Latent Trait Variables Research Articles

Online Monitoring of Test‐Taking Behavior Based on Item Responses and Response Times

AbstractThe study presents multivariate sequential monitoring procedures for examining test‐taking behaviors online. The procedures monitor examinee's responses and response times and signal aberrancy as soon as significant change is identifieddetected in the test‐taking behavior. The study in particular proposes three schemes to track different indicators of a test‐taking mode—the observable manifest variables, latent trait variables, and measurement likelihood. For each procedure, sequential sampling strategies are presented to implement online monitoring. Numerical experimentation based on simulated data suggests that the proposed procedures demonstrate adequate performance. The procedures identified examinees with aberrant behaviors with high detection power and timeliness, while maintaining error rates reasonably small. Experimental application to real data also suggested that the procedures have practical relevance to real assessments. Based on the observations from the experiential analysis, the study discusses implications and guidelines for practical use.

Characterizing the Manifest Probability Distributions of Three Latent Trait Models for Accuracy and Response Time

In this paper we study the statistical relations between three latent trait models for accuracies and response times: the hierarchical model (HM) of van der Linden (Psychometrika 72(3):287–308, 2007), the signed residual time model (SM) proposed by Maris and van der Maas (Psychometrika 77(4):615–633, 2012), and the drift diffusion model (DM) as proposed by Tuerlinckx and De Boeck (Psychometrika 70(4):629–650, 2005). One important distinction between these models is that the HM and the DM either assume or imply that accuracies and response times are independent given the latent trait variables, while the SM does not. In this paper we investigate the impact of this conditional independence property—or a lack thereof—on the manifest probability distribution for accuracies and response times. We will find that the manifest distributions of the latent trait models share several important features, such as the dependency between accuracy and response time, but we also find important differences, such as in what function of response time is being modeled. Our method for characterizing the manifest probability distributions is related to the Dutch identity (Holland in Psychometrika 55(6):5–18, 1990).

Skew t Mixture Latent State-Trait Analysis: A Monte Carlo Simulation Study on Statistical Performance.

This simulation study assessed the statistical performance of a skew t mixture latent state-trait (LST) model for the analysis of longitudinal data. The model aims to identify interpretable latent classes with class-specific LST model parameters. A skew t-distribution within classes is allowed to account for non-normal outcomes. This flexible function covers heavy tails and may reduce the risk of identifying spurious classes, e.g., in case of outliers. Sample size, number of occasions and skewness of the trait variable were varied. Generally, parameter estimation accuracy increases with increasing numbers of observations and occasions. Larger bias compared to other parameters occurs for parameters referring to the skew t-distribution and variances of the latent trait variables. Standard error estimation accuracy shows diffuse patterns across conditions and parameters. Overall model performance is acceptable for large conditions, even though none of the models is free from bias. The application of the skew t mixture model in case of large numbers of occasions and observations may be possible, but results should be treated with caution. Moreover, the skew t approach may be useful for other mixture models.

Dual‐Objective Item Selection Criteria in Cognitive Diagnostic Computerized Adaptive Testing

The development of cognitive diagnostic‐computerized adaptive testing (CD‐CAT) has provided a new perspective for gaining information about examinees' mastery on a set of cognitive attributes. This study proposes a new item selection method within the framework of dual‐objective CD‐CAT that simultaneously addresses examinees' attribute mastery status and overall test performance. The new procedure is based on the Jensen‐Shannon (JS) divergence, a symmetrized version of the Kullback‐Leibler divergence. We show that the JS divergence resolves the noncomparability problem of the dual information index and has close relationships with Shannon entropy, mutual information, and Fisher information. The performance of the JS divergence is evaluated in simulation studies in comparison with the methods available in the literature. Results suggest that the JS divergence achieves parallel or more precise recovery of latent trait variables compared to the existing methods and maintains practical advantages in computation and item pool usage.

