The DINA model as a constrained general diagnostic model: Two variants of a model equivalency

The ‘deterministic‐input noisy‐AND’ (DINA) model is one of the more frequently applied diagnostic classification models for binary observed responses and binary latent variables. The purpose of this paper is to show that the model is equivalent to a special case of a more general compensatory family of diagnostic models. Two equivalencies are presented. Both project the original DINA skill space and design Q ‐matrix using mappings into a transformed skill space as well as a transformed Q ‐matrix space. Both variants of the equivalency produce a compensatory model that is mathematically equivalent to the (conjunctive) DINA model. This equivalency holds for all DINA models with any type of Q ‐matrix, not only for trivial (simple‐structure) cases. The two versions of the equivalency presented in this paper are not implied by the recently suggested log‐linear cognitive diagnosis model or the generalized DINA approach. The equivalencies presented here exist independent of these recently derived models since they solely require a linear – compensatory – general diagnostic model without any skill interaction terms. Whenever it can be shown that one model can be viewed as a special case of another more general one, conclusions derived from any particular model‐based estimates are drawn into question. It is widely known that multidimensional models can often be specified in multiple ways while the model‐based probabilities of observed variables stay the same. This paper goes beyond this type of equivalency by showing that a conjunctive diagnostic classification model can be expressed as a constrained special case of a general compensatory diagnostic modelling framework.     

Q矩阵包含错误的诊断测验分类准确性比较

Q矩阵是认知诊断测验的重要组成部分之一,围绕Q矩阵构建的诊断模型对Q矩阵中包含的错误较敏感。贝叶斯网分类模型是基于网络结点之间的关系构建的模型,将朴素贝叶斯网作为诊断模型,与DINA模型进行比较。模拟实验结果表明：Q矩阵中是否包含可达矩阵和错误界定的项目数量对DINA模型影响较大,对贝叶斯网模型影响较小;项目数量对DINA和贝叶斯网模型影响都较大;样本大小对贝叶斯网模型影响较大,对DINA模型影响较小。模拟研究结果显示,当Q矩阵中不包含可达阵、包含5个以上错误项目或样本数较大时,贝叶斯网分类模型优于DINA模型;而当Q矩阵中包含可达阵和5个(以下)错误项目时,DINA模型优于贝叶斯分类模型。     

Precipitate characteristics and selected area diffraction patterns of the β′ and Q′ precipitates in Al–Mg–Si–Cu alloys

In this study, the precipitate characteristics and selected area diffraction patterns (SADP) of the β?′ and Q?′ precipitates formed at the over-aged state of Al–Mg–Si–Cu alloys are systematically investigated by means of high-resolution transmission electron microscopy and transition matrix. The β?′ precipitates have two cross-sections, rectangle-shaped and round-shaped aligned with [0?0?1]_Al direction, but only rectangle-shaped cross-section exists for Q?′ precipitates. And, both of them have 12 variants and orientations with Al matrix. However, there are only three different zone axes, [0?0?0?1]_β?′, [1?4?5?0]_β?′, and [5?4?1?0]_β?′ for β?′ precipitates, and [0?0?0?1]_Q?′, [1?4?5?0]_Q?′, and [3?2 1?0]_Q?′ for Q?′ precipitates, parallel to the [0?0?1]_Al direction when they are precipitated from the Al matrix, respectively. Then, a new [0?0?1]_Al SADP model, which superposes diffraction patterns of the β?′ and Q?′ precipitates, is established. Furthermore, some “cross-shaped” diffraction streaks appeared at over-aged state can be explained reasonably by this model, which is good in agreement with the experimental data.     

Relation Formulas for Protoalgebraic Equality Free Quasivarieties; Pałasińska’s Theorem Revisited

We provide a new proof of the following Pa?asińska's theorem: Every finitely generated protoalgebraic relation distributive equality free quasivariety is finitely axiomatizable. The main tool we use are ${\mathcal{Q}}$ Q -relation formulas for a protoalgebraic equality free quasivariety ${\mathcal{Q}}$ Q . They are the counterparts of the congruence formulas used for describing the generation of congruences in algebras. Having this tool in hand, we prove a finite axiomatization theorem for ${\mathcal{Q}}$ Q when it has definable principal ${\mathcal{Q}}$ Q -subrelations. This is a property obtained by carrying over the definability of principal subcongruences, invented by Baker and Wang for varieties, and which holds for finitely generated protoalgebraic relation distributive equality free quasivarieties.     

