A note on computing Louis’ observed information matrix identity for IRT and cognitive diagnostic models

Using Louis’ formula, it is possible to obtain the observed information matrix and the corresponding large-sample standard error estimates after the expectation–maximization (EM) algorithm has converged. However, Louis’ formula is commonly de-emphasized due to its relatively complex integration representation, particularly when studying latent variable models. This paper provides a holistic overview that demonstrates how Louis’ formula can be applied efficiently to item response theory (IRT) models and other popular latent variable models, such as cognitive diagnostic models (CDMs). After presenting the algebraic components required for Louis’ formula, two real data analyses, with accompanying numerical illustrations, are presented. Next, a Monte Carlo simulation is presented to compare the computational efficiency of Louis’ formula with previously existing methods. Results from these presentations suggest that Louis’ formula should be adopted as a standard method when computing the observed information matrix for IRT models and CDMs fitted with the EM algorithm due to its computational efficiency and flexibility.     

Generating interior search directions for multiobjective linear programming

A new multiobjective linear programming (MOLP) algorithm is presented. The algorithm uses a variant of Karmarkar's interior-point algorithm known as the affine-scaling primal algorithm. Using this single-objective algorithm, interior search directions are generated and used to provide an approximation to the gradient of the (implicitly known) utility function. The approximation is guided by assessing locally relevant preference information for the various interior directions through interaction with a decision maker (DM). The resulting algorithm is an interactive approach that makes its progress towards the solution through the interior of the constraints polytope.     

Health Focused Psychotherapy In Treating a Dual Diagnosed Patient

Health-focused psychotherapy offers a contemporary model used in assessment, treatment planning and evaluation in addressing patients with both medical and psychiatric diagnoses. Clinicians in the health and mental health disciplines must know and understand the importance of standards of care and models of intervention and evaluation in clinical practice for this type of patient. Examined is the use of a specific model providing a tailored orientation to patient education, along with the development and use of a clinical algorithm and care pathway for clinical practice. Provided is a case study for applying the development and use of a clinical algorithm and care pathway for a dual diagnosed patient receiving health-focused psychotherapy.     

Model comparison of nonlinear structural equation models with fixed covariates

Recently, it has been recognized that the commonly used linear structural equation model is inadequate to deal with some complicated substantive theory. A new nonlinear structural equation model with fixed covariates is proposed in this article. A procedure, which utilizes the powerful path sampling for computing the Bayes factor, is developed for model comparison. In the implementation, the required random observations are simulated via a hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm. It is shown that the proposed procedure is efficient and flexible; and it produces Bayesian estimates of the parameters, latent variables, and their highest posterior density intervals as by-products. Empirical performances of the proposed procedure such as sensitivity to prior inputs are illustrated by a simulation study and a real example.This research is fully supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region, China (Project No. CUHK 4346/01H). The authors are thankful to the Editor, the Associate Editor, and anonymous reviewers for valuable comments which improve the paper significantly, and grateful to ICPSR and the relevant funding agency for allowing use of the data in the example. The assistance of Michael K.H. Leung and Esther L.S. Tam is gratefully acknowledged.     

融合反应时的多级评分IRT模型开发及其应用研究

当前大多数融合反应时的IRT模型仅适用于0-1评分数据资料,极大的限制了IRT反应时模型在实际中的应用。本文在传统的二级计分反应时IRT模型基础上,拟开发一种多级评分反应时模型。在层次建模框架下,分别采用拓广分部评分模型(GPCM)和对数正态模型构建融合反应时的多级评分IRT模型(本文记为JRT-GPCM),并采用全息贝叶斯MCMC算法实现新模型的参数估计。为验证新开发的JRT-GPCM模型的可行性及其在实践中的应用,本文开展了两项研究:研究1为模拟实验研究,研究2为新模型在大五人格-神经质分量表中的应用。研究1结果表明,JRT-GPCM模型的估计精度较高,且具有较好的稳健性。研究2表明,被试的潜在特质与作答速度具有一定的正相关,且本研究结果支持Ferrando和Lorenzo-Seva(2007)提出的“距离-困难度假设”,即当被试的潜在特质与项目的难度阈限距离越远,那么被试会花费更多的时间对项目进行作答。总之,本研究为拓展反应时信息在心理测量及教育中的应用提供新的方法支持。     

一种多级评分的广义认知诊断模型

认知诊断是近些年教育测量研究中的热点,大多数的认知诊断模型仅适用于0～1评分的情况.本文提出一种有多个潜变量多个滑动参数的多级评分认知诊断模型——GP-D1NA,只要由评分标准和知识状态能确定理想反应模式,就可以利用此方法进行认知诊断分析.在该方法中,我们给出项目滑动矩阵的概念,将被试的观测得分均看成由某个理想得分的滑动,并采用EM算法估计滑动矩阵.在模拟研究中,采用每掌握一个属性得1分的评分标准,结果表明线性型、收敛型、发散型、无结构型和独立型五种属性层级结构均有较高的判准率.     

Finding Creativity in an Artificial Artist

Creativity is an important component of human intelligence, and imbuing artificially intelligent systems with creativity is an interesting challenge. In particular, it is difficult to quantify (or even qualify) creativity. Recently, it has been suggested that conditions for attributing creativity to a system include: appreciation, imagination, and skill. We demonstrate and describe an original computer system (called DARCI) that is designed to produce images through creative means. We present methods for evaluating DARCI and other artificially creative systems with respect to appreciation, imagination, and skill, and use these methods to show that DARCI is arguably a creative system.     

Multicriteria Classification with Unknown Categories: A Clustering–Sorting Approach and an Application to Conflict Management

This work proposes an approach to cluster and sort a set of alternatives considering multi‐criteria categories with a partial order structure. It can be considered a heuristic approach because it does not attempt to derive an optimal partial order among all conceivable clusters of alternatives. Rather than this, it intends to be a simple approach that is transparent to the Decision Maker (DM) whose assistance is sought to help shaping the results. The approach proposed arises from the conjugation of traditional Clustering analysis and Multi‐criteria sorting tools. At the outset, the number of categories and their characteristics is unknown. First, we need to detect only the clusters themselves on the basis of a similarity measure independent of the preferences of the DM. Next, we detect potential partial order relations that might exist between them, according to the subjective preferences of the DM. Such preferences are elicited only after the DM has examined the clusters detected and deemed that these categories made sense. The new approach performs very well in a real‐world problem of management of intragroup conflicts and conflict handling strategies. Copyright © 2012 John Wiley & Sons, Ltd.