An accumulator model for responses and response times in tests based on the proportional hazards model

Latent trait models for responses and response times in tests often lack a substantial interpretation in terms of a cognitive process model. This is a drawback because process models are helpful in clarifying the meaning of the latent traits. In the present paper, a new model for responses and response times in tests is presented. The model is based on the proportional hazards model for competing risks. Two processes are assumed, one reflecting the increase in knowledge and the second the tendency to discontinue. The processes can be characterized by two proportional hazards models whose baseline hazard functions correspond to the temporary increase in knowledge and discouragement. The model can be calibrated with marginal maximum likelihood estimation and an application of the ECM algorithm. Two tests of model fit are proposed. The amenability of the proposed approaches to model calibration and model evaluation is demonstrated in a simulation study. Finally, the model is used for the analysis of two empirical data sets.     

An alternating least squares algorithm for fitting the two- and three-way dedicom model and the idioscal model

The DEDICOM model is a model for representing asymmetric relations among a set of objects by means of a set of coordinates for the objects on a limited number of dimensions. The present paper offers an alternating least squares algorithm for fitting the DEDICOM model. The model can be generalized to represent any number of sets of relations among the same set of objects. An algorithm for fitting this three-way DEDICOM model is provided as well. Based on the algorithm for the three-way DEDICOM model an algorithm is developed for fitting the IDIOSCAL model in the least squares sense.The author is obliged to Jos ten Berge and Richard Harshman.     

A quantum probability account of order effects in inference

Order of information plays a crucial role in the process of updating beliefs across time. In fact, the presence of order effects makes a classical or Bayesian approach to inference difficult. As a result, the existing models of inference, such as the belief-adjustment model, merely provide an ad hoc explanation for these effects. We postulate a quantum inference model for order effects based on the axiomatic principles of quantum probability theory. The quantum inference model explains order effects by transforming a state vector with different sequences of operators for different orderings of information. We demonstrate this process by fitting the quantum model to data collected in a medical diagnostic task and a jury decision-making task. To further test the quantum inference model, a new jury decision-making experiment is developed. Using the results of this experiment, we compare the quantum inference model with two versions of the belief-adjustment model, the adding model and the averaging model. We show that both the quantum model and the adding model provide good fits to the data. To distinguish the quantum model from the adding model, we develop a new experiment involving extreme evidence. The results from this new experiment suggest that the adding model faces limitations when accounting for tasks involving extreme evidence, whereas the quantum inference model does not. Ultimately, we argue that the quantum model provides a more coherent account for order effects that was not possible before.     

项目反应时间的对数偏正态模型

近年来,项目反应时间数据的建模是心理和教育测量领域的热门方向之一。针对反应时间的对数正态模型和Box-Cox正态模型的不足,本文在van der Linden的分层模型框架下基于偏正态分布建立一个反应时间的对数线性模型,并成功给出模型参数估计的马尔科夫链蒙特卡罗（Markov Chain Monte Carlo, MCMC）算法。模拟研究和实例分析的结果均表明,与对数正态模型和Box-Cox正态模型相比,对数偏正态模型表现出更加优良的拟合效果,具有更强的灵活性和适用性。     

A Measurement Model for Likert Responses That Incorporates Response Time

This article describes a model for response times that is proposed as a supplement to the usual factor-analytic model for responses to graded or more continuous typical-response items. The use of the proposed model together with the factor model provides additional information about the respondent and can potentially increase the accuracy of the individual trait estimates. First, the rationale of the model is discussed in relation to previous developments in binary responses. Second, procedures for fitting the model and for assessing model-data fit at both overall and individual level (person-fit) are proposed. Third, the usefulness of the model and its potential applications in the typical-response domain are discussed. All the proposed developments are used in 2 empirical applications in the personality domain. The first application analyzes 2 scales from a Big Five questionnaire. The second example analyzes a sociability scale developed from Eysenck's questionnaires.     

