Using diffusion models to understand clinical disorders

Sequential sampling models provide an alternative to traditional analyses of reaction times and accuracy in two-choice tasks. These models are reviewed with particular focus on the diffusion model (Ratcliff, 1978) and how its application can aid research on clinical disorders. The advantages of a diffusion model analysis over traditional comparisons are shown through simulations and a simple lexical decision experiment. Application of the diffusion model to a clinically relevant topic is demonstrated through an analysis of data from nonclinical participants with high- and low-trait anxiety in a recognition memory task. The model showed that after committing an error, participants with high-trait anxiety responded more cautiously by increasing their boundary separation, whereas participants with low-trait anxiety did not. The article concludes with suggestions for ways to improve and broaden the application of these models to studies of clinical disorders.     

Rating scale analysis with latent class models

A general approach for analyzing rating data with latent class models is described, which parallels rating models in the framework of latent trait theory. A general rating model as well as a two-parameter model with location and dispersion parameters, analogous to Andrich's Dislocmodel are derived, including parameter estimation via the EM-algorithm. Two examples illustrate the application of the models and their statisticalcontrol. Model restrictions through equality constrains are discussed and multiparameter generalizations are outlined.     

Drawing conclusions from choice response time models: A tutorial using the linear ballistic accumulator

Cognitive models of choice and response times can lead to deeper insights into the processes underlying decisions than standard analyses of accuracy and response time data. The application of these models, however, has historically been reserved for the authors of the models, and their associates. Recently, choice response time models have become more accessible through the release of user-friendly software for estimating their parameters. The aim of this tutorial is to provide guidance about the process of using these parameter estimates and associated model fits to make conclusions about experimental data. We use an application of one response time model, the linear ballistic accumulator, as an example to demonstrate the steps required to select an appropriate parametric characterization of a data set. We also discuss how to evaluate the quality of the agreement between model and data, including guidelines for presenting model predictions for group-level data.     

Global model analysis by parameter space partitioning

To model behavior, scientists need to know how models behave. This means learning what other behaviors a model can produce besides the one generated by participants in an experiment. This is a difficult problem because of the complexity of psychological models (e.g., their many parameters) and because the behavioral precision of models (e.g., interval-scale performance) often mismatches their testable precision in experiments, where qualitative, ordinal predictions are the norm. Parameter space partitioning is a solution that evaluates model performance at a qualitative level. There exists a partition on the model's parameter space that divides it into regions that correspond to each data pattern. Three application examples demonstrate its potential and versatility for studying the global behavior of psychological models.     

Hierarchical diffusion models for two-choice response times

Two-choice response times are a common type of data, and much research has been devoted to the development of process models for such data. However, the practical application of these models is notoriously complicated, and flexible methods are largely nonexistent. We combine a popular model for choice response times-the Wiener diffusion process-with techniques from psychometrics in order to construct a hierarchical diffusion model. Chief among these techniques is the application of random effects, with which we allow for unexplained variability among participants, items, or other experimental units. These techniques lead to a modeling framework that is highly flexible and easy to work with. Among the many novel models this statistical framework provides are a multilevel diffusion model, regression diffusion models, and a large family of explanatory diffusion models. We provide examples and the necessary computer code.     

Hierarchical classes models for three-way three-mode binary data: interrelations and model selection

Several hierarchical classes models can be considered for the modeling of three-way three-mode binary data, including the INDCLAS model (Leenen, Van Mechelen, De Boeck, and Rosenberg, 1999), the Tucker3-HICLAS model (Ceulemans, Van Mechelen, and Leenen, 2003), the Tucker2-HICLAS model (Ceulemans and Van Mechelen, 2004), and the Tucker1-HICLAS model that is introduced in this paper. Two questions then may be raised: (1) how are these models interrelated, and (2) given a specific data set, which of these models should be selected, and in which rank? In the present paper, we deal with these questions by (1) showing that the distinct hierarchical classes models for three-way three-mode binary data can be organized into a partially ordered hierarchy, and (2) by presenting model selection strategies based on extensions of the well-known scree test and on the Akaike information criterion. The latter strategies are evaluated by means of an extensive simulation study and are illustrated with an application to interpersonal emotion data. Finally, the presented hierarchy and model selection strategies are related to corresponding work by Kiers (1991) for principal component models for three-way three-mode real-valued data.     

