A Hierarchical Ornstein–Uhlenbeck Model for Continuous Repeated Measurement Data

In this paper, we present a diffusion model for the analysis of continuous-time change in multivariate longitudinal data. The central idea is to model the data from a single person with an Ornstein–Uhlenbeck diffusion process. We extend it hierarchically by allowing the parameters of the diffusion process to vary randomly over different persons. With this approach, both intra and interindividual differences are analyzed simultaneously. Furthermore, the individual difference parameters can be regressed on covariates, thereby providing an explanation of between-person differences. Unstructured and unbalanced data pose no problem for the model to be applied. We demonstrate the method on data from an experience sampling study to investigate changes in the core affect. It can be concluded that different factors from the five factor model of personality are related to features of the trajectories in the core affect space, such as the cross-correlation and variability of the changes.     

Measuring Growth in a Longitudinal Large-Scale Assessment with a General Latent Variable Model

The aim of the research presented here is the use of extensions of longitudinal item response theory (IRT) models in the analysis and comparison of group-specific growth in large-scale assessments of educational outcomes.     

A Robust Bayesian Approach for Structural Equation Models with Missing Data

In this paper, normal/independent distributions, including but not limited to the multivariate t distribution, the multivariate contaminated distribution, and the multivariate slash distribution, are used to develop a robust Bayesian approach for analyzing structural equation models with complete or missing data. In the context of a nonlinear structural equation model with fixed covariates, robust Bayesian methods are developed for estimation and model comparison. Results from simulation studies are reported to reveal the characteristics of estimation. The methods are illustrated by using a real data set obtained from diabetes patients.     

Exploratory Restricted Latent Class Models with Monotonicity Requirements under PÒLYA–GAMMA Data Augmentation

Psychometrika - Restricted latent class models (RLCMs) provide an important framework for supporting diagnostic research in education and psychology. Recent research proposed fully exploratory...     

Multidimensional Adaptive Testing with Optimal Design Criteria for Item Selection

Several criteria from the optimal design literature are examined for use with item selection in multidimensional adaptive testing. In particular, it is examined what criteria are appropriate for adaptive testing in which all abilities are intentional, some should be considered as a nuisance, or the interest is in the testing of a composite of the abilities. Both the theoretical analyses and the studies of simulated data in this paper suggest that the criteria of A-optimality and D-optimality lead to the most accurate estimates when all abilities are intentional, with the former slightly outperforming the latter. The criterion of E-optimality showed occasional erratic behavior for this case of adaptive testing, and its use is not recommended. If some of the abilities are nuisances, application of the criterion of A _s -optimality (or D _s -optimality), which focuses on the subset of intentional abilities is recommended. For the measurement of a linear combination of abilities, the criterion of c-optimality yielded the best results. The preferences of each of these criteria for items with specific patterns of parameter values was also assessed. It was found that the criteria differed mainly in their preferences of items with different patterns of values for their discrimination parameters. The first author is now at the Department of Methodology and Statistics, Statistics, Faculty of Social Sciences, Utrecht University, Heidelberglaan 1, 3854 Utrecht, The Netherlands. The second author is now at Research Department, CTB/McGraw-Hill, Monterey, CA, USA.     

Modeling Concordance Correlation Coefficient for Longitudinal Study Data

Measures of agreement are used in a wide range of behavioral, biomedical, psychosocial, and health-care related research to assess reliability of diagnostic test, psychometric properties of instrument, fidelity of psychosocial intervention, and accuracy of proxy outcome. The concordance correlation coefficient (CCC) is a popular measure of agreement for continuous outcomes. In modern-day applications, data are often clustered, making inference difficult to perform using existing methods. In addition, as longitudinal study designs become increasingly popular, missing data have become a serious issue, and the lack of methods to systematically address this problem has hampered the progress of research in the aforementioned fields. In this paper, we develop a novel approach to tackle the complexities involved in addressing missing data and other related issues for performing CCC analysis within a longitudinal data setting. The approach is illustrated with both real and simulated data.     

A Note on Comparing the Estimates of Models for Cluster-Correlated or Longitudinal Data with Binary or Ordinal Outcomes

When using linear models for cluster-correlated or longitudinal data, a common modeling practice is to begin by fitting a relatively simple model and then to increase the model complexity in steps. New predictors might be added to the model, or a more complex covariance structure might be specified for the observations. When fitting models for binary or ordered-categorical outcomes, however, comparisons between such models are impeded by the implicit rescaling of the model estimates that takes place with the inclusion of new predictors and/or random effects. This paper presents an approach for putting the estimates on a common scale to facilitate relative comparisons between models fit to binary or ordinal outcomes. The approach is developed for both population-average and unit-specific models.     