Beyond An Informal Everyday Concept of Self-Esteem

Abstract. The present study investigated a state-trait model of self-esteem. Analyses focused on determining if the trait of the observables measuring state self-esteem is equivalent to the trait of the observables measuring trait self-esteem. N = 439 college students completed the Multidimensional Scale of Self-Esteem (MSES) on two measurement occasions spaced 10 weeks apart. Structural equation models were used to test latent state-trait measurement models and the relation between the state and trait components of self-esteem. The results suggest that (1) except for physical self-esteem, the multi-state-single-trait models are suitable for all self-esteem dimensions investigated. This holds for the state test halves as well as for the trait test halves. (2) Concerning the association between the components of trait and state self-esteem, results were supportive of a model, including two latent trait variables, assumed to explain the latent state variables for the respective state form and trait form for the dimensions of general self-esteem. These latent trait factors correlate substantively with .94 ≤ r ≤ .99.

Dynamic latent trait models with mixed hidden Markov structure for mixed longitudinal outcomes

We propose a general Bayesian joint modeling approach to model mixed longitudinal outcomes from the exponential family for taking into account any differential misclassification that may exist among categorical outcomes. Under this framework, outcomes observed without measurement error are related to latent trait variables through generalized linear mixed effect models. The misclassified outcomes are related to the latent class variables, which represent unobserved real states, using mixed hidden Markov models (MHMMs). In addition to enabling the estimation of parameters in prevalence, transition and misclassification probabilities, MHMMs capture cluster level heterogeneity. A transition modeling structure allows the latent trait and latent class variables to depend on observed predictors at the same time period and also on latent trait and latent class variables at previous time periods for each individual. Simulation studies are conducted to make comparisons with traditional models in order to illustrate the gains from the proposed approach. The new approach is applied to data from the Southern California Children Health Study to jointly model questionnaire-based asthma state and multiple lung function measurements in order to gain better insight about the underlying biological mechanism that governs the inter-relationship between asthma state and lung function development.

The effects of the interplay of genetics and early environmental risk on the course of internalizing symptoms from late childhood through adolescence.

Internalizing symptoms during adolescence and beyond is a major public health concern, particularly because severe symptoms can lead to the diagnosis of a number of serious psychiatric conditions. This study utilizes a unique sample with a complex statistical method in order to explore Gene × Environment interactions found in internalizing symptoms during adolescence. Data for this study were drawn from a longitudinal prevention intervention study (n = 798) of Baltimore city school children. Internalizing symptom data were collected using self-report and blood or saliva samples genotyped using Affymetrix 6.0 microarrays. A major depression polygenic score was created for each individual using information from the major depressive disorder Psychiatric Genetics Consortium and used as a predictor in a latent trait-state-occasion model. The major depressive disorder polygenic score was a significant predictor of the stable latent trait variable, which captures time-independent phenotypic variability. In addition, an early childhood stressor of death or divorce was a significant predictor of occasion-specific variables. A Gene × Environment interaction was not a significant predictor of the latent trait or occasion variables. These findings support the importance of genetics on the stable latent trait portion of internalizing symptoms across adolescence.

再来店までの日数を幾何分布で表現した項目反応理論による顧客ロイヤルティの測定法

This paper proposes a new model that measures customer loyalty from the days taken to repurchase in a shop. This model is based on IRT (Item Response Theory) and geometric distribution. It enables us not only to estimate customer loyalty as latent trait variables of each customer, but also to quantify the ability to pull in customers of shops. Moreover these shops could be any selling segment, for example, brand stores, manufacturers, or articles. In order to check the validity of this model, it is applied to actual ID-POS (point-of-sale with identification) data. In addition, another model using exponential distribution is proposed as an alternative model.

The Psychometric Latent Agreement Model (PLAM) for Discrete Latent Variables Measured by Multiple Items.

The Psychometric Latent Agreement Model (PLAM) is proposed for estimating the subpopulation membership of individuals (e.g., satisfactory performers vs. unsatisfactory performers) at discrete levels of multiple latent trait variables. A binary latent Type variable is introduced to take account of the possibility that, for a given set of observed variables, the latent group memberships of some individuals are indeterminate. The latent Type variable allows for separating individuals who can reliably be assigned to satisfactory versus unsatisfactory performers classes from those individuals whose ratings do not contain the necessary information to make the class assignment possible for a particular set of rating items. Agreements among discrete latent trait variables are also estimated. The PLAM was illustrated with two examples using real data on behavioral rating measures. One example involved ratings of two behavioral constructs by a single rater type, whereas the other involved ratings of one construct by three rater types. Implications were presented for using behavioral ratings to determine the subpopulation membership, such as qualified versus unqualified groupings in hiring decisions and pass versus fail groupings in performance evaluations.