Sequential sampling models of human text classification

Text classification involves deciding whether or not a document is about a given topic. It is an important problem in machine learning, because automated text classifiers have enormous potential for application in information retrieval systems. It is also an interesting problem for cognitive science, because it involves real world human decision making with complicated stimuli. This paper develops two models of human text document classification based on random walk and accumulator sequential sampling processes. The models are evaluated using data from an experiment where participants classify text documents presented one word at a time under task instructions that emphasize either speed or accuracy, and rate their confidence in their decisions. Fitting the random walk and accumulator models to these data shows that the accumulator provides a better account of the decisions made, and a “balance of evidence” measure provides the best account of confidence. Both models are also evaluated in the applied information retrieval context, by comparing their performance to established machine learning techniques on the standard Reuters‐21578 corpus. It is found that they are almost as accurate as the benchmarks, and make decisions much more quickly because they only need to examine a small proportion of the words in the document. In addition, the ability of the accumulator model to produce useful confidence measures is shown to have application in prioritizing the results of classification decisions.     

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.     

Testing the Rasch model by means of the mixture fit index

Rudas, Clogg, and Lindsay (RCL) proposed a new index of fit for contingency table analysis. Using the overparametrized two‐component mixture, where the first component with weight 1?w represents the model to be tested and the second component with weight w is unstructured, the mixture index of fit was defined to be the smallest w compatible with the saturated two‐component mixture. This index of fit, which is insensitive to sample size, is applied to the problem of assessing the fit of the Rasch model. In this application, use is made of the equivalence of the semi‐parametric version of the Rasch model to specifically restricted latent class models. Therefore, the Rasch model can be represented by the structured component of the RCL mixture, with this component itself consisting of two or more subcomponents corresponding to the classes, and the unstructured component capturing the discrepancies between the data and the model. An empirical example demonstrates the application of this approach. Based on four‐item data, the one‐ and two‐class unrestricted latent class models and the one‐ to three‐class models restricted according to the Rasch model are considered, with respect to both their chi‐squared statistics and their mixture fit indices.     

Measurement of Ability in Adaptive Learning and Assessment Systems when Learners Use On-Demand Hints

Adaptive learning and assessment systems support learners in acquiring knowledge and skills in a particular domain. The learners’ progress is monitored through them solving items matching their level and aiming at specific learning goals. Scaffolding and providing learners with hints are powerful tools in helping the learning process. One way of introducing hints is to make hint use the choice of the student. When the learner is certain of their response, they answer without hints, but if the learner is not certain or does not know how to approach the item they can request a hint. We develop measurement models for applications where such on-demand hints are available. Such models take into account that hint use may be informative of ability, but at the same time may be influenced by other individual characteristics. Two modeling strategies are considered: (1) The measurement model is based on a scoring rule for ability which includes both response accuracy and hint use. (2) The choice to use hints and response accuracy conditional on this choice are modeled jointly using Item Response Tree models. The properties of different models and their implications are discussed. An application to data from Duolingo, an adaptive language learning system, is presented. Here, the best model is the scoring-rule-based model with full credit for correct responses without hints, partial credit for correct responses with hints, and no credit for all incorrect responses. The second dimension in the model accounts for the individual differences in the tendency to use hints.     

Computational models inform clinical science and assessment: An application to category learning in striatal-damaged patients

In this article we develop a new model of classification that is intermediate between the static, single strategy decision-bound models and the dynamic trial by trial multiple systems model, dCOVIS. The new model, referred to as the sCOVIS model, assumes hypothesis-testing and procedural-based subsystems are active on each trial, but that the parameters that govern behavior of the system are fixed (static) within a block of trials. To determine the clinical utility of the model, it was applied to nonlinear information-integration classification data from patients with Parkinson’s (PD) and Huntington’s disease (HD). In one application, the models suggest that the locus of HD patients’ nonlinear information-integration deficits is in their increased reliance on hypothesis-testing strategies, whereas the locus of PD patients’ deficit is in the application of sub-optimal procedural-based strategies. In a second application, the weight associated with the hypothesis-testing subsystem is shown to account for a significant amount of the variance in longitudinal cognitive decline in non-demented PD patients above and beyond that predicted by accuracy alone. Together, the accuracy rate and this model index account for 72% of the total variance associated with cognitive decline in this sample of PD patients. Interestingly, the Wisconsin Card Sort task added no additional predictive power above and beyond that predicted by nonlinear accuracy alone.     

Models with discrete latent variables for analysis of categorical data: A framework and a MATLAB MDLV toolbox

Studies in the social and behavioral sciences often involve categorical data, such as ratings, and define latent constructs underlying the research issues as being discrete. In this article, models with discrete latent variables (MDLV) for the analysis of categorical data are grouped into four families, defined in terms of two dimensions (time and sampling) of the data structure. A MATLAB toolbox (referred to as the “MDLV toolbox”) was developed for applying these models in practical studies. For each family of models, model representations and the statistical assumptions underlying the models are discussed. The functions of the toolbox are demonstrated by fitting these models to empirical data from the European Values Study. The purpose of this article is to offer a framework of discrete latent variable models for data analysis, and to develop the MDLV toolbox for use in estimating each model under this framework. With this accessible tool, the application of data modeling with discrete latent variables becomes feasible for a broad range of empirical studies.     