Polytomous Latent Scales for the Investigation of the Ordering of Items

We propose three latent scales within the framework of nonparametric item response theory for polytomously scored items. Latent scales are models that imply an invariant item ordering, meaning that the order of the items is the same for each measurement value on the latent scale. This ordering property may be important in, for example, intelligence testing and person-fit analysis. We derive observable properties of the three latent scales that can each be used to investigate in real data whether the particular model adequately describes the data. We also propose a methodology for analyzing test data in an effort to find support for a latent scale, and we use two real-data examples to illustrate the practical use of this methodology.     

Finite Mixture Multilevel Multidimensional Ordinal IRT Models for Large Scale Cross-Cultural Research

We present a class of finite mixture multilevel multidimensional ordinal IRT models for large scale cross-cultural research. Our model is proposed for confirmatory research settings. Our prior for item parameters is a mixture distribution to accommodate situations where different groups of countries have different measurement operations, while countries within these groups are still allowed to be heterogeneous. A simulation study is conducted that shows that all parameters can be recovered. We also apply the model to real data on the two components of affective subjective well-being: positive affect and negative affect. The psychometric behavior of these two scales is studied in 28 countries across four continents.     

Discrete Choice Models for Ordinal Response Variables: A Generalization of the Stereotype Model

In this paper I present a class of discrete choice models for ordinal response variables based on a generalization of the stereotype model. The stereotype model can be derived and generalized as a random utility model for ordered alternatives. Random utility models can be specified to account for heteroscedastic and correlated utilities. In the case of the generalized stereotype model this includes category-specific random effects due to individual differences in response style. But unlike standard random utility models the generalized stereotype model is better suited for ordinal response variables and can be interpreted as a kind of unidimensional unfolding model. This paper discusses the specification, interpretation, identification, and estimation of generalized stereotype models. Two applications are provided for illustration. This paper benefited significantly from the comments and suggestions of the editor, associate editor, and three anonymous reviewers. It is dedicated to my late colleague, peer, and friend Bradley D. Crouch.     

A Bayesian Semiparametric Item Response Model with Dirichlet Process Priors

In Item Response Theory (IRT), item characteristic curves (ICCs) are illustrated through logistic models or normal ogive models, and the probability that examinees give the correct answer is usually a monotonically increasing function of their ability parameters. However, since only limited patterns of shapes can be obtained from logistic models or normal ogive models, there is a possibility that the model applied does not fit the data. As a result, the existing method can be rejected because it cannot deal with various item response patterns. To overcome these problems, we propose a new semiparametric IRT model using a Dirichlet process mixture logistic distribution. Our method does not rely on assumptions but only requires that the ICCs be a monotonically nondecreasing function; that is, our method can deal with more types of item response patterns than the existing methods, such as the one-parameter normal ogive models or the two- or three-parameter logistic models.     

Model Evaluation and Multiple Strategies in Cognitive Diagnosis: An Analysis of Fraction Subtraction Data

This paper studies three models for cognitive diagnosis, each illustrated with an application to fraction subtraction data. The objective of each of these models is to classify examinees according to their mastery of skills assumed to be required for fraction subtraction. We consider the DINA model, the NIDA model, and a new model that extends the DINA model to allow for multiple strategies of problem solving. For each of these models the joint distribution of the indicators of skill mastery is modeled using a single continuous higher-order latent trait, to explain the dependence in the mastery of distinct skills. This approach stems from viewing the skills as the specific states of knowledge required for exam performance, and viewing these skills as arising from a broadly defined latent trait resembling the θ of item response models. We discuss several techniques for comparing models and assessing goodness of fit. We then implement these methods using the fraction subtraction data with the aim of selecting the best of the three models for this application. We employ Markov chain Monte Carlo algorithms to fit the models, and we present simulation results to examine the performance of these algorithms. The work reported here was performed under the auspices of the External Diagnostic Research Team funded by Educational Testing Service. Views expressed in this paper does not necessarily represent the views of Educational Testing Service.     

A Generalized Speed–Accuracy Response Model for Dichotomous Items

We propose a generalization of the speed–accuracy response model (SARM) introduced by Maris and van der Maas (Psychometrika 77:615–633, 2012). In these models, the scores that result from a scoring rule that incorporates both the speed and accuracy of item responses are modeled. Our generalization is similar to that of the one-parameter logistic (or Rasch) model to the two-parameter logistic (or Birnbaum) model in item response theory. An expectation–maximization (EM) algorithm for estimating model parameters and standard errors was developed. Furthermore, methods to assess model fit are provided in the form of generalized residuals for item score functions and saddlepoint approximations to the density of the sum score. The presented methods were evaluated in a small simulation study, the results of which indicated good parameter recovery and reasonable type I error rates for the residuals. Finally, the methods were applied to two real data sets. It was found that the two-parameter SARM showed improved fit compared to the one-parameter SARM in both data sets.     

