Bayesian Hierarchical Classes Analysis

Hierarchical classes models are models for N-way N-mode data that represent the association among the N modes and simultaneously yield, for each mode, a hierarchical classification of its elements. In this paper we present a stochastic extension of the hierarchical classes model for two-way two-mode binary data. In line with the original model, the new probabilistic extension still represents both the association among the two modes and the hierarchical classifications. A fully Bayesian method for fitting the new model is presented and evaluated in a simulation study. Furthermore, we propose tools for model selection and model checking based on Bayes factors and posterior predictive checks. We illustrate the advantages of the new approach with applications in the domain of the psychology of choice and psychiatric diagnosis. Iwin Leenen is now at the Instituto Mexicano de Investigación de Familia y Población (IMIFAP), Mexico. The research reported in this paper was partially supported by the Spanish Ministerio de Educación y Ciencia (programa Ramón y Cajal) and by the Research Council of K.U.Leuven (PDM/99/037, GOA/2000/02, and GOA/2005/04). The authors are grateful to Johannes Berkhof for fruitful discussions.     

Mixed effects modeling of Morris water maze data: Advantages and cautionary notes

Morris water maze data are most commonly analyzed using repeated measures analysis of variance in which daily test sessions are analyzed as an unordered categorical variable. This approach, however, may lack power, relies heavily on post hoc tests of daily performance that can complicate interpretation, and does not target the nonlinear trends evidenced in learning data. The present project used Monte Carlo simulation to compare the relative strengths of the traditional approach with both linear and nonlinear mixed effects modeling that identifies the learning function for each animal and condition. Both trend-based mixed effects modeling approaches showed much greater sensitivity to identifying real effects, and the nonlinear approach provided uniformly better fits of learning trends. The common practice of removing a rat from the maze after 90 s, however, proved more problematic for the nonlinear approach and produced an underestimate of y-axis intercepts.     

标准参照测验及格线设定研究中的模拟实验法

针对标准参照测验及格线设定研究中存在的问题,该文首先分析了Monte Carlo模拟实验法的基本原理,然后提出及格线设定研究的模拟实验思路,即：将专家的主观判断视为概率事件,对专家判断过程中的各种误差的概率分布做出合理假设,依据项目反应理论模型模拟得到专家的主观判断,然后采用重复抽样手段获得专家设定及格线的误差分布,据此衡量及格线的修复能力。文中给出了实例演示．文末讨论了模拟实验法的优点与不足．并展望了后续研究。     

Power of the likelihood ratio test in covariance structure analysis

A procedure for computing the power of the likelihood ratio test used in the context of covariance structure analysis is derived. The procedure uses statistics associated with the standard output of the computer programs commonly used and assumes that a specific alternative value of the parameter vector is specified. Using the noncentral Chi-square distribution, the power of the test is approximated by the asymptotic one for a sequence of local alternatives. The procedure is illustrated by an example. A Monte Carlo experiment also shows how good the approximation is for a specific case.This research was made possible by a grant from the Dutch Organization for Advancement of Pure Research (ZWO). The authors also like to acknowledge the helpful comments and suggestions from the editor and anonymous reviewers.     

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。     

On local influence analysis of full information item factor models

The full information item factor (FIIF) model is very useful for analyzing relations of dichotomous variables. In this article, we present a feasible procedure to assess local influence of minor perturbations for identifying influence aspects of the FIIF model. The development is based on a Q-displacement function which is closely related with the Monte Carlo EM algorithm in the ML estimation. In the E-step of this algorithm, the conditional expectations are approximated by sample means of observations simulated by the Gibbs sampler from the appropriate conditional distributions. It turns out that these observations can be utilized for computing the building blocks of the proposed diagnostic measures. The diagnoses are based on the conformal normal curvature that can be computed easily. A number of interesting perturbation schemes are considered. The methodology is illustrated with two real examples.The research is fully supported by a grant (CUHK 4356/00H) from the Research Grant Council of the Hong Kong Special Administration Region. The authors are thankful to the Editor, Associate Editor, anonymous reviewers, and W.Y. Poon for valuable comments for improving the paper, and to ICPSR and the relevant founding agency for allowing us to use of their data. The assistance of Michael Leung and Esther Tam is gratefully acknowledged.     

Compatibility due to the coding of the relative position of the effectors

Response latencies emitted with the hands crossed are slower than those emitted with the hands uncrossed. Two explanations are available for the so-called crossed-hand effect. One attributes it to the non-natural posture of the arms in the crossed position, whereas the other is in terms of a conflict between the code describing the hand and the code describing its position. Experiment 1 disproved the postural hypothesis by showing that crossing the hands has no effect on response latencies in a simple reaction time task. Experiments 2 and 3 replicated the crossed-hand effect in a choice reaction time task and showed that it depends on the relative position of the two hands. In other words, responses are slower when the hand is located in the “wrong” position with respect to the other (e.g., the right hand is located to the left of the left hand), whereas the absolute position, that is the side of the body where the responding hand is located, does not seem to effect the speed of response.     

Multidimensional scaling of nominal data: The recovery of metric information with alscal

Multidimensional scaling has recently been enhanced so that data defined at only the nominal level of measurement can be analyzed. The efficacy of ALSCAL, an individual differences multidimensional scaling program which can analyze data defined at the nominal, ordinal, interval and ratio levels of measurement, is the subject of this paper. A Monte Carlo study is presented which indicates that (a) if we know the correct level of measurement then ALSCAL can be used to recover the metric information presumed to underlie the data; and that (b) if we do not know the correct level of measurement then ALSCAL can be used to determine the correct level and to recover the underlying metric structure. This study also indicates, however, that with nominal data ALSCAL is quite likely to obtain solutions which are not globally optimal, and that in these cases the recovery of metric structure is quite poor. A second study is presented which isolates the potential cause of these problems and forms the basis for a suggested modification of the ALSCAL algorithm which should reduce the frequency of locally optimal solutions.     

EM and beyond

The basic theme of the EM algorithm, to repeatedly use complete-data methods to solve incomplete data problems, is also a theme of several more recent statistical techniques. These techniques—multiple imputation, data augmentation, stochastic relaxation, and sampling importance resampling—combine simulation techniques with complete-data methods to attack problems that are difficult or impossible for EM.A preliminary version of this article was the Keynote Address at the 1987 European Meeting of the Psychometric Society June 24–26, 1987 in Enschede, The Netherlands. The author wishes to thank the editor and reviewers for helpful comments.