A Latent Block Distance-Association Model for Profile by Profile Cross-Classified Categorical Data

Abstract

Distance association models constitute a useful tool for the analysis and graphical representation of cross-classified data in which distances between points inversely describe the association between two categorical variables. When the number of cells is large and the data counts result in sparse tables, the combination of clustering and representation reduces the number of parameters to be estimated and facilitates interpretation. In this article, a latent block distance-association model is proposed to apply block clustering to the outcomes of two categorical variables while the cluster centers are represented in a low dimensional space in terms of a distance-association model. This model is particularly useful for contingency tables in which both the rows and the columns are characterized as profiles of sets of response variables. The parameters are estimated under a Poisson sampling scheme using a generalized EM algorithm. The performance of the model is tested in a Monte Carlo experiment, and an empirical data set is analyzed to illustrate the model.     

ADPROCLUS: a graphical user interface for fitting additive profile clustering models to object by variable data matrices

In many areas of psychology, one is interested in disclosing the underlying structural mechanisms that generated an object by variable data set. Often, based on theoretical or empirical arguments, it may be expected that these underlying mechanisms imply that the objects are grouped into clusters that are allowed to overlap (i.e., an object may belong to more than one cluster). In such cases, analyzing the data with Mirkin’s additive profile clustering model may be appropriate. In this model: (1) each object may belong to no, one or several clusters, (2) there is a specific variable profile associated with each cluster, and (3) the scores of the objects on the variables can be reconstructed by adding the cluster-specific variable profiles of the clusters the object in question belongs to. Until now, however, no software program has been publicly available to perform an additive profile clustering analysis. For this purpose, in this article, the ADPROCLUS program, steered by a graphical user interface, is presented. We further illustrate its use by means of the analysis of a patient by symptom data matrix.     

Beyond left and right: Automaticity and flexibility of number-space associations

Close links exist between the processing of numbers and the processing of space: relatively small numbers are preferentially associated with a left-sided response while relatively large numbers are associated with a right-sided response (the SNARC effect). Previous work demonstrated that the SNARC effect is triggered in an automatic manner and is highly flexible. Besides the left-right dimension, numbers associate with other spatial response mappings such as close/far responses, where small numbers are associated with a close response and large numbers with a far response. In two experiments we investigate the nature of this association. Associations between magnitude and close/far responses were observed using a magnitude-irrelevant task (Experiment 1: automaticity) and using a variable referent task (Experiment 2: flexibility). While drawing a strong parallel between both response mappings, the present results are also informative with regard to the question about what type of processing mechanism underlies both the SNARC effect and the association between numerical magnitude and close/far response locations.     

Single and Multiple Ability Estimation in the SEM Framework: A Noninformative Bayesian Estimation Approach

Latent variable models with many categorical items and multiple latent constructs result in many dimensions of numerical integration, and the traditional frequentist estimation approach, such as maximum likelihood (ML), tends to fail due to model complexity. In such cases, Bayesian estimation with diffuse priors can be used as a viable alternative to ML estimation. This study compares the performance of Bayesian estimation with ML estimation in estimating single or multiple ability factors across 2 types of measurement models in the structural equation modeling framework: a multidimensional item response theory (MIRT) model and a multiple-indicator multiple-cause (MIMIC) model. A Monte Carlo simulation study demonstrates that Bayesian estimation with diffuse priors, under various conditions, produces results quite comparable with ML estimation in the single- and multilevel MIRT and MIMIC models. Additionally, an empirical example utilizing the Multistate Bar Examination is provided to compare the practical utility of the MIRT and MIMIC models. Structural relationships among the ability factors, covariates, and a binary outcome variable are investigated through the single- and multilevel measurement models. The article concludes with a summary of the relative advantages of Bayesian estimation over ML estimation in MIRT and MIMIC models and suggests strategies for implementing these methods.     

Ordinal state-trait regression for intensive longitudinal data

In many psychological studies, in particular those conducted by experience sampling, mental states are measured repeatedly for each participant. Such a design allows for regression models that separate between- from within-person, or trait-like from state-like, components of association between two variables. But these models are typically designed for continuous variables, whereas mental state variables are most often measured on an ordinal scale. In this paper we develop a model for disaggregating between- from within-person effects of one ordinal variable on another. As in standard ordinal regression, our model posits a continuous latent response whose value determines the observed response. We allow the latent response to depend nonlinearly on the trait and state variables, but impose a novel penalty that shrinks the fit towards a linear model on the latent scale. A simulation study shows that this penalization approach is effective at finding a middle ground between an overly restrictive linear model and an overfitted nonlinear model. The proposed method is illustrated with an application to data from the experience sampling study of Baumeister et al. (2020, Personality and Social Psychology Bulletin, 46, 1631).     