Cognitive processes and conflict in close relationships: an attribution-efficacy model

A recently proposed model of cognitive processes underlying conflict in close relationships (Doherty, 1978, 1981a, 1981b) is revised and tested in two studies. Central to the original model are the causal attributions made for conflict and the perceived efficacy or ability to resolve conflict. The model is revised to incorporate judgments of responsibility and to provide a closer link to self-efficacy theory. The first study examines attributions and efficacy expectations in mother-child relationships. As anticipated, only weak evidence was obtained for predictions retained from the original model, high-lighting the relationship-specific nature of cognitive processes for conflict in families. A second study examines husband-wife relationships and provides evidence for the usefulness of an attribution-efficacy model for marital conflict. The attributional component of the model received greater support than that pertaining to efficacy expectations. In both studies, support was obtained for the proposal that the relation between conflict dimensions (e.g., blame) and causal dimensions is mediated by judgments of responsibility. The significance of the revisions to Doherty's model for understanding conflict in close relationships is discussed, and several avenues for further research are outlined.     

A predictive coding model of gaze shifts and the underlying neurophysiology

A comprehensive model of gaze control must account for a number of empirical observations at both the behavioural and neurophysiological levels. The computational model presented in this article can simulate the coordinated movements of the eye, head, and body required to perform horizontal gaze shifts. In doing so it reproduces the predictable relationships between the movements performed by these different degrees of freedom (DOFs) in the primate. The model also accounts for the saccadic undershoot that accompanies large gaze shifts in the biological visual system. It can also account for our perception of a stable external world despite frequent gaze shifts and the ability to perform accurate memory-guided and double-step saccades. The proposed model also simulates peri-saccadic compression: the mis-localization of a briefly presented visual stimulus towards the location that is the target for a saccade. At the neurophysiological level, the proposed model is consistent with the existence of cortical neurons tuned to the retinal, head-centred, body-centred, and world-centred locations of visual stimuli and cortical neurons that have gain-modulated responses to visual stimuli. Finally, the model also successfully accounts for peri-saccadic receptive field (RF) remapping which results in reduced responses to stimuli in the current RF location and an increased sensitivity to stimuli appearing at the location that will be occupied by the RF after the saccade. The proposed model thus offers a unified explanation for this seemingly diverse range of phenomena. Furthermore, as the proposed model is an implementation of the predictive coding theory, it offers a single computational explanation for these phenomena and relates gaze shifts to a wider framework for understanding cortical function.     

Model Predictive Impedance Control: A Model for Joint Movement

Impedance control has been suggested as the strategy employed by the central nervous system to control human postures and movements. A realization of this strategy is presented that uses a model predictive control algorithm as a higher motor controller. External disturbances are explicitly included in the model. The combination of 3 key factors-joint impedance control, model predictive controller, and external disturbance input-forms the basis for the generality of this model. The model was applied to 3 different types of joint movements: a tracking movement with an unpredicted disturbance, a rhythmic movement, and an unstable biped model of human walking. Computer simulation results showed excellent performance of the model in all 3 cases for optimal values of active joint impedances and an exact match between the musculoskeletal system and the model internal to the model predictive controller. The controller was also able to maintain acceptable performance in the presence of a 25% mismatch between the musculoskeletal system and its internal model.     

Developing TODAM: Three models for serial-order information

TODAM2, a theory of distributed associative memory, shows how item and associative information can be considered special cases of serial-order information. Consequently, it is important to get the right model for serial-order information. Here, we analyze and compare three distributed-memory models for serial-order information that use TODAM’s convolution-correlation formalism. These models are the chaining model, the chunking model, and a new model, the power-set model. The chaining model associates each item with its predecessor; the chunking model uses multiple convolutions andn-grams to form chunks; and the power-set model interassociates all items in a set in a particular way to form a chunk. The models are compared in terms of their performance on seven basic tests of serial-order information—namely, serial recall, backward recall, recall of missing items, sequential probe tests, positional probe tests, serial-to-paired-associate transfer, and item recognition. The strengths and weaknesses of each model are discussed.     

