Bayesian Extended Redundancy Analysis: A Bayesian Approach to Component-based Regression with Dimension Reduction

Abstract

Extended redundancy analysis (ERA) combines linear regression with dimension reduction to explore the directional relationships between multiple sets of predictors and outcome variables in a parsimonious manner. It aims to extract a component from each set of predictors in such a way that it accounts for the maximum variance of outcome variables. In this article, we extend ERA into the Bayesian framework, called Bayesian ERA (BERA). The advantages of BERA are threefold. First, BERA enables to make statistical inferences based on samples drawn from the joint posterior distribution of parameters obtained from a Markov chain Monte Carlo algorithm. As such, it does not necessitate any resampling method, which is on the other hand required for (frequentist’s) ordinary ERA to test the statistical significance of parameter estimates. Second, it formally incorporates relevant information obtained from previous research into analyses by specifying informative power prior distributions. Third, BERA handles missing data by implementing multiple imputation using a Markov Chain Monte Carlo algorithm, avoiding the potential bias of parameter estimates due to missing data. We assess the performance of BERA through simulation studies and apply BERA to real data regarding academic achievement.     

The use of item scores and response times to detect examinees who may have benefited from item preknowledge

According to Wollack and Schoenig (2018, The Sage encyclopedia of educational research, measurement, and evaluation. Thousand Oaks, CA: Sage, 260), benefiting from item preknowledge is one of the three broad types of test fraud that occur in educational assessments. We use tools from constrained statistical inference to suggest a new statistic that is based on item scores and response times and can be used to detect examinees who may have benefited from item preknowledge for the case when the set of compromised items is known. The asymptotic distribution of the new statistic under no preknowledge is proved to be a simple mixture of two χ² distributions. We perform a detailed simulation study to show that the Type I error rate of the new statistic is very close to the nominal level and that the power of the new statistic is satisfactory in comparison to that of the existing statistics for detecting item preknowledge based on both item scores and response times. We also include a real data example to demonstrate the usefulness of the suggested statistic.     

两宋瘟疫灾害考述

两宋时期爆发的瘟疫次数比较多,在时间上,不是呈平均之势,而是不规则,无周期的;空间分布上呈现出南方比北方多,东部比西部多的特征。由于瘟疫造成的危害比较大,当时人们在和瘟疫的多次斗争中摸索出一些防治措施,积累了相当丰富的经验。     

Human group choice: discrete-trial and free-operant tests of the ideal free distribution

Ideal free distribution theory predicts that foragers will form groups proportional in number to the resources available in alternative resource sites or patches, a phenomenon termed habitat matching. Three experiments tested this prediction with college students in discrete-trial simulations and a free-operant simulation. Sensitivity to differences in programmed reinforcement rates was quantified by using the sensitivity parameter of the generalized matching law (s). The first experiment, replicating prior published experiments, produced a greater degree of undermatching for the initial choice (s = 0.59) compared to final choices (s = 0.86). The second experiment, which extended prior findings by allowing only one choice per trial, produced comparable undermatching (s = 0.82). The third experiment used free-operant procedures more typical of laboratory studies of habitat matching with other species and produced the most undermatching (s = 0.71). The results of these experiments replicated previous results with human groups, supported predictions of the ideal free distribution, and suggested that undermatching represents a systematic deviation from the ideal free distribution. These results are consistent with a melioration account of individual behavior as the basis for group choice.     

Group choice: the ideal free distribution of human social behavior

Group choice refers to the distribution of group members between two choice alternatives over time. The ideal free distribution (IFD), an optimal foraging model from behavioral ecology, predicts that the ratio of foragers at two resource sites should equal the ratio of obtained resources, a prediction that is formally analogous to the matching law of individual choice, except that group choice is a social phenomenon. Two experiments investigated the usefulness of IFD analyses of human group choice and individual-based explanations that might account for the group-level events. Instead of nonhuman animals foraging at two sites for resources, a group of humans chose blue and red cards to receive points that could earn cash prizes. The groups chose blue and red cards in ratios in positive relation to the ratios of points associated with the cards. When group choice ratios and point ratios were plotted on logarithmic coordinates and fitted with regression lines, the slopes (i.e., sensitivity measures) approached 1.0 but tended to fall short of it (i.e., undermatching), with little bias and little unaccounted for variance. These experiments demonstrate that an IFD analysis of group choice is possible and useful, and suggest that group choice may be explained by the individual members' tendency to optimize reinforcement.     