Analysis of clustered data in community psychology: With an example from a worksite smoking cessation project

Although it is common in community psychology research to have data at both the community, or cluster, and individual level, the analysis of such clustered data often presents difficulties for many researchers. Since the individuals within the cluster cannot be assumed to be independent, the use of many traditional statistical techniques that assumes independence of observations is problematic. Further, there is often interest in assessing the degree of dependence in the data resulting from the clustering of individuals within communities. In this paper, a random-effects regression model is described for analysis of clustered data. Unlike ordinary regression analysis of clustered data, random-effects regression models do not assume that each observation is independent, but do assume data within clusters are dependent to some degree. The degree of this dependency is estimated along with estimates of the usual model parameters, thus adjusting these effects for the dependency resulting from the clustering of the data. Models are described for both continuous and dichotomous outcome variables, and available statistical software for these models is discussed. An analysis of a data set where individuals are clustered within firms is used to illustrate fetatures of random-effects regression analysis, relative to both individual-level analysis which ignores the clustering of the data, and cluster-level analysis which aggregates the individual data. Preparation of this article was supported by National Heart, Lung, and Blood Institute Grant R18 HL42987-01A1, National Institutes of Mental Health Grant MH44826-01A2, and University of Illinois at Chicago Prevention Research Center Developmental Project CDC Grant R48/CCR505025.     

The BUMP model of response planning: variable horizon predictive control accounts for the speed-accuracy tradeoffs and velocity profiles of aimed movement

The BUMP model is a comprehensive discrete-time computational model of response planning. Developed within the Adaptive Model Theory framework, it is based on intermittent optimal control. The theory posits a basic unit of motor production (BUMP) that is determined by a planning system that operates intermittently at fixed intervals of time. Given sensory information about the position and velocity of the actual response as well as the predicted future state of the target, the response planning system generates an optimal response trajectory to reach the predicted future state of the target and to compensate for executional error. The ability to vary the duration, or prediction horizon, of the trajectory gives rise to the concept of variable horizon predictive control. We propose that the combination of signal-dependent noise in the nervous system and variable horizon predictive control accounts for the well-known speed-accuracy tradeoffs and velocity profiles in aimed movements. Conducting a simulation study, we found that on one extreme of variable horizon control, a receding horizon strategy reproduced Fitts' law and corresponding asymmetrical velocity profiles. On the other extreme, a fixed horizon strategy reproduced the linear tradeoff and corresponding symmetrical velocity profiles. We conclude that the BUMP model provides a unifying theoretical bridge between speed-accuracy tradeoffs and the accompanying velocity profiles of aimed movement.     

Improved stopping rules for the design of efficient small-sample experiments in biomedical and biobehavioral research

Sequential stopping rules (SSRs) should augment traditional hypothesis tests in many planned experiments, because they can provide the same statistical power with up to 30% fewer subjects without additional education or software. This article includes new Monte-Carlo-generated power curves and tables of stopping criteria based on the p values from simulated t tests and one-way ANOVAs. The tables improve existing SSR techniques by holding alpha very close to a target value when 1–10 subjects are added at each iteration. The emphasis is on small sample sizes (3–40 subjects per group) and large standardized effect sizes (0.8–2.0). The generality of the tables for dependent samples and one-tailed tests is discussed. SSR methods should be of interest to ethics bodies governing research when it is desirable to limit the number of subjects tested, such as in studies of pain, experimental disease, or surgery with animal or human subjects.     

Kinetic analysis of oxygen dynamics under a variable work rate

Measurements of oxygen uptake are central to methods for the assessment of physical fitness and endurance capabilities in athletes. Two important parameters extracted from such data of incremental exercise tests are the maximal oxygen uptake and the critical power. A commonly accepted model of the dynamics of oxygen uptake during exercise at a constant work rate comprises a constant baseline oxygen uptake, an exponential fast component, and another exponential slow component for heavy and severe work rates. We have generalized this model to variable load protocols with differential equations that naturally correspond to the standard model for a constant work rate. This provides the means for predicting the oxygen uptake response to variable load profiles including phases of recovery. The model parameters have been fitted for individual subjects from a cycle ergometer test, including the maximal oxygen uptake and critical power. The model predictions have been validated by data collected in separate tests. Our findings indicate that the oxygen kinetics for a variable exercise load can be predicted using the generalized mathematical standard model. Such models can be applied in the field where the constant work rate assumption generally is not valid.     