<Literal>flankr</Literal>: An R package implementing computational models of attentional selectivity

The Eriksen flanker task (Eriksen and Eriksen, Perception & Psychophysics, 16, 143–149, 1974) is a classic test in cognitive psychology of visual selective attention. Two recent computational models have formalised the dynamics of the apparent increasing attentional selectivity during stimulus processing, but with very different theoretical underpinnings: The shrinking spotlight (SSP) model (White et al., Cognitive Psychology, 210–238, 2011) assumes attentional selectivity improves in a gradual, continuous manner; the dual stage two phase (DSTP) model (Hübner et al., Psychological Review, 759–784, 2010) assumes attentional selectivity changes from a low- to a high-mode of selectivity at a discrete time-point. This paper presents an R package—flankr—that instantiates both computational models. flankr allows the user to simulate data from both models, and to fit each model to human data. flankr provides statistics of the goodness-of-fit to human data, allowing users to engage in competitive model comparison of the DSTP and the SSP models on their own data. It is hoped that the utility of flankr lies in allowing more researchers to engage in the important issue of the dynamics of attentional selectivity.     

Estimating the average need of semantic knowledge from distributional semantic models

Continuous bag of words (CBOW) and skip-gram are two recently developed models of lexical semantics (Mikolov, Chen, Corrado, & Dean, Advances in Neural Information Processing Systems, 26, 3111–3119, 2013). Each has been demonstrated to perform markedly better at capturing human judgments about semantic relatedness than competing models (e.g., latent semantic analysis; Landauer & Dumais, Psychological Review, 104(2), 1997 211; hyperspace analogue to language; Lund & Burgess, Behavior Research Methods, Instruments, & Computers, 28(2), 203–208, 1996). The new models were largely developed to address practical problems of meaning representation in natural language processing. Consequently, very little attention has been paid to the psychological implications of the performance of these models. We describe the relationship between the learning algorithms employed by these models and Anderson’s rational theory of memory (J. R. Anderson & Milson, Psychological Review, 96(4), 703, 1989) and argue that CBOW is learning word meanings according to Anderson’s concept of needs probability. We also demonstrate that CBOW can account for nearly all of the variation in lexical access measures typically attributable to word frequency and contextual diversity—two measures that are conceptually related to needs probability. These results suggest two conclusions: One, CBOW is a psychologically plausible model of lexical semantics. Two, word frequency and contextual diversity do not capture learning effects but rather memory retrieval effects.     

Bayesian inference with Stan: A tutorial on adding custom distributions

When evaluating cognitive models based on fits to observed data (or, really, any model that has free parameters), parameter estimation is critically important. Traditional techniques like hill climbing by minimizing or maximizing a fit statistic often result in point estimates. Bayesian approaches instead estimate parameters as posterior probability distributions, and thus naturally account for the uncertainty associated with parameter estimation; Bayesian approaches also offer powerful and principled methods for model comparison. Although software applications such as WinBUGS (Lunn, Thomas, Best, & Spiegelhalter, Statistics and Computing, 10, 325–337, 2000) and JAGS (Plummer, 2003) provide “turnkey”-style packages for Bayesian inference, they can be inefficient when dealing with models whose parameters are correlated, which is often the case for cognitive models, and they can impose significant technical barriers to adding custom distributions, which is often necessary when implementing cognitive models within a Bayesian framework. A recently developed software package called Stan (Stan Development Team, 2015) can solve both problems, as well as provide a turnkey solution to Bayesian inference. We present a tutorial on how to use Stan and how to add custom distributions to it, with an example using the linear ballistic accumulator model (Brown & Heathcote, Cognitive Psychology, 57, 153–178. doi: 10.1016/j.cogpsych.2007.12.002, 2008).     