A generalized longitudinal mixture IRT model for measuring differential growth in learning environments

This article describes a generalized longitudinal mixture item response theory (IRT) model that allows for detecting latent group differences in item response data obtained from electronic learning (e-learning) environments or other learning environments that result in large numbers of items. The described model can be viewed as a combination of a longitudinal Rasch model, a mixture Rasch model, and a random-item IRT model, and it includes some features of the explanatory IRT modeling framework. The model assumes the possible presence of latent classes in item response patterns, due to initial person-level differences before learning takes place, to latent class-specific learning trajectories, or to a combination of both. Moreover, it allows for differential item functioning over the classes. A Bayesian model estimation procedure is described, and the results of a simulation study are presented that indicate that the parameters are recovered well, particularly for conditions with large item sample sizes. The model is also illustrated with an empirical sample data set from a Web-based e-learning environment.     

Marginal and Random Intercepts Models for Longitudinal Binary Data With Examples From Criminology

Two models for the analysis of longitudinal binary data are discussed: the marginal model and the random intercepts model. In contrast to the linear mixed model (LMM), the two models for binary data are not subsumed under a single hierarchical model. The marginal model provides group-level information whereas the random intercepts model provides individual-level information including information about heterogeneity of growth. It is shown how a type of numerical averaging can be used with the random intercepts model to obtain group-level information, thus approximating individual and marginal aspects of the LMM. The types of inferences associated with each model are illustrated with longitudinal criminal offending data based on N = 506 males followed over a 22-year period. Violent offending indexed by official records and self-report were analyzed, with the marginal model estimated using generalized estimating equations and the random intercepts model estimated using maximum likelihood. The results show that the numerical averaging based on the random intercepts can produce prediction curves almost identical to those obtained directly from the marginal model parameter estimates. The results provide a basis for contrasting the models and the estimation procedures and key features are discussed to aid in selecting a method for empirical analysis.     

An item response tree model with not-all-distinct end nodes for non-response modelling

The non-response model in Knott et al. (1991, Statistician, 40, 217) can be represented as a tree model with one branch for response/non-response and another branch for correct/incorrect response, and each branch probability is characterized by an item response theory model. In the model, it is assumed that there is only one source of non-responses. However, in questionnaires or educational tests, non-responses might come from different sources, such as test speededness, inability to answer, lack of motivation, and sensitive questions. To better accommodate such more realistic underlying mechanisms, we propose a a tree model with four end nodes, not all distinct, for non-response modelling. The Laplace-approximated maximum likelihood estimation for the proposed model is suggested. The validation of the proposed estimation procedure and the advantage of the proposed model over traditional methods are demonstrated in simulations. For illustration, the methodologies are applied to data from the 2012 Programme for International Student Assessment (PISA). The analysis shows that the proposed tree model has a better fit to PISA data than other existing models, providing a useful tool to distinguish the sources of non-responses.     

Uniqueness of three-mode factor models with sparse cores: The 3 × 3 × 3 case

Three-Mode Factor Analysis (3MFA) and PARAFAC are methods to describe three-way data. Both methods employ models with components for the three modes of a three-way array; the 3MFA model also uses a three-way core array for linking all components to each other. The use of the core array makes the 3MFA model more general than the PARAFAC model (thus allowing a better fit), but also more complicated. Moreover, in the 3MFA model the components are not uniquely determined, and it seems hard to choose among all possible solutions. A particularly interesting feature of the PARAFAC model is that it does give unique components. The present paper introduces a class of 3MFA models in between 3MFA and PARAFAC that share the good properties of the 3MFA model and the PARAFAC model: They fit (almost) as well as the 3MFA model, they are relatively simple and they have the same uniqueness properties as the PARAFAC model.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author. Part of this research has been presented at the first conference on ThRee-way methods In Chemistry (TRIC), a meeting of Psychometrics and Chemometrics, Epe, The Netherlands, August 1993. The authors are obliged to Age Smilde for stimulating this research, and two anonymous reviewers for many helpful suggestions.     

Obtaining separate measures for implicit and explicit memory

In this paper a new model, the Implicit/Explicit Separation (IES) model, is developed and applied. The model is designed to obtain separate probability measures for explicit memory storage, implicit memory storage, fractional storage, and non-storage. The model is needed because memory research has shown the importance of the distinction between a conscious memory of a target event and a memory residue that is unable to support conscious recall or confident recognition, but it is still able to support guessing at rates above chance. Maximum likelihood and population-parameter mapping estimates for the parameters of the IES model are provided. The accuracy of parameter estimates is studied as a function of sample size. Three experiments are reported to demonstrate how the IES model is used to achieve a more fine grained assessment of the quality of information storage. These experiments also provide strong validation support for the IES model itself. Across the three experiments, each of the four components for representing target information (explicit, implicit, fractional, and non-storage) demonstrates a different pattern. The IES model is discussed in terms of alternative models such as the dual-process model and the process-dissociation model.     