Numerical-spatial representation affects spatial coding: binding errors across the numerical distance effect

Does numerical-spatial representation affect feature binding? Studies of visual attention show that poor spatial coding leads to illusory conjunctions (ICs). In numerical cognition, it has been shown that numbers and space are not totally dissociated. This association underlies the numerical distance effect (DE): faster responses as the distance between the compared digits becomes larger (2 7 vs. 2 4). We used the DE to test whether numerical-spatial representation is available to visual processes that rely on spatial coding, such as feature binding. Participants reported the larger of two colored numbers. Both numerical distance (distances 2 and 5) and number–space congruity (e.g., congruent pair, 1 3; incongruent pair, 3 1) were analyzed. Results showed a higher proportion of ICs for distance 2 than for distance 5, providing strong evidence that numerical-spatial representation (1) entails a strong location code and (2) is available to visual processes that rely on location information.     

Crossmodal integration in the identification of consonant segments

Although speechreading can be facilitated by auditory or tactile supplements, the process that integrates cues across modalities is not well understood. This paper describes two “optimal processing” models for the types of integration that can be used in speechreading consonant segments and compares their predictions with those of the Fuzzy Logical Model of Perception (FLMP, Massaro, 1987). In “pre-labelling” integration, continuous sensory data is combined across modalities before response labels are assigned. In “post-labelling” integration, the responses that would be made under unimodal conditions are combined, and a joint response is derived from the pair. To describe pre-labelling integration, confusion matrices are characterized by a multidimensional decision model that allows performance to be described by a subject's sensitivity and bias in using continuous-valued cues. The cue space is characterized by the locations of stimulus and response centres. The distance between a pair of stimulus centres determines how well two stimuli can be distinguished in a given experiment. In the multimodal case, the cue space is assumed to be the product space of the cue spaces corresponding to the stimulation modes. Measurements of multimodal accuracy in five modern studies of consonant identification are more consistent with the predictions of the pre-labelling integration model than the FLMP or the post-labelling model.     

运用规则空间模型识别解题中的认知错误

运用规则空间模型识别学生解题中的认知错误,该模型将认知心理学,项目反应理论和数据库的代数理论相结合,将被试的二值反应模式映射为笛卡尔乘积空间的一组序偶,然后计算被试和错误规则在该空间的代表性位置之间的马氏距离,并通过贝叶斯决策准则划分被试的错误类型,根据６４４名中学生对３０个数学题目的反应,识别出其中８６％的学生可以被划分人１８种认知错误类型中。     

Telling things apart: the distance between response keys influences categorization times

People use spatial distance to talk and think about differences between concepts, and it has been argued that using space to think about different categories provides a scaffold for the categorization process. In the current study, we investigated the possibility that the distance between response keys can influence categorization times in binary classification tasks. In line with the hypothesis that distance between response keys can facilitate response selection in a key-press version of the Stroop task, our results showed that responses on incongruent Stroop trials were significantly facilitated when participants performed the Stroop task with response keys located far apart, compared with when they performed the task with response keys located close together. These results support the idea that the spatial structuring of response options facilitates categorizations that require cognitive effort, and that people can incorporate environmental structures such as spatial distance in their thought processes. Keeping your hands apart might actually help to keep things apart in your mind.     

Evaluating Fund Performance by Compromise Programming with Linear‐Quadratic Composite Metric: An Actual Case on The CaixaBank in Spain

This paper proposes an additive measure on the basis of compromise programming to evaluate fund performance from multiple criteria, of which the most usual are profitability and risk. This proposal is motivated by the fact that compromise programming is a sound decision support model to obtain scores of alternatives by minimizing weighted distances to an ideal point, the weights reflecting the investor's preferences for the criteria. To define the distance objective function, the linear‐quadratic composite metric is used, which combines advantages of linear and non‐linear objective functions. A critical advantage of compromise programming for fund performance evaluation is that the model can be extended to more than two financial criteria while other measures currently used (either ratio‐based or leverage‐based measures) only consider two criteria, say, profitability and risk. In the application, three investor's profiles are defined, which involve different weighting systems and lead to different fund rankings. These rankings are compared with domination relationships, the latter formulating if a fund is dominated or non‐dominated by convex combinations of other funds. Numerical tables are provided with data, computational process and results, which are analysed. Copyright © 2012 John Wiley & Sons, Ltd.     

Mechanics of the animate.