A Polytomous Model of Cognitive Diagnostic Assessment for Graded Data

Pursuing the line of the difference models in IRT (Thissen &; Steinberg, 1986 Thissen, D., &; Steinberg, L. (1986). A taxonomy of item response models. Psychometrika, 51:567–577. doi:10.1007/BF02295596.[Crossref], [Web of Science ®] , [Google Scholar]), this article proposed a new cognitive diagnostic model for graded/polytomous data based on the deterministic input, noisy, and gate (Haertel, 1989 Haertel, E. H. (1989). Using restricted latent class models to map the skill structure of achievement items. Journal of Educational Measurement, 26, 333–352. doi:10.1111/j.1745-3984.1989.tb00336.x.[Crossref], [Web of Science ®] , [Google Scholar]; Junker &; Sijtsma, 2001 Junker, B. W., &; Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25, 258–272. doi:10.1177/01466210122032064.[Crossref], [Web of Science ®] , [Google Scholar]), which is named the DINA model for graded data (DINA-GD). We investigated the performance of a full Bayesian estimation of the proposed model. In the simulation, the classification accuracy and item recovery for the DINA-GD model were investigated. The results indicated that the proposed model had acceptable examinees' correct attribute classification rate and item parameter recovery. In addition, a real-data example was used to illustrate the application of this new model with the graded data or polytomously scored items.     

Evidence for independent parallel channels in tachistoscopic perception

This paper reviews the implications of a number of experimental results for a test between two different types of models of perceptual processing: models that assume a limitation of perceptual capacity vs models that postulate independent, parallel perceptual channels. The results of recent “detection” experiments (e.g., Estes & Taylor, 1966) have been consistent with the limited-capacity model developed by Rumelhart (1970). The same results, however, are predicted by the “ICC” independent-parallel-channels model, an extension of work by Eriksen and Spencer (1969) developed in the present paper. This model emphasizes the interaction of two factors: decisional properties of the detection task, plus perceptual confusion phenomena known to occur under tachistoscopic conditions.Two experiments relevant to a test between the ICC and Rumelhart conceptions are reported. Experiment I involved a “time-sharing” paradigm that varied the demands of two detection tasks performed within a single trial. Experiment II involved the elimination of certain perceptual confusion phenomena. The results of Expts I and II appeared consistent with the ICC model but inconsistent with the Rumelhart model. After consideration of alternative limited-capacity models, it was concluded that: (1) a decision-confusion interaction is a necessary component of information-processing models, and that (2) the ICC independent-parallel-channels model is sufficient to account for the broad spectrum of experimental results reviewed.     

When “All the Five Circles” are Four: New Exercises in Domain Restriction

The domain of a quantifier is determined by a variety of factors, which broadly speaking fall into two types. On the one hand, the context of utterance plays a role: if the focus of attention is on a particular collection of kangaroos, for example, then “Q kangaroos” is likely to range over the individuals in that set. On the other hand, the utterance itself will help to establish the quantificational domain, inter alia through presuppositions triggered within the sentence. In this paper, we concentrate our attention on constructions like the following, in which “the square to which ... ” is the critical presupposition trigger:

1. (i)
   Q circles ...
    
2. (ii)
   Q of these circles ...
    
3. (iii)
   Q of these five circles ... ... have the same colour as the square to which they are connected.
    

Many theories predict that all instances of these schemata will give rise to the presupposition that every circle is connected to a square. We present an analysis which predicts that these sentences should generally be accepted in a context in which not all the circles are connected to a square, with one exception only: if a quantified sentence is of type (iii) and Q is non-intersective, then the sentence should be more likely to be rejected. Furthermore, we predict that manipulating the context so as to make the connected circles more or less salient should have an effect on statements with non-intersective quantifiers only. These predictions were tested in a series of experiments.     

Protoalgebraic logics

There exist important deductive systems, such as the non-normal modal logics, that are not proper subjects of classical algebraic logic in the sense that their metatheory cannot be reduced to the equational metatheory of any particular class of algebras. Nevertheless, most of these systems are amenable to the methods of universal algebra when applied to the matrix models of the system. In the present paper we consider a wide class of deductive systems of this kind called protoalgebraic logics. These include almost all (non-pathological) systems of prepositional logic that have occurred in the literature. The relationship between the metatheory of a protoalgebraic logic and its matrix models is studied. The following results are obtained for any finite matrix model U of a filter-distributive protoalgebraic logic : (I) The extension _U of is finitely axiomatized (provided has only finitely many inference rules); (II) _U has only finitely many extensions.     

