A simplified accurate algorithm for the fisher-yates exact test

An algorithm, using a short cut due to Feldman and Klingler, for the Fisher-Yates exact test is presented: the algorithm is quick, simple and accurate.I am grateful to the Editor and two reviewers for a number of constructive and helpful suggestions.     

Piecewise method of reciprocal averages for dual scaling of multiple-choice data

The proposed method handles the classical method of reciprocal averages (MRA) in a piecewise (item-by-item) mode, whereby one can deal with smaller matrices and attain faster convergence to a solution than the MRA. A new concept the principle of constant proportionality is introduced to provide an interesting interpretation for scaling multiple-choice data a la Guttman. A small example is presented for discussion of the technique.This study was supported by the Natural Sciences and Engineering Research Council Canada Grant (No. A4581) to S. Nishisato. The authors are indebted to reviewers for valuable comments.     

Psychometric latent response models

In this paper, some psychometric models will be presented that belong to the larger class oflatent response models (LRMs). First, LRMs are introduced by means of an application in the field ofcomponential item response theory (Embretson, 1980, 1984). Second, a general definition of LRMs (not specific for the psychometric subclass) is given. Third, some more psychometric LRMs, and examples of how they can be applied, are presented. Fourth, a method for obtaining maximum likelihood (ML) and some maximum a posteriori (MAP) estimates of the parameters of LRMs is presented. This method is then applied to theconjunctive Rasch model. Fifth and last, an application of the conjunctive Rasch model is presented. This model was applied to responses to typical verbal ability items (open synonym items).This paper presents theoretical and empirical results of a research project supported by the Research Council [Onderzoeksraad] of the University of Leuven (grant number 89-9) to Paul De Boeck and Luc Delbeke.     

Bayesian Modal Estimation for the One-Parameter Logistic Ability-Based Guessing (1PL-AG) Model

The calibration of the one-parameter logistic ability-based guessing (1PL-AG) model in item response theory (IRT) with a modest sample size remains a challenge for its implausible estimates and difficulty in obtaining standard errors of estimates. This article proposes an alternative Bayesian modal estimation (BME) method, the Bayesian Expectation-Maximization-Maximization (BEMM) method, which is developed by combining an augmented variable formulation of the 1PL-AG model and a mixture model conceptualization of the three-parameter logistic model (3PLM). By comparing with marginal maximum likelihood estimation (MMLE) and Markov Chain Monte Carlo (MCMC) in JAGS, the simulation shows that BEMM can produce stable and accurate estimates in the modest sample size. A real data example and the MATLAB codes of BEMM are also provided.     

Bayesian Diagnostics of Hidden Markov Structural Equation Models with Missing Data

Cocaine is a type of drug that functions to increase the availability of the neurotransmitter dopamine in the brain. However, cocaine dependence or abuse is highly related to an increased risk of psychiatric disorders and deficits in cognitive performance, attention, and decision-making abilities. Given the chronic and persistent features of drug addiction, the progression of abstaining from cocaine often evolves across several states, such as addiction to, moderate dependence on, and swearing off cocaine. Hidden Markov models (HMMs) are well suited to the characterization of longitudinal data in terms of a set of unobservable states, and have increasingly been used to uncover the dynamic heterogeneity in progressive diseases or activities. However, the existence of outliers or influential points may misidentify the hidden states and distort the associated inference. In this study, we develop a Bayesian local influence procedure for HMMs with latent variables in the presence of missing data. The proposed model enables us to investigate the dynamic heterogeneity of multivariate longitudinal data, reveal how the interrelationships among latent variables change from one state to another, and simultaneously conduct statistical diagnosis for the given data, model assumptions, and prior inputs. We apply the proposed procedure to analyze a dataset collected by the UCLA center for advancing longitudinal drug abuse research. Several outliers or influential points that seriously influence estimation results are identified and removed. The proposed procedure also discovers the effects of treatment and individuals’ psychological problems on cocaine use behavior and delineates their dynamic changes across the cocaine-addiction states.     

Bayesian inference for graphical factor analysis models

We generalize factor analysis models by allowing the concentration matrix of the residuals to have nonzero off-diagonal elements. The resulting model is named graphical factor analysis model. Allowing a structure of associations gives information about the correlation left unexplained by the unobserved variables, which can be used both in the confirmatory and exploratory context. We first present a sufficient condition for global identifiability of this class of models with a generic number of factors, thereby extending the results in Stanghellini (1997) and Vicard (2000). We then consider the issue of model comparison and show that fast local computations are possible for this purpose, if the conditional independence graphs on the residuals are restricted to be decomposable and a Bayesian approach is adopted. To achieve this aim, we propose a new reversible jump MCMC method to approximate the posterior probabilities of the considered models. We then study the evolution of political democracy in 75 developing countries based on eight measures of democracy in two different years. We acknowledge support from M.U.R.S.T. of Italy and from the European Science Foundation H.S.S.S. Network. We are grateful to the referees and the Editor for many useful suggestions and comments which led to a substantial improvement of the paper. We also thank Nanny Wermuth for stimulating discussions and Kenneth A. Bollen for kindly providing us with the data-set.     

Maximum likelihood estimation of latent interaction effects with the LMS method

In the context of structural equation modeling, a general interaction model with multiple latent interaction effects is introduced. A stochastic analysis represents the nonnormal distribution of the joint indicator vector as a finite mixture of normal distributions. The Latent Moderated Structural Equations (LMS) approach is a new method developed for the analysis of the general interaction model that utilizes the mixture distribution and provides a ML estimation of model parameters by adapting the EM algorithm. The finite sample properties and the robustness of LMS are discussed. Finally, the applicability of the new method is illustrated by an empirical example. This research has been supported by a grant from the Deutsche Forschungsgemeinschaft, Germany, No. Mo 474/1 and Mo 474/2. The data for the empirical example have been provided by Andreas Thiele of the University of Frankfurt, Germany. The authors are indebted to an associate editor and to three anonymous reviewers ofPsychometrika whose comments and suggestions have been very helpful.     

A New Concurrent Calibration Method for Nonequivalent Group Design under Nonrandom Assignment

This study proposes a new item parameter linking method for the common-item nonequivalent groups design in item response theory (IRT). Previous studies assumed that examinees are randomly assigned to either test form. However, examinees can frequently select their own test forms and tests often differ according to examinees’ abilities. In such cases, concurrent calibration or multiple group IRT modeling without modeling test form selection behavior can yield severely biased results. We proposed a model wherein test form selection behavior depends on test scores and used a Monte Carlo expectation maximization (MCEM) algorithm. This method provided adequate estimates of testing parameters.     

2PL模型的两种马尔可夫蒙特卡洛缺失数据处理方法比较

马尔科夫蒙特卡洛（MCMC）是项目反应理论中处理缺失数据的一种典型方法。文章通过模拟研究比较了在不同被试人数,项目数,缺失比例下两种MCMC方法（M-H within Gibbs和DA-T Gibbs）参数估计的精确性,并结合了实证研究。研究结果表明,两种方法是有差异的,项目参数估计均受被试人数影响很大,受缺失比例影响相对更小。在样本较大缺失比例较小时,M-H within Gibbs参数估计的均方误差（RMSE）相对略小,随着样本数的减少或缺失比例的增加,DA-T Gibbs方法逐渐优于M-H within Gibbs方法