several explanations of the findings among which item-intensity specificity, the response style of social desirability and the model of positive and negative affectivity are discussed.     

A latent trait model for dichotomous choice data

The PARELLA model is a probabilistic parallelogram model that can be used for the measurement of latent attitudes or latent preferences. The data analyzed are the dichotomous responses of persons to stimuli, with a one (zero) indicating agreement (disagreement) with the content of the stimulus. The model provides a unidimensional representation of persons and items. The response probabilities are a function of the distance between person and stimulus: the smaller the distance, the larger the probability that a person will agree with the content of the stimulus. An estimation procedure based on expectation maximization and marginal maximum likelihood is developed and the quality of the resulting parameter estimates evaluated.I gratefully acknowledge Ivo Molenaar and Wijbrandt van Schuur for their advice and encouragement during the course of the investigation, Derk-Jan Kiewiet who constructed the program for the ML estimator for the person parameter and Anne Boomsma, Wendy Post, Tom Snijders, and David Thissen for their comments on smaller aspects of the investigation.     

A latent class approach to fitting the weighted Euclidean model,clascal

A weighted Euclidean distance model for analyzing three-way proximity data is proposed that incorporates a latent class approach. In this latent class weighted Euclidean model, the contribution to the distance function between two stimuli is per dimension weighted identically by all subjects in the same latent class. This model removes the rotational invariance of the classical multidimensional scaling model retaining psychologically meaningful dimensions, and drastically reduces the number of parameters in the traditional INDSCAL model. The probability density function for the data of a subject is posited to be a finite mixture of spherical multivariate normal densities. The maximum likelihood function is optimized by means of an EM algorithm; a modified Fisher scoring method is used to update the parameters in the M-step. A model selection strategy is proposed and illustrated on both real and artificial data.The second author is supported as Bevoegdverklaard Navorser of the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek.     

Sufficient statistics and latent trait models

For questionnaires with two answer categories, it has been proven in complete generality that if a minimal sufficient statistic exists for the individual parameter and if it is the same statistic for all values of the item parameters, then the raw score (or the number of correct answers) is the minimal sufficient statistic. It follows that the model must by of the Rasch type with logistic item characteristic curves and equal item-discriminating powers.This paper extends these results to multiple choice questionnaires. It is shown that the minimal sufficient statistic for the individual parameter is a function of the so-called score vector. It is also shown that the so-called equidistant scoring is the only scoring of a questionnaire that allows for a real valued sufficient statistic that is independent of the item parameters, if a certain ordering property for the sufficient statistic holds.     

A rasch model for partial credit scoring

A unidimensional latent trait model for responses scored in two or more ordered categories is developed. This “Partial Credit” model is a member of the family of latent trait models which share the property of parameter separability and so permit “specifically objective” comparisons of persons and items. The model can be viewed as an extension of Andrich's Rating Scale model to situations in which ordered response alternatives are free to vary in number and structure from item to item. The difference between the parameters in this model and the “category boundaries” in Samejima's Graded Response model is demonstrated. An unconditional maximum likelihood procedure for estimating the model parameters is developed. Preparation of this paper was supported by grants from the Spencer Foundation and the National Institute for Justice. I would like to thank Professor Benjamin D. Wright of the University of Chicago for his very kind help with the various drafts of this paper.     

A generalized rasch model for manifest predictors

A logistic regression model is suggested for estimating the relation between a set of manifest predictors and a latent trait assumed to be measured by a set ofk dichotomous items. Usually the estimated subject parameters of latent trait models are biased, especially for short tests. Therefore, the relation between a latent trait and a set of predictors should not be estimated with a regression model in which the estimated subject parameters are used as a dependent variable. Direct estimation of the relation between the latent trait and one or more independent variables is suggested instead. Estimation methods and test statistics for the Rasch model are discussed and the model is illustrated with simulated and empirical data.     

On the existence and uniqueness of maximum-likelihood estimates in the Rasch model

Necessary and sufficient conditions for the existence and uniqueness of a solution of the so-called unconditional (UML) and the conditional (CML) maximum-likelihood estimation equations in the dichotomous Rasch model are given. The basic critical condition is essentially the same for UML and CML estimation. For complete data matricesA, it is formulated both as a structural property ofA and in terms of the sufficient marginal sums. In case of incomplete data, the condition is equivalent to complete connectedness of a certain directed graph. It is shown how to apply the results in practical uses of the Rasch model.Paper read at the European Meeting of the Psychometric Society, Groningen, June 19–21, 1980.Part of the research reported herein was done while the author was staying at the Pulmologisches Zentrum der Stadt Wien; he is indebted to Professor Dr. F. Muhar and Dr. R. Mutschlechner for providing excellent working conditions.     