中国古代心理学思想中的注意问题

本文根据古代思想家的有关言论,探讨了他们的注意心理思想,即注意的慨念。特征,分心与分散,分配与集中,注意与感知、记忆、思维的关系,注意在学习中的作用。     

A Unified Approach to Power Calculation and Sample Size Determination for Random Regression Models

The underlying statistical models for multiple regression analysis are typically attributed to two types of modeling: fixed and random. The procedures for calculating power and sample size under the fixed regression models are well known. However, the literature on random regression models is limited and has been confined to the case of all variables having a joint multivariate normal distribution. This paper presents a unified approach to determining power and sample size for random regression models with arbitrary distribution configurations for explanatory variables. Numerical examples are provided to illustrate the usefulness of the proposed method and Monte Carlo simulation studies are also conducted to assess the accuracy. The results show that the proposed method performs well for various model specifications and explanatory variable distributions. The author would like to thank the editor, the associate editor, and the referees for drawing attention to pertinent references that led to improved presentation. This research was partially supported by National Science Council grant NSC-94-2118-M-009-004.     

Delta图分析方法及其在冲突控制研究中的应用

近年来,反应时分布分析方法被应用于冲突控制研究领域,以弥补只计算平均反应时和错误率的不足。所谓delta指的是不一致条件与一致条件反应时之差,即冲突效应量。冲突效应量随反应时间的变化图称为delta图。与该分析方法相应的理论模型包括双通路模型和激活－抑制模型。本文介绍了delta图分析的具体方法及其与冲突控制理论模型的关系,然后列举了有关的研究例证,并强调了其优缺点与适用范围     

Task difficulty and inertial properties of hand-held tools: An assessment of their concurrent effects on precision aiming

Aiming hand-held tools at targets in space entails adjustments in the dynamical organization of aiming patterns according to the required precision. We asked whether and how these adjustments are modified by the tool’s mass distribution. Twelve participants performed reciprocal aiming movements with a 50-cm long wooden probe. Kinematic patterns of probe movements were used as a window into the behavioral dynamic underlying performance of a reciprocal aiming task. We crossed three levels of task difficulty (IDs 2.8, 4.5 and 6.1) with two types of probe varying in their mass distribution (proximal vs distal loading). Movement duration was affected by task difficulty and probe loading (shorter for larger targets and proximal probe loading). Progressive deviations from a sinusoidal movement pattern were observed as task difficulty increased. Such deviations were more pronounced with proximal probe loading. Results point to a higher degree of non-linearity in aiming dynamics when the probe was loaded proximally, which might reflect employment of additional perceptual-motor processes to control the position of its less stable tip at the vicinity of the targets. More generally, the effects of probe loading on aiming pattern and dynamics suggest that perceptual-motor processes responding to task level constraints are sensitive to, and not independent from, biomechanical, end-effector constraints.     

资源的交换价值和工资性质对其分配公平感的影响

如何公平合理地分配有限的资源是每一个组织都要面对的基本问题。在组织资源分配中存在一个有趣的现象, 即平均分配金钱往往会比平均分配特定商品让人感到更不公平。前人研究认为, 这是因金钱较之特定的商品具有更多交换价值导致的。3个实验对这一重要的心理现象进行了重新研究发现, 不仅交换价值影响资源分配的公平感, 而且资源的工资性质对其分配的公平感也有重要影响。这一发现丰富了Adams的公平理论, 同时也为组织更好地分配资源提供重要参考。