Expanding the rasch model to a general model having more than one dimension

The well-known Rasch model is generalized to a multicomponent model, so that observations of component events are not needed to apply the model. It is shown that the generalized model has retained the property of the specific objectivity of the Rasch model. For a restricted variant of the model, maximum likelihood estimates of its parameters and a statistical test of the model are given. The results of an application to a mathematics test involving six components are described.     

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.     

G-DINA认知诊断模型在语言测验中的验证

G-DINA模型是DINA 模型的一般化模型,具有补偿性和饱和性两个主要特征。G-DINA模型的补偿性特征契合了语言测验的综合性和多元性,G-DINA模型的饱和性特征则可以比较理想地应对语言技能的抽象性和难区分性。此项研究以代表性的语言测验类型阅读测验为案例,应用G-DINA模型对1029名被试的PISA英语阅读测验结果进行实证分析,证明了两个假设：补偿饱和型认知诊断模型对多元抽象的语言测验的适应程度较高;G-DINA这一新生认知诊断模型可以被用来诊断较为复杂抽象的语言测验,且经得起统计学和语言学理论的双重考验。     

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.     

Exemplars, prototypes, and the flexibility of classification models

J. P. Minda and J. D. Smith (2001) showed that a prototype model outperforms an exemplar model, especially in larger categories or categories that contained more complex stimuli. R. M. Nosofsky and S. R. Zaki (2002) showed that an exemplar model with a response-scaling mechanism outperforms a prototype model. The authors of the current study investigated whether excessive model flexibility could explain these results. Using cross-validation, the authors demonstrated that both the prototype model and the exemplar model with a response-scaling mechanism suffered from overfilling in the linearly separable category structure. The results illustrate the need to make sure that the best-fitting model is not chasing error variance instead of variance attributed to the cognitive process it is supposed to model.     

Models for ordinal hierarchical classes analysis

This paper proposes an ordinal generalization of the hierarchical classes model originally proposed by De Boeck and Rosenberg (1998). Any hierarchical classes model implies a decomposition of a two-way two-mode binary arrayM into two component matrices, called bundle matrices, which represent the association relation and the set-theoretical relations among the elements of both modes inM. Whereas the original model restricts the bundle matrices to be binary, the ordinal hierarchical classes model assumes that the bundles are ordinal variables with a prespecified number of values. This generalization results in a classification model with classes ordered along ordinal dimensions. The ordinal hierarchical classes model is shown to subsume Coombs and Kao's (1955) model for nonmetric factor analysis. An algorithm is described to fit the model to a given data set and is subsequently evaluated in an extensive simulation study. An application of the model to student housing data is discussed.     

MASS COMMUNICATION AND BELIEF CHANGE: A TEST OF THREE MATHEMATICAL MODELS

Three mathematical models of communication and belief change were proposed and tested: a proportional change model, a belief certainty model, and an accumulated information model. A quick correlational check of the three models suggested that the accumulated information model was the superior with the belief certainty model being the most inferior of the three. Stronger support for the accumulated information model obtained using a more stringent test: a nonlinear bivariate regression which produced visual “plots” of empirical data that nearly duplicated the visual “plots” produced by the theoretical model. The accumulated information model states that belief change is proportional to the discrepancy between the original belief and the belief communicated in the message, and inversely proportional to the amount of information which the receiver has about the topic at the time the message is received. The belief certainty model was the most inferior of the three indicating that the degree to which a receiver is certain in conviction is unrelated to the communication-belief change relationship.     

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.     

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.     

