验证性因素分析:问卷题数及小样本应用策略

验证性因素分析在心理、教育等研究应用日广。本文引用三个模拟数据研究,提出一些在分析时的应用策略,包括用较多题目及强制同一因子的负荷相等。样本容量一般愈大愈好,但当资源等条件有限制时,上述两个技巧,可协助解决叠代收敛问题,并能更准确估计各重要参数。此外,一些方法如：每因子只得两题目、当样本只得约１００人时每因子用少於四题目、将题目合并以其平均数为指标,均可能导致不收敛、高标准误及偏差估计量等问题,不值得推荐。     

Bayesian estimation and testing of structural equation models

The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameters can be computed from these samples. If the prior distribution over the parameters is uninformative, the posterior is proportional to the likelihood, and asymptotically the inferences based on the Gibbs sample are the same as those based on the maximum likelihood solution, for example, output from LISREL or EQS. In small samples, however, the likelihood surface is not Gaussian and in some cases contains local maxima. Nevertheless, the Gibbs sample comes from the correct posterior distribution over the parameters regardless of the sample size and the shape of the likelihood surface. With an informative prior distribution over the parameters, the posterior can be used to make inferences about the parameters underidentified models, as we illustrate on a simple errors-in-variables model.We thank David Spiegelhalter for suggesting applying the Gibbs sampler to structural equation models to the first author at a 1994 workshop in Wiesbaden. We thank Ulf Böckenholt, Chris Meek, Marijtje van Duijn, Clark Glymour, Ivo Molenaar, Steve Klepper, Thomas Richardson, Teddy Seidenfeld, and Tom Snijders for helpful discussions, mathematical advice, and critiques of earlier drafts of this paper.     

CAT选题策略分类概述

选题是计算机化自适应测验（CAT）测试过程的关键环节,选题策略的目标是要达到较高的测量精度,同时也实现试题曝光率控制及其他测验目标的实现.本文根据选题策略的基本原理和衍生发展,将众多CAT选题策略分为五大选题策略系列：Fisher函数系列、K-LI函数系列、α分层系列、贝叶斯系列、b匹配系列;并根据测验目标（测验精度、试题曝光率控制、内容平衡、多条件约束）对这些选题策略进行了细分,并对CAT选题策略的选择思路进行归纳.     

Finding MAPs using strongly equivalent high order recurrent symmetric connectionist networks

Belief revision is the problem of finding the most plausible explanation for an observed set of evidences. It has many applications in various scientific domains like natural language understanding, medical diagnosis and computational biology. Bayesian Networks (BN) is an important probabilistic graphical formalism widely used for belief revision tasks. In BN, belief revision can be achieved by finding the maximum a posteriori (MAP) assignment. Finding MAP is an NP-Hard problem. In previous work, we showed how to find the MAP assignment in BN using High Order Recurrent Neural Networks (HORN) through an intermediate representation of Cost-Based Abduction. This method eliminates the need to explicitly construct the energy function in two steps, objective and constraints. This paper builds on that previous work by providing the theoretical foundation and proving that the resultant HORN used to find MAP is strongly equivalent to the original BN it tries to solve.     

Multilevel Reliability Measures of Latent Scores Within an Item Response Theory Framework

Abstract

This paper evaluated multilevel reliability measures in two-level nested designs (e.g., students nested within teachers) within an item response theory framework. A simulation study was implemented to investigate the behavior of the multilevel reliability measures and the uncertainty associated with the measures in various multilevel designs regarding the number of clusters, cluster sizes, and intraclass correlations (ICCs), and in different test lengths, for two parameterizations of multilevel item response models with separate item discriminations or the same item discrimination over levels. Marginal maximum likelihood estimation (MMLE)-multiple imputation and Bayesian analysis were employed to evaluate the accuracy of the multilevel reliability measures and the empirical coverage rates of Monte Carlo (MC) confidence or credible intervals. Considering the accuracy of the multilevel reliability measures and the empirical coverage rate of the intervals, the results lead us to generally recommend MMLE-multiple imputation. In the model with separate item discriminations over levels, marginally acceptable accuracy of the multilevel reliability measures and empirical coverage rate of the MC confidence intervals were found in a limited condition, 200 clusters, 30 cluster size, .2 ICC, and 40 items, in MMLE-multiple imputation. In the model with the same item discrimination over levels, the accuracy of the multilevel reliability measures and the empirical coverage rate of the MC confidence intervals were acceptable in all multilevel designs we considered with 40 items under MMLE-multiple imputation. We discuss these findings and provide guidelines for reporting multilevel reliability measures.     