Formulation and Application of the Hierarchical Generalized Random-Situation Random-Weight MIRID

The process-component approach has become quite popular for examining many psychological concepts. A typical example is the model with internal restrictions on item difficulty (MIRID) described by Butter (1994) Butter, R. 1994. Item response models with internal restrictions on item difficulty, Doctoral thesis Leuven, , Belgium: Katholieke Universiteit..  [Google Scholar] and Butter, De Boeck, and Verhelst (1998). This study proposes a hierarchical generalized random-situation random-weight MIRID. The proposed model is more flexible for formulating endogenous latent variables within a multilevel framework, allowing the analysis of polytomous data with complex models (e.g., including item discriminations, random situations, random weights, and heteroskedasticity). The parameters in the proposed model can be estimated using the computer program WinBUGS, which adopts Markov Chain Monte Carlo algorithms. To illustrate the application of the proposed model, a real data set about guilt is analyzed and a comparison of MIRIDs for various conditions is conducted.     

Detecting Multiple Random Changepoints in Bayesian Piecewise Growth Mixture Models

Piecewise growth mixture models are a flexible and useful class of methods for analyzing segmented trends in individual growth trajectory over time, where the individuals come from a mixture of two or more latent classes. These models allow each segment of the overall developmental process within each class to have a different functional form; examples include two linear phases of growth, or a quadratic phase followed by a linear phase. The changepoint (knot) is the time of transition from one developmental phase (segment) to another. Inferring the location of the changepoint(s) is often of practical interest, along with inference for other model parameters. A random changepoint allows for individual differences in the transition time within each class. The primary objectives of our study are as follows: (1) to develop a PGMM using a Bayesian inference approach that allows the estimation of multiple random changepoints within each class; (2) to develop a procedure to empirically detect the number of random changepoints within each class; and (3) to empirically investigate the bias and precision of the estimation of the model parameters, including the random changepoints, via a simulation study. We have developed the user-friendly package BayesianPGMM for R to facilitate the adoption of this methodology in practice, which is available at https://github.com/lockEF/BayesianPGMM. We describe an application to mouse-tracking data for a visual recognition task.     

Fixed- and random-effects meta-analytic structural equation modeling: Examples and analyses in R

Meta-analytic structural equation modeling (MASEM) combines the ideas of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Cheung and Chan (Psychological Methods 10:40–64, 2005b, Structural Equation Modeling 16:28–53, 2009) proposed a two-stage structural equation modeling (TSSEM) approach to conducting MASEM that was based on a fixed-effects model by assuming that all studies have the same population correlation or covariance matrices. The main objective of this article is to extend the TSSEM approach to a random-effects model by the inclusion of study-specific random effects. Another objective is to demonstrate the procedures with two examples using the metaSEM package implemented in the R statistical environment. Issues related to and future directions for MASEM are discussed.     

Testing the validity of conflict drift-diffusion models for use in estimating cognitive processes: A parameter-recovery study

Researchers and clinicians are interested in estimating individual differences in the ability to process conflicting information. Conflict processing is typically assessed by comparing behavioral measures like RTs or error rates from conflict tasks. However, these measures are hard to interpret because they can be influenced by additional processes like response caution or bias. This limitation can be circumvented by employing cognitive models to decompose behavioral data into components of underlying decision processes, providing better specificity for investigating individual differences. A new class of drift-diffusion models has been developed for conflict tasks, presenting a potential tool to improve analysis of individual differences in conflict processing. However, measures from these models have not been validated for use in experiments with limited data collection. The present study assessed the validity of these models with a parameter-recovery study to determine whether and under what circumstances the models provide valid measures of cognitive processing. Three models were tested: the dual-stage two-phase model (Hübner, Steinhauser, & Lehle, Psychological Review, 117(3), 759–784, 2010), the shrinking spotlight model (White, Ratcliff, & Starns, Cognitive Psychology, 63(4), 210–238, 2011), and the diffusion model for conflict tasks (Ulrich, Schröter, Leuthold, & Birngruber, Cogntive Psychology, 78, 148–174, 2015). The validity of the model parameters was assessed using different methods of fitting the data and different numbers of trials. The results show that each model has limitations in recovering valid parameters, but they can be mitigated by adding constraints to the model. Practical recommendations are provided for when and how each model can be used to analyze data and provide measures of processing in conflict tasks.     

