A Bayesian Nonparametric Approach to Test Equating

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are compared through the analysis of data sets famous in the equating literature. Also, the classical percentile-rank, linear, and mean equating models are each proven to be a special case of a Bayesian model under a highly-informative choice of prior distribution.     

Bayes modal estimation in item response models

This article describes a Bayesian framework for estimation in item response models, with two-stage prior distributions on both item and examinee populations. Strategies for point and interval estimation are discussed, and a general procedure based on the EM algorithm is presented. Details are given for implementation under one-, two-, and three-parameter binary logistic IRT models. Novel features include minimally restrictive assumptions about examinee distributions and the exploitation of dependence among item parameters in a population of interest. Improved estimation in a moderately small sample is demonstrated with simulated data.This research was supported by a grant from the Spencer Foundation, Chicago, IL. Comments and suggestions on earlier drafts by Charles Lewis, Frederic Lord, Rosenbaum, James Ramsey, Hiroshi Watanabe, the editor, and two anonymous referees are gratefully acknowledged.     

三类多层中介效应分析方法比较

比较了贝叶斯法、Monte Carlo法和参数Bootstrap法在2-1-1多层中介分析中的表现。结果发现：1)有先验信息的贝叶斯法的中介效应点估计和区间估计都最准确;2)无先验信息的贝叶斯法、Monte Carlo法、偏差校正和未校正的参数Bootstrap法的中介效应点估计和区间估计表现相当,但Monte Carlo法在第Ⅰ类错误率和区间宽度指标上表现略优于其他三种方法,偏差校正的Bootstrap法在统计检验力上表现略优于其他三种方法,但在第Ⅰ类错误率上表现最差;结果表明,当有先验信息时,推荐使用贝叶斯法;当先验信息不可得时,推荐使用Monte Carlo法。     

Underestimation of prior remembering and susceptibility to false memories: two sides of the same coin?

In two studies, we explored whether susceptibility to false memories and the underestimation of prior memories (i.e., forgot-it-all-along effect) tap overlapping memory phenomena. Study 1 investigated this issue by administering the Deese/Roediger–McDermott task (DRM) and the forgot-it-all-along (FIA) task to an undergraduate sample (N = 110). It was furthermore explored how performances on these tasks correlate with clinically relevant traits such as fantasy proneness, dissociative experiences, and cognitive efficiency. Results show that FIA and DRM performances are relatively independent from each other, suggesting that these measures empirically apparently refer to separate dimensions. However, they do not seem to define different profiles in terms of dissociation, fantasy proneness, and cognitive efficiency. Study 2 replicated the finding of relative independence between false memory propensity (as measured with the DRM task) and the underestimation of prior memories (as measured with an autobiographical memory dating task) in people with a history of childhood sexual abuse (N = 35).     

丁超五易卦探源说

20世纪初,西方文化对中国文化产生强烈冲击,并导致中西文化之间空前交织和会通,处在这一大的文化背景下,丁超五试图会通易学与科学,收集了大量易学文献资料,追溯《易》之源头,探讨了《易》与卜筮、卜筮与科学的关系,提出易道是建立在科学的基础之上的,易学不是专为卜筮而作,易学起源“坤先乾后”等观点。虽然在易学起源问题上他有些提法值得商榷,但对于我们今天探讨易卦起源,揭示易学中的科学思想,解读《周易》中的刚柔关系,把握历史上易与道家互动关系有重要启发意义。     

Leaving patches: effects of economy, deprivation, and session duration

Three pigeons pecked keys for food reinforcers in a laboratory analogue of foraging in patches. Half the patches contained food (were prey patches). In prey patches, pecks to one key occasionally produced a reinforcer, followed by a fixed travel time and then the start of a new patch. Pecks to another key were exit responses, and immediately produced travel time and then a new patch. Travel time was varied from 0.25 to 16 s at each of three session durations: 1, 4, and 23.5 hr. This part of the experiment arranged a closed economy, in that the only source of food was reinforcers obtained in prey patches. In another part, food deprivation was manipulated by varying postsession feeding so as to maintain the subjects' body weights at percentages ranging from 85% to 95% of their ad lib weights, in 1-hr sessions with a travel time of 12 s. This was an open economy. Patch residence time, defined as the time between the start of a patch and an exit response, increased with increasing travel time, and consistently exceeded times predicted by an optimal foraging model, supporting previously published results. However, residence times also increased with increasing session duration and, in longer sessions, consistently exceeded previously reported residence times in comparable open-economy conditions. Residence times were not systematically affected by deprivation levels. In sum, the results show that the long residence times obtained in long closed-economy sessions should probably be attributed to session duration rather than to economy or deprivation. This conclusion is hard to reconcile with previous interpretations of longer-than-optimal residence times but is consistent with, in economic terms, a predicted shift in consumption towards a preferred commodity when income is increased.     

An investigation of hierarchical Bayes procedures in item response theory

Hierarchical Bayes procedures for the two-parameter logistic item response model were compared for estimating item and ability parameters. Simulated data sets were analyzed via two joint and two marginal Bayesian estimation procedures. The marginal Bayesian estimation procedures yielded consistently smaller root mean square differences than the joint Bayesian estimation procedures for item and ability estimates. As the sample size and test length increased, the four Bayes procedures yielded essentially the same result.The authors wish to thank the Editor and anonymous reviewers for their insightful comments and suggestions.     

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.     

Why Bayesian Psychologists Should Change the Way They Use the Bayes Factor

The discussion following Bem’s (2011 Bem, D. J. (2011). Feeling the future: Experimental evidence for anomalous retroactive influences on cognition and affect. Journal of Personality and Social Psychology, 100, 407–425. doi: 10.1037/a0021524[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) psi research highlights that applications of the Bayes factor in psychological research are not without problems. The first problem is the omission to translate subjective prior knowledge into subjective prior distributions. In the words of Savage (1961 Savage, L. J. (1961). The foundations of statistical inference reconsidered. In J. Neyman, (Ed.), Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics, pp. 575–586. BerkeleyCA: University of California. [Google Scholar]): “they make the Bayesian omelet without breaking the Bayesian egg.” The second problem occurs if the Bayesian egg is not broken: the omission to choose default prior distributions such that the ensuing inferences are well calibrated. The third problem is the adherence to inadequate rules for the interpretation of the size of the Bayes factor. The current paper will elaborate these problems and show how to avoid them using the basic hypotheses and statistical model used in the first experiment described in Bem (2011 Bem, D. J. (2011). Feeling the future: Experimental evidence for anomalous retroactive influences on cognition and affect. Journal of Personality and Social Psychology, 100, 407–425. doi: 10.1037/a0021524[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). It will be argued that a thorough investigation of these problems in the context of more encompassing hypotheses and statistical models is called for if Bayesian psychologists want to add a well-founded Bayes factor to the tool kit of psychological researchers.