Analyzing Individual and Average Causal Effects via Structural Equation Models

Abstract. Although both individual and average causal effects are defined in Rubin's approach to causality, in this tradition almost all papers center around learning about the average causal effects. Almost no efforts deal with developing designs and models to learn about individual effects. This paper takes a first step in this direction. In the first and general part, Rubin's concepts of individual and average causal effects are extended replacing Rubin's deterministic potential-outcome variables by the stochastic expected-outcome variables. Based on this extension, in the second and main part specific designs, assumptions and models are introduced which allow identification of (1) the variance of the individual causal effects, (2) the regression of the individual causal effects on the true scores of the pretests, (3) the regression of the individual causal effects on other explanatory variables, and (4) the individual causal effects themselves. Although random assignment of the observational unit to one of the treatment conditions is useful and yields stronger results, much can be achieved with a nonequivalent control group. The simplest design requires two pretests measuring a pretest latent trait that can be interpreted as the expected outcome under control, and two posttests measuring a posttest latent trait: The expected outcome under treatment. The difference between these two latent trait variables is the individual-causal-effect variable, provided some assumptions can be made. These assumptions - which rule out alternative explanations in the Campbellian tradition - imply a single-trait model (a one-factor model) for the untreated control condition in which no treatment takes place, except for change due to measurement error. These assumptions define a testable model. More complex designs and models require four occasions of measurement, two pretest occasions and two posttest occasions. The no-change model for the untreated control condition is then a single-trait-multistate model allowing for measurement error and occasion-specific effects.

Measuring Variability and Change With an Item Response Model for Polytomous Variables

An extension of the graded response model of Samejima (1969) for the measurement of variability and change is presented. In this model it is assumed that an occasion-specific latent variable is decomposed into (a) a person-specific variable (a trait variable) and (b) an occasion-specific deviation variable measuring the variability caused by situational and/or interactional effects. Furthermore, it is assumed that interindividual differences in intraindividual trait change occur between a priori specified periods of time. The correlations of the latent trait variables between periods of time indicate the degree of (trait) change. It is shown how the parameters of the model can be estimated and some implications of the model can be tested with structural equation models for ordered variables. Finally, the model is illustrated by an application to the measurement of students’ interest in the topic of radioactivity. Based on the results of a longitudinal study of students over 4’years, it is shown that a model considering two periods of time—one before and one after the incident in Chernobyl—fits well. According to the accepted model, it can be concluded that 30% to 60% of the variance of interest in radioactivity on an occasion of measurement are due to situational and/or interactional effects. The autocorrelations of the latent trait variables between both periods of time (r = .72 and r = .76, respectively) indicate that there are interindividual differences in intraindividual changes on the level of the latent trait variables.

Validating scales for the assessment of mood level and variability by latent state-trait analyses

Results concerning the validity of the mood survey, a questionnaire assessing two enduring aspects of mood— mood level and mood reactivity—are reported. The analyses show that both subscales are suitable for the assessment of relatively stable aspects of mood: sutuational and/or interactional effects only determine 3–11% of the variances of the scale scores, whereas 77–89% are due to true individual differences (not determined by situational and/or interactional effects). Furthermore, in order to examine to which degree the mood level scale assesses the mood level of a person averaged across several occasions, the correlation between the latent trait variable underlying the mood level scale and a latent trait variable defined as the expectation of repeatedly measured mood states was estimated. The correlation between these latent trait variables of r=0.78 indicates that the mood level scale is useful for the assessment of the average mood level. Finally, to validate the reactivity scale, subgroups differing with regard to the scores on the reactivity scale were analysed to examine the degree to which their actual mood is influenced by situational and/or interactional effects. The results show that the actual mood of people with high mood reactivity scores is influenced to a much higher degree by situational and/or interactional effects that the momentary mood of people with low mood reactivity scores.