Independent race of colour and word can predict the Stroop effect

Mainstream theories of the Stroop effect suggest that faster colour classification on congruent trials (say, the word RED printed in red colour) relative to incongruent trials (GREEN in red) is due to channel interaction. Namely, information from the irrelevant word channel perturbs processing of the print colour, causing in turn slower processing of incongruent displays. In this note, I advance a new model in which colour and word are processed in parallel and completely independent channels. The Stroop effect is then the outcome of signal redundancy in congruent displays, where both colour and word contribute to the same response. Numerical computations show that the model can produce the Stroop effect (along with high accuracy rates) for a subset of parameter values. Thus, it provides a proof of existence for a separate channel theory, and a challenge to many existing theories.     

A rational analysis of the acquisition of multisensory representations

How do people learn multisensory, or amodal, representations, and what consequences do these representations have for perceptual performance? We address this question by performing a rational analysis of the problem of learning multisensory representations. This analysis makes use of a Bayesian nonparametric model that acquires latent multisensory features that optimally explain the unisensory features arising in individual sensory modalities. The model qualitatively accounts for several important aspects of multisensory perception: (a) it integrates information from multiple sensory sources in such a way that it leads to superior performances in, for example, categorization tasks; (b) its performances suggest that multisensory training leads to better learning than unisensory training, even when testing is conducted in unisensory conditions; (c) its multisensory representations are modality invariant; and (d) it predicts ‘‘missing” sensory representations in modalities when the input to those modalities is absent. Our rational analysis indicates that all of these aspects emerge as part of the optimal solution to the problem of learning to represent complex multisensory environments.     

Hierarchical models of simple mechanisms underlying confidence in decision making

Choice confidence is a central measure in psychological decision research, often being reported on a probabilistic scale. Simple mechanisms that describe the psychological processes underlying choice confidence, including those based on error and confirmation biases, have typically received support via fits to data averaged over subjects. While averaged data ease model development, they can also destroy important aspects of the confidence data distribution. In this paper, we develop a hierarchical model of raw confidence judgments using the beta distribution, and we implement two simple confidence mechanisms within it. We use Bayesian methods to fit the hierarchical model to data from a two-alternative confidence experiment, and we use a variety of Bayesian tools to diagnose shortcomings of the simple mechanisms that are overlooked when applied to averaged data. Bugs code for estimating the models is also supplied.     

潜变量交互效应标准化估计：方法比较与选用策略

标准化估计对模型的解释和效应大小的比较有重要作用。虽然潜变量交互效应的恰当标准化估计公式已经面世超过10年, 国内外都在使用和引用, 但至今未见到关于不同估计方法得到的恰当标准化估计的系统比较。通过模拟实验, 比较了乘积指标法、潜调节结构方程(LMS)、无先验信息和有先验信息的贝叶斯法的潜变量交互效应标准化估计在不同条件下的表现。结果发现, 在正态条件下, LMS和有信息贝叶斯法表现较好; 而在非正态条件下, 乘积指标法比较稳健, 但需要较大的样本(不小于500), 小样本且外生潜变量之间相关很低时可使用无信息贝叶斯法。     

计算机化分类测验终止规则的类别、特点及应用

计算机化分类测验(Computerized Classification Testing, CCT)能够高效地对被试进行分类, 已广泛应用于合格性测验及临床心理学中。作为CCT的重要组成部分, 终止规则决定测验何时停止以及将被试最终划分到何种类别, 因此直接影响测验效率及分类准确率。已有的三大类终止规则(似然比规则、贝叶斯决策理论规则及置信区间规则)的核心思想分别为构造假设检验、设计损失函数和比较置信区间相对位置。同时, 在不同测验情境下, CCT的终止规则发展出不同的具体形式。未来研究可以继续开发贝叶斯规则、考虑多维多类别情境以及结合作答时间和机器学习算法。针对测验实际需求, 三类终止规则在合格性测验上均有应用潜力, 而临床问卷则倾向应用贝叶斯规则。