Hypothesis Testing of the <Emphasis Type="Italic">Q</Emphasis>-matrix

The recent surge of interests in cognitive assessment has led to the development of cognitive diagnosis models. Central to many such models is a specification of the Q-matrix, which relates items to latent attributes that have natural interpretations. In practice, the Q-matrix is usually constructed subjectively by the test designers. This could lead to misspecification, which could result in lack of fit of the underlying statistical model. To test possible misspecification of the Q-matrix, traditional goodness of fit tests, such as the Chi-square test and the likelihood ratio test, may not be applied straightforwardly due to the large number of possible response patterns. To address this problem, this paper proposes a new statistical method to test the goodness fit of the Q-matrix, by constructing test statistics that measure the consistency between a provisional Q-matrix and the observed data for a general family of cognitive diagnosis models. Limiting distributions of the test statistics are derived under the null hypothesis that can be used for obtaining the test p-values. Simulation studies as well as a real data example are presented to demonstrate the usefulness of the proposed method.     

The Reduced RUM as a Logit Model: Parameterization and Constraints

Cognitive diagnosis models (CDMs) for educational assessment are constrained latent class models. Examinees are assigned to classes of intellectual proficiency defined in terms of cognitive skills called attributes, which an examinee may or may not have mastered. The Reduced Reparameterized Unified Model (Reduced RUM) has received considerable attention among psychometricians. Markov Chain Monte Carlo (MCMC) or Expectation Maximization (EM) are typically used for estimating the Reduced RUM. Commercial implementations of the EM algorithm are available in the latent class analysis (LCA) routines of Latent GOLD and Mplus, for example. Fitting the Reduced RUM with an LCA routine requires that it be reparameterized as a logit model, with constraints imposed on the parameters. For models involving two attributes, these have been worked out. However, for models involving more than two attributes, the parameterization and the constraints are nontrivial and currently unknown. In this article, the general parameterization of the Reduced RUM as a logit model involving any number of attributes and the associated parameter constraints are derived. As a practical illustration, the LCA routine in Mplus is used for fitting the Reduced RUM to two synthetic data sets and to a real-world data set; for comparison, the results obtained by using the MCMC implementation in OpenBUGS are also provided.     

Finite and infinite state confusion models

A confusion model is defined as a model that decomposes response probabilities in stimulus identification experiments into perceptual parameters and response parameters. Historically, confusion models fall into two groups. Models in Group I, which includes Townsend's (Perception and Psychophysics, 1971, 9, 40–50) overlap model, were developed on the basis of the notion that stimulus identification is mediated by a finite number of internal states. We call the general class of models that have this processing interpretation finite state confusion models. Models in Group II, which includes Luce's (R. O. Luce et al., Eds., Handbook of Mathematical Psychology (Vol. I), New York: Wiley, 1963) biased choice model, were not developed on the basis of an explicit processing interpretation. It is shown here that models in Group II are not finite state confusion models. We prove in addition that except for Falmagne's (Journal of Mathematical Psychology, 1972, 9, 206–224) simply biased model models in Group II belong to a certain class of infinite state confusion models, namely, models asserting that stimulus identification is mediated by a continuous space of vectors representing detector activation levels.     

A New Model for Acquiescence at the Interface of Psychometrics and Cognitive Psychology

ABSTRACT

When measuring psychological traits, one has to consider that respondents often show content-unrelated response behavior in answering questionnaires. To disentangle the target trait and two such response styles, extreme responding and midpoint responding, Böckenholt (2012a Böckenholt, U. (2012a). Modeling multiple response processes in judgment and choice. Psychological Methods, 17, 665–678. doi:10.1037/a0028111[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) developed an item response model based on a latent processing tree structure. We propose a theoretically motivated extension of this model to also measure acquiescence, the tendency to agree with both regular and reversed items. Substantively, our approach builds on multinomial processing tree (MPT) models that are used in cognitive psychology to disentangle qualitatively distinct processes. Accordingly, the new model for response styles assumes a mixture distribution of affirmative responses, which are either determined by the underlying target trait or by acquiescence. In order to estimate the model parameters, we rely on Bayesian hierarchical estimation of MPT models. In simulations, we show that the model provides unbiased estimates of response styles and the target trait, and we compare the new model and Böckenholt’s model in a recovery study. An empirical example from personality psychology is used for illustrative purposes.