Behavior is treated as basic physics. Dimensions are identified and their transformations from physical specification to axes in behavioral space are suggested. Responses are treated as action patterns arrayed along a continuum of activation energy. Behavior is seen as movement along a trajectory through this behavior space. Incentives or reinforcers are attractors in behavior space, at the centers of basins of lowered potential. Trajectories impinging on such basins may be captured; repeated capture will warp the trajectory toward a geodesic, a process called conditioning. Conditioning is enhanced by contiguity, the proximity between the measured behavior and the incentive at the end of the trajectory, and by contingency, the depth of the trajectory below the average level of the potential energy landscape. Motivation is seen as the potential of an organism for motion under the forces impinging on it. Degree of motivation is characterized by the depth of the potential field, with low motivation corresponding to a flat field and a flat gradient of activation energy. Drives are the forces of incentives propagated through behavior space. Different laws for the attenuation of drive with behavioral distance are discussed, as is the dynamics of action. The basic postulate of behavior mechanics is incentive-tracking in behavior space, the energy for which is provided by decreases in potential. The relation of temporal gradients to response differentiation and temporal discrimination is analyzed. Various two-body problems are sketched to illustrate the application of these ideas to association, choice, scalar timing, self-control, and freedom.     

Intensity and reverberation as factors in the auditory perception of egocentric distance

Both auditory intensity and reverberation have previously been shown to be sufficient to produce systematically varying judgments of perceived distance when several values of the variable are presented repeatedly to the same observer. Such studies do not, however, indicate clearly whether these cues are functioning in an absolute or in a relative manner. An absolute cue to auditory distance would require that two groups presented with different values of the variable in question should report different values of perceived distance. Two experiments are reported in which intensity variation and reverberation are examined. The results showed that auditory intensity differences over a range of 20 dB did not serve as an absolute cue to auditory distance, but could serve as a strong cue to changes in such distance. A comparison of data obtained in a normally reverberatory setting (Experiment 1) and an anechoic chamber (Experiment 2) indicated that the state of reverberation could serve as an absolute cue, with greater reverberation being associated with greater perceived distances. Some of the results were discussed in terms of the possibility that the specific distance tendency (a concept developed to handle some phenomena in visual space perception) might have applicability to the study of auditory perceived distance as well.

     

谱聚类算法在不同属性层级结构诊断评估中的应用

聚类分析已成功用于认知诊断评估(CDA)中,使用广泛的聚类分析方法为K-means算法,有研究已证明K-means在CDA中具有较好的聚类效果。而谱聚类算法通常比K-means分类效果更佳,本研究将谱聚类算法引进CDA,探讨了属性层级结构、属性个数、样本量和失误率对该方法的影响。研究发现：（1）谱聚类算法要比K-means提供更好的聚类结果,尤其在实验条件较苛刻时,谱聚类算法更加稳健;（2）线型结构聚类效果最好,收敛型和发散型相近,独立型结构表现较差;（3）属性个数和失误率增加后,聚类效果会下降;（4）样本量增加后,聚类效果有所提升,但K-means方法有时会有反向结果出现。     

Idiosyncratic profiles of collinearity error using segments and dot pairs

It is well known that judgments of oblique line segments are more variable and less accurate than are judgments of horizontal or vertical segments, i.e., the “oblique effect.” A prior study from our laboratories confirmed these differentials for a task in which the collinearity of segments at various angular positions was judged. Further, that study found that each observer manifests a distinct, idiosyncratic profile of errors across the 360° range. These error tendencies are conspicuous in models derived by harmonic analysis, and we describe significant excursions of a given model as “delta errors.” The present experiments found complex profiles of delta error with various stimulus and test conditions. A given subject manifested similar models of delta error when judging collinearity of dot pairs versus line segments. In the prior work the segments to be judged were asymmetrically positioned upon the test sheet. However, the asymmetric positioning is not responsible for the errors, as the present work found errors excursions with a round display field. Similar profiles of delta error were found when subjects were allowed to mark an open space, versus being required to respond at a specific distance (indicated by a target circle). This addresses questions of whether the error should be measured as an angle. In the two final experiments, we present evidence that the source of delta error within the nervous system is at the point of binocular synthesis of the information from the two eyes, or beyond, and the effects are not due to errors of reaching. Potential neural substrates for these complex, idiosyncratic error tendencies are discussed. Received: 16 June 2000 / Accepted: 10 March 2001     

Multilevel multidimensional item response model with a multilevel latent covariate

In a pre‐test–post‐test cluster randomized trial, one of the methods commonly used to detect an intervention effect involves controlling pre‐test scores and other related covariates while estimating an intervention effect at post‐test. In many applications in education, the total post‐test and pre‐test scores, ignoring measurement error, are used as response variable and covariate, respectively, to estimate the intervention effect. However, these test scores are frequently subject to measurement error, and statistical inferences based on the model ignoring measurement error can yield a biased estimate of the intervention effect. When multiple domains exist in test data, it is sometimes more informative to detect the intervention effect for each domain than for the entire test. This paper presents applications of the multilevel multidimensional item response model with measurement error adjustments in a response variable and a covariate to estimate the intervention effect for each domain.