A Note on Stochastic Ordering of the Latent Trait Using the Sum of Polytomous Item Scores

In contrast to dichotomous item response theory (IRT) models, most well-known polytomous IRT models do not imply stochastic ordering of the latent trait by the total test score (SOL). This has been thought to make the ordering of respondents on the latent trait using the total test score questionable and throws doubt on the justifiability of using nonparametric polytomous IRT models for ordinal measurement. We show that a broad class of polytomous IRT models has a weaker form of SOL, denoted weak SOL, and argue that weak SOL justifies ordering respondents on the latent trait using the total test score and, therefore, the use of nonparametric polytomous IRT models for ordinal measurement.     

Using State-Space Model with Regime Switching to Represent the Dynamics of Facial Electromyography (EMG) Data

Facial electromyography (EMG) is a useful physiological measure for detecting subtle affective changes in real time. A time series of EMG data contains bursts of electrical activity that increase in magnitude when the pertinent facial muscles are activated. Whereas previous methods for detecting EMG activation are often based on deterministic or externally imposed thresholds, we used regime-switching models to probabilistically classify each individual’s time series into latent “regimes” characterized by similar error variance and dynamic patterns. We also allowed the association between EMG signals and self-reported affect ratings to vary between regimes and found that the relationship between these two markers did in fact vary over time. The potential utility of using regime-switching models to detect activation patterns in EMG data and to summarize the temporal characteristics of EMG activities is discussed.     

Muscular Imaginings—A Phenomenological and Enactive Model for Imagination*

A phenomenological model (labeled ‘EC’) is developed as an alternative to current analyses of the imagination in sport philosophy, heirs to an Enlightenment notion that conceptualizes imaginings as abstract, eidetic, and representational. EC describes how Eidetic and Corporeal Imaginings (EIs & CIs) phenomenologically structure our imaginative undertakings. EIs keep the ‘ideal’ aspect, but CIs—enacted, corporeal, non-representational—are more fundamental and foundational. Sports are particularly suited to express CIs’ muscular imaginings, which result in novel performances. An enactive framework theorizes CIs as non-representational interactions.     

College Women��s Feminist Identity: A Multidimensional Analysis with Implications for Coping with Sexism

This study examined components of women's feminist identity and possible relations to their reported coping responses to sexism. A sample of 169 undergraduate women (M?=?19.4?y, SD?=?1.2) from diverse ethnic backgrounds completed surveys assessing their experiences and gender-related views. The first set of analyses revealed that women's social gender identity, exposure to feminism, and gender-egalitarian attitudes independently contributed to feminist identification; moreover, non-stereotyping of feminists further predicted feminist self-identification. A second set of analyses tested the relative contribution of feminist identity components to women's cognitive appraisals of coping responses to sexual harassment. Seeking social support was predicted by self-identification as a feminist (for White European American women only). Confronting was predicted by social gender identity, non-stereotyping of feminists, and public identification as a feminist. Findings highlight possible components of women's feminist identity and their possible impact on coping responses to sexism.     

User-related assessment of a Driver Assistance System for Continuous Support – A field trial

A Driver Assistance System for Continuous Support continuously evaluates the status of the host vehicle as well as the surrounding traffic based on information from on-board sensors. When the system detects a hazard, it issues a warning to the driver, depending on the degree of the hazard. The effects of this system on driver behaviour and acceptance were evaluated in a field trial carried out in 2013. Twenty-four drivers took part in test drives with a within-subject design along a 53 km test route containing motorway and rural-road sections. Driving data was logged and the test drivers were observed by means of an in-car observation method (Wiener Fahrprobe); in this case by two observers in the car along with the driver. Questionnaires were used to assess the drivers’ comprehension of and reaction to the system. The system was successful in affecting driver behaviour in terms of lower speed when negotiating curves. Positive effects were found in the form of better speed adaptation to the situation during driving with the system activated. Also, lane choice and lane change improved with the system on. When it came to speed limit compliance, driving speed in general and longitudinal and lateral positioning, no effects could be found. No major differences were found regarding distance to the vehicle in front, overtaking manoeuvres, stopping behaviour at intersections, driving against yellow at traffic lights and interaction behaviour with other road users while driving with or without the system. On the negative side, it was noted that only during driving with the system activated did the test drivers make turns at intersections at too high speeds. In addition, more errors associated with dangerous distance to the side were observed with the system activated. In terms of the emotional state of the driver, the only difference found was that the drivers felt an increase in irritation. Regarding subjective workload, the drivers only assessed one item, i.e. whether their performance decreased statistically significantly while driving with the system. The test drivers were of the opinion that the system was useful, and that it would enhance safety especially in overtaking manoeuvres on motorways. The blind-spot warning was found especially useful in the overtaking process. The drivers appreciated the fact that the system did not give information all the time.