Missing not at random models for latent growth curve analyses

The past decade has seen a noticeable shift in missing data handling techniques that assume a missing at random (MAR) mechanism, where the propensity for missing data on an outcome is related to other analysis variables. Although MAR is often reasonable, there are situations where this assumption is unlikely to hold, leading to biased parameter estimates. One such example is a longitudinal study of substance use where participants with the highest frequency of use also have the highest likelihood of attrition, even after controlling for other correlates of missingness. There is a large body of literature on missing not at random (MNAR) analysis models for longitudinal data, particularly in the field of biostatistics. Because these methods allow for a relationship between the outcome variable and the propensity for missing data, they require a weaker assumption about the missing data mechanism. This article describes 2 classic MNAR modeling approaches for longitudinal data: the selection model and the pattern mixture model. To date, these models have been slow to migrate to the social sciences, in part because they required complicated custom computer programs. These models are now quite easy to estimate in popular structural equation modeling programs, particularly Mplus. The purpose of this article is to describe these MNAR modeling frameworks and to illustrate their application on a real data set. Despite their potential advantages, MNAR-based analyses are not without problems and also rely on untestable assumptions. This article offers practical advice for implementing and choosing among different longitudinal models.     

Density versus feature weights as predictors of visual identifications: comment on Appelman and Mayzner

Appleman and Mayzner's application of the distance-density model to confusion data is compared with Keren and Baggen's application of the feature-matching model. In both applications, the distinctive features of two stimuli are predictors of the number of confusion errors. However, the models differ in that the feature-matching model assigns weights to the features and assumes that the shared feature weights also affect the probability of confusion. In contrast, the distance-density model assumes that the number of confusions between two stimuli is affected by the number of stimuli in the entire stimulus set that are similar to the two stimuli (density). The two models are compared in the context of a set of digit identification data.     

Bayesian Thurstonian models for ranking data using JAGS

A Thurstonian model for ranking data assumes that observed rankings are consistent with those of a set of underlying continuous variables. This model is appealing since it renders ranking data amenable to familiar models for continuous response variables—namely, linear regression models. To date, however, the use of Thurstonian models for ranking data has been very rare in practice. One reason for this may be that inferences based on these models require specialized technical methods. These methods have been developed to address computational challenges involved in these models but are not easy to implement without considerable technical expertise and are not widely available in software packages. To address this limitation, we show that Bayesian Thurstonian models for ranking data can be very easily implemented with the JAGS software package. We provide JAGS model files for Thurstonian ranking models for general use, discuss their implementation, and illustrate their use in analyses.     

Separating trait effects from trait-specific method effects in multitrait-multimethod models: a multiple-indicator CT-C(M-1) model

An overview of several models of confirmatory factor analysis for analyzing multitrait-multimethod (MTMM) data and a discussion of their advantages and limitations are provided. A new class of multi-indicator MTMM models combines several strengths and avoids a number of serious shortcomings inherent in previously developed MTMM models. The new models enable researchers to specify and to test trait-specific-method effects. The trait and method concepts composing these models are explained in detail and are contrasted with those of previously developed MTMM models for multiple indicators. The definitions of the models are explained step by step, and a practical empirical application of the models to the measurement of 3 traits x 3 methods is used to demonstrate their advantages and limitations.     

Acceleration model in the heterogeneous case of the general graded response model

A new model, called acceleration model, is proposed in the framework of the heterogenous case of the graded response model, based on processing functions defined for a finite or enumerable number of steps. The model is expected to be useful in cognitive assessment, as well as in more traditional areas of application of latent trait models. Criteria for evaluating models are proposed, and soundness and robustness of the acceleration model are discussed. Graded response models based on individual choice behavior are also discussed, and criticisms on model selection in terms of fitnesses of models to the data are also given.This research was supported by the Office of Naval Research (N00014-90-J-1456).     

J scale models for preference behavior

Three models for preference behavior are developed within the framework of Coombs' theory of data, an absolute difference model, a ratio model, and a two-stage model. Each of these models describes a mechanism by which unilateral preferences may be determined on a unidimensionalJ scale. Differential implications of the models for response latencies are derived, and some early data employing an application of the unfolding technique are presented in support of the two-stage model.Based upon portions of the author's doctoral dissertation, University of Michigan, 1962. This research was supported in part by NSF Grant No. G5820 to Professor C. H. Coombs. The writer also wishes to thank Professor William Hays, who served as committee chairman and offered considerable support and assistance.