Veracity is in the eye of the beholder: A lens model examination of consistency and deception

Research has attempted to explain perceived cues to deception based upon self-report of what participants believe are ‘good’ cues to deception, or self-report of what cues participants say they base their veracity judgements on. However, it is not clear to what extent participants can accurately self-report what influences their decision-making. Using a within-subjects design, 285 participants completed a questionnaire regarding their beliefs about deception before rating a selection of truthful and deceptive statements on a variety of cues. Expert coders also rated the statements for the same cues. Laypeople and expert coders do not conceptualise between-subject consistency in the same way. A lens model showed that whilst perceptions of cues, such as consistency and amount of detail, influence veracity judgements, these perceptions (and overall veracity judgements) are mostly inaccurate. Fundamentally, there seems to be inconsistencies between how deception research examines consistency and how it is understood and used by laypeople.     

A latent class unfolding model for analyzing single stimulus preference ratings

A multidimensional unfolding model is developed that assumes that the subjects can be clustered into a small number of homogeneous groups or classes. The subjects that belong to the same group are represented by a single ideal point. Since it is not known in advance to which group of class a subject belongs, a mixture distribution model is formulated that can be considered as a latent class model for continuous single stimulus preference ratings. A GEM algorithm is described for estimating the parameters in the model. The M-step of the algorithm is based on a majorization procedure for updating the estimates of the spatial model parameters. A strategy for selecting the appropriate number of classes and the appropriate number of dimensions is proposed and fully illustrated on some artificial data. The latent class unfolding model is applied to political science data concerning party preferences from members of the Dutch Parliament. Finally, some possible extensions of the model are discussed.The first author is supported as Bevoegdverklaard Navorser of the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek. Part of this paper was presented at the Distancia meeting held in Rennes, France, June 1992.     

Considering sex differences in anxiety and its disorders across the life span: A construct-validation approach

One neglected avenue to understanding anxiety disorders is through studying patterns of sex differences, which may suggest the need for modification in definitions of anxiety and its disorders, their operationalization and measurement, and the theories associated with these constructs. This article begins with a comprehensive review of sex diffrences across the life span that supports the widely held view that most anxiety disorders are more common among females than males. Subsequently, we offer an analysis of the possible sources of sex differences from a construct-validity perspective, with emphasis on understanding whether sex differences have their basis in methodological problems, measurement or definitional problems, or problems in extant theories of anxiety themselves.     

A rasch model for continuous ratings

A unidimensional latent trait model for continuous ratings is developed. This model is an extension of Andrich's rating formulation which assumes that the response process at latent thresholds is governed by the dichotomous Rasch model. Item characteristic functions and information functions are used to illustrate that the model takes ceiling and floor effects into account. Both the dichotomous Rasch model and a linear model with normally distributed error can be derived as limiting cases. The separability of the structural and incidental parameters is demonstrated and a procedure for estimating the parameters is outlined.     

A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the metropolis-hastings algorithm

Nonlinear latent variable models are specified that include quadratic forms and interactions of latent regressor variables as special cases. To estimate the parameters, the models are put in a Bayesian framework with conjugate priors for the parameters. The posterior distributions of the parameters and the latent variables are estimated using Markov chain Monte Carlo methods such as the Gibbs sampler and the Metropolis-Hastings algorithm. The proposed estimation methods are illustrated by two simulation studies and by the estimation of a non-linear model for the dependence of performance on task complexity and goal specificity using empirical data.     

Anxiety sensitivity and intolerance of uncertainty: Evidence of incremental specificity in relation to health anxiety

Anxiety sensitivity (AS) reflects the fear of arousal-related sensations and intolerance of uncertainty (IU) represents the dispositional fear of the unknown. Within cognitive–behavioral models, AS and IU are individual difference variables considered central to the phenomenology of health anxiety. However, prior studies have cast doubt on whether both variables incrementally contribute to our understanding of health anxiety. Addressing limitations of these prior studies, the present study examined the incremental specificity of AS and IU as these two variables relate to health anxiety in a large medically healthy sample of community adults (N = 474). Both AS and IU incrementally contributed to the concurrent prediction of health anxiety beyond both negative affect and one another. However, within these analyses, the physical dimension of AS and the inhibitory dimension of IU were the only AS and IU dimensions to evidence incremental specificity in relation to health anxiety.     

A latent class distance association model for cross‐classified data with a categorical response variable

In this paper we propose a latent class distance association model for clustering in the predictor space of large contingency tables with a categorical response variable. The rows of such a table are characterized as profiles of a set of explanatory variables, while the columns represent a single outcome variable. In many cases such tables are sparse, with many zero entries, which makes traditional models problematic. By clustering the row profiles into a few specific classes and representing these together with the categories of the response variable in a low‐dimensional Euclidean space using a distance association model, a parsimonious prediction model can be obtained. A generalized EM algorithm is proposed to estimate the model parameters and the adjusted Bayesian information criterion statistic is employed to test the number of mixture components and the dimensionality of the representation. An empirical example highlighting the advantages of the new approach and comparing it with traditional approaches is presented.