纳入式分类分析法在潜在剖面模型的后续多元回归中的应用

纳入式分类分析法能克服传统的分类分析法对后续一元回归模型参数的低估,发挥潜在类别模型的后续分析简化变量间交互作用的功能。本文进一步将纳入式分类分析法拓展至潜在剖面模型后续的多元统计分析中。通过蒙特卡洛模拟实验,比较各种纳入变量的方法思路与后续分析模型在四种常见的多元回归模型中参数估计的表现。结果发现,纳入式分类分析法所需纳入的变量取决于后续分析中与因变量、潜类别变量的关系,且后续分析使用含交互作用的模型更为稳健。     

A unitary Neo-Piagetian/Neo-Eriksonian model of development: Fundamental assumptions and meta-issues

The article briefly reviews a stage model of change in human development that integrates a Neo-Piagetian model and a Neo-Eriksonian model into one unitary stage model across the lifespan (as presented in Young, 2011). The model suggests a generic model of stages in change. The article explores the fundamental assumptions underlying the model as well as considering meta-issues. The article adds to the book by describing the Neo-Eriksonian stages as reflections of a social “participatory” process. It adds to the change process in development by describing it as possibly reflecting “punctuated disequilibrium.” Finally, it adds a “multiple psychodynamics” 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.     

Hierarchical versus nonhierarchical models of movement sequence control: a reply to Klein

Klein (1983) has proposed a nonhierarchical logogen model to account for response timing and error data from a rapid finger-tapping task reported by Rosenbaum, Kenny, and Derr (1983). On grounds of parsimony, Klein's model cannot be easily distinguished from the hierarchical model proposed by Rosenbaum et al. However, the two models can be distinguished on other grounds. First, the logogen model cannot account for results from a second experiment reported in the Rosenbaum et al. article that the hierarchical model can account for. Second, the logogen model gives rise to a preponderence of incorrect response orders, whereas the hierarchical model does not. Third, the logogen model, unlike the hierarchical model, cannot account for the fact that people can produce complex, extended sequences of responses from memory.     

Paired comparisons with individual differences

A model of Bradley-Terry type for paired comparisons is considered. In addition to the usual parameters, the model allows for individual parameters and corresponding parameters for the choice-alternatives. The model is applied to a set of data from a Danish investigation of the attitude of blue collar workers towards alternative social gains. The proposed model is finally compared to a model recently suggested by Schönemann and Wang.     

A parallel rule activation and rule synthesis model for generalization in category learning

This paper proposes a distinction between primary generalization (transfer from stored exemplars to perceived targets) and secondary generalization (transfer from inferred abstractions to perceived targets). This distinction is embodied in the parallel rule activation and rule synthesis (PRAS) model, a production model capable of exemplar-based and abstraction-based categorization. As an exemplar model, the PRAS model is related to the generalized context model (Nosofsky, 1984). Exemplars are stored in memory encoded as condition-action rules. Working as an exemplar-based model, rules are activated on the basis of their strength and their similarity to the current to-be-categorized instance. Similarity between a target and a stored exemplar is weighted for attention to the dimensions of the psychological space. Depending on the value of a special parameter, the PRAS model is also able to operate as an abstraction model. In the latter case, it attempts to construct generalizing productions, which are activated according to the same rules as the exemplar-specific rules. The model is described in detail. It is applied to a number of important observations described in the research literature, and an experiment is reported that tested the usefulness of the proposed secondary-generalization mechanism. Finally, the discussion elaborates on the implications of the present study for further research.     

Five Licensure Portability Models for the Counseling Profession to Consider

This article presents licensure portability models for the counseling profession to consider. On the basis of a review of licensure portability literature discussed in other professions, the authors found 5 distinctive models: (a) nonprofit organization model, (b) mutual recognition model, (c) federal licensure model, (d) national licensure model, and (e) licensure language model. The article includes examples of professions using the models, application and implications of each model, and a call to the counseling profession for next steps.     

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.     

Markov Decision Process Measurement Model

Within-task actions can provide additional information on student competencies but are challenging to model. This paper explores the potential of using a cognitive model for decision making, the Markov decision process, to provide a mapping between within-task actions and latent traits of interest. Psychometric properties of the model are explored, and simulation studies report on parameter recovery within the context of a simple strategy game. The model is then applied to empirical data from an educational game. Estimates from the model are found to correlate more strongly with posttest results than a partial-credit IRT model based on outcome data alone.