The intuitive personologist and the individual differences model

Subjects are required to estimate sociability as expressed in questionnaires supposedly completed by different individuals and make a prediction of conduct for each of these individuals. The results are compared to four models: three versions of the individual differences model (IDM) and a dialectical model. Two rudimentary versions of the IDM give the best approximations to results obtained, one for absolute value judgments of sociability, the other for conduct prediction. The conclusion is that the IDM does exist as a model in implicit psychology before becoming a model in learned psychology. The fact that such a model be preponderant in intuitive psychology in spite of its known inadequacies is discussed in terms of self-fulfilling prophecy in the exercise of power.     

Robust estimation of the hierarchical model for responses and response times

Van der Linden's (2007, Psychometrika, 72, 287) hierarchical model for responses and response times in tests has numerous applications in psychological assessment. The success of these applications requires the parameters of the model to have been estimated without bias. The data used for model fitting, however, are often contaminated, for example, by rapid guesses or lapses of attention. This distorts the parameter estimates. In the present paper, a novel estimation approach is proposed that is robust against contamination. The approach consists of two steps. In the first step, the response time model is fitted on the basis of a robust estimate of the covariance matrix. In the second step, the item response model is extended to a mixture model, which allows for a proportion of irregular responses in the data. The parameters of the mixture model are then estimated with a modified marginal maximum likelihood estimator. The modified marginal maximum likelihood estimator downweights responses of test-takers with unusual response time patterns. As a result, the estimator is resistant to several forms of data contamination. The robustness of the approach is investigated in a simulation study. An application of the estimator is demonstrated with real data.     

Extractive document summarization using an adaptive,knowledge based cognitive model

Document summarization involves identifying the salient text in a document and creating a representative summary. The event-index cognitive model describes the human cognitive processes involved in generating situational models from a given text to comprehend that text. This paper proposes an adaptive, knowledge based event-index cognitive model that creates an extractive summary for a given document. The proposed cognitive model uses the hierarchical human memory model and emotion to create the extractive summary. The performance of the proposed cognitive model was compared with the existing state-of-art methods using the DUC (Document Understanding Conference) 2001 dataset and the ROUGE (Recall-Oriented Understudy for Gisting Evaluation) summary evaluation tool. Under ROUGE-N, ROUGE-L, ROUGE-S and ROUGE-SU evaluations, the proposed cognitive model for document summarization achieved an improvement of 25%, 12%, 24% and 18% in mean F-measure values. The results are statistically verified as significantly better than existing state-of-art methods using one way ANOVA with post-hoc Tukey-HSD test. In addition, this paper discusses the possible future research directions in document summarization based on the proposed cognitive model.     

Tucker3 hierarchical classes analysis

This paper presents a new model for binary three-way three-mode data, called Tucker3 hierarchical classes model (Tucker3-HICLAS). This new model generalizes Leenen, Van Mechelen, De Boeck, and Rosenberg's (1999) individual differences hierarchical classes model (INDCLAS). Like the INDCLAS model, the Tucker3-HICLAS model includes a hierarchical classification of the elements of each mode, and a linking structure among the three hierarchies. Unlike INDCLAS, Tucker3-HICLAS (a) does not restrict the hierarchical classifications of the three modes to have the same rank, and (b) allows for more complex linking structures among the three hierarchies. An algorithm to fit the Tucker3-HICLAS model is described and evaluated in an extensive simulation study. An application of the model to hostility data is discussed.The first author is a Research Assistant of the Fund for Scientific Research-Flanders (Belgium). The research reported in this paper was partially supported by the Research Council of K.U. Leuven (GOA/2000/02). We are grateful to Kristof Vansteelandt for providing us with an interesting data set.