An EM algorithm for fitting two-level structural equation models

Maximum likelihood is an important approach to analysis of two-level structural equation models. Different algorithms for this purpose have been available in the literature. In this paper, we present a new formulation of two-level structural equation models and develop an EM algorithm for fitting this formulation. This new formulation covers a variety of two-level structural equation models. As a result, the proposed EM algorithm is widely applicable in practice. A practical example illustrates the performance of the EM algorithm and the maximum likelihood statistic.We are thankful to the reviewers for their constructive comments that have led to significant improvement on the first version of this paper. Special thanks are due to the reviewer who suggested a comparison with the LISREL program in the saturated means model, and provided its setup and output. This work was supported by National Institute on Drug Abuse grants DA01070, DA00017, and a UNH 2002 Summer Faculty Fellowship.     

计算机自适应测验中测验安全控制方法评述

计算机自适应测验在实际应用中曾经受到了测验安全问题质疑。国内外学者主要从两种研究思路提出了测验安全控制的方法：一是控制项目的最大曝光率, 沿着这个思路发展出来的方法有SH法、项目合格方法、多重最大曝光率法等; 二是改进选题策略, 沿着这个思路发展的方法主要是 分层法及其变式。此外, 近年来出现了测验安全控制方法之间相结合的研究思路。本文从均方误差、项目曝光率、题库利用率等指标论述了测验安全控制方法的优缺点, 并概述了这些测验安全控制方法的研究发展历程与发展思路, 展望了今后的研究趋势。     

When to Refrain from Using Likelihood Surface Methods for Geographic Offender Profiling: An Ex Ante Test of Assumptions

Likelihood surface methods for geographic offender profiling rely on several assumptions regarding the underlying location choice mechanism of an offender. We propose an ex ante test for checking whether a given set of crime locations is compatible with two necessary assumptions: circular symmetry and distance decay. The proposed (SDD) test compares the observed inter point distances of a given series of crimes with a theoretical distribution function governed by these assumptions, using a Monte Carlo simulation procedure for approximating that distribution function. We apply the SDD test to data on serial burglary from both the UK and the Netherlands. In most cases, the assumption of an underlying symmetric distance decay function has to be rejected. Copyright © 2011 John Wiley & Sons, Ltd.     

Mean Comparison: Manifest Variable Versus Latent Variable

Mean comparisons are of great importance in the application of statistics. Procedures for mean comparison with manifest variables have been well studied. However, few rigorous studies have been conducted on mean comparisons with latent variables, although the methodology has been widely used and documented. This paper studies the commonly used statistics in latent variable mean modeling and compares them with parallel manifest variable statistics. Our results indicate that, under certain conditions, the likelihood ratio and Wald statistics used for latent mean comparisons do not always have greater power than the Hotelling T² statistics used for manifest mean comparisons. The noncentrality parameter corresponding to the T² statistic can be much greater than those corresponding to the likelihood ratio and Wald statistics, which we find to be different from those provided in the literature. Under a fixed alternative hypothesis, our results also indicate that the likelihood ratio statistic can be stochastically much greater than the corresponding Wald statistic. The robustness property of each statistic is also explored when the model is misspecified or when data are nonnormally distributed. Recommendations and advice are provided for the use of each statistic. The research was supported by NSF grant DMS-0437167 and Grant DA01070 from the National Institute on Drug Abuse. We would like to thank three referees for suggestions that helped in improving the paper.     

Difference in the Formation of Attitude Toward Nuclear Power

Determinants of attitudes toward nuclear power in Japan were assessed in a March 1999 survey. The results suggested that persons with interest in and knowledge about nuclear power judged its acceptability on the basis of their perceptions of the sufficiency of electric power and the risks of nuclear power, whereas persons with no interest in and knowledge of nuclear power did not respond on this basis. Although both types of respondents based acceptability on their trust in nuclear power operation and their perception of efficiency, the influence of perception of efficiency on acceptability was stronger for the interested and knowledgeable respondents than for the others. These results partially support the elaboration likelihood model or dual process theory.     

Detecting Differential Item Functioning Using Multiple-Group Cognitive Diagnosis Models

This study proposes a multiple-group cognitive diagnosis model to account for the fact that students in different groups may use distinct attributes or use the same attributes but in different manners (e.g., conjunctive, disjunctive, and compensatory) to solve problems. Based on the proposed model, this study systematically investigates the performance of the likelihood ratio (LR) test and Wald test in detecting differential item functioning (DIF). A forward anchor item search procedure was also proposed to identify a set of anchor items with invariant item parameters across groups. Results showed that the LR and Wald tests with the forward anchor item search algorithm produced better calibrated Type I error rates than the ordinary LR and Wald tests, especially when items were of low quality. A set of real data were also analyzed to illustrate the use of these DIF detection procedures.     

Spurious Latent Class Problem in the Mixed Rasch Model: A Comparison of Three Maximum Likelihood Estimation Methods under Different Ability Distributions

Recent research has shown that over-extraction of latent classes can be observed in the Bayesian estimation of the mixed Rasch model when the distribution of ability is non-normal. This study examined the effect of non-normal ability distributions on the number of latent classes in the mixed Rasch model when estimated with maximum likelihood estimation methods (conditional, marginal, and joint). Three information criteria fit indices (Akaike information criterion, Bayesian information criterion, and sample size adjusted BIC) were used in a simulation study and an empirical study. Findings of this study showed that the spurious latent class problem was observed with marginal maximum likelihood and joint maximum likelihood estimations. However, conditional maximum likelihood estimation showed no overextraction problem with non-normal ability distributions.     

The mitigating role of leader‒member exchange when perceiving psychological contract violation: a diary survey study among volunteers

Several scholars in the field of volunteering emphasized the pivotal role of psychological contract (PC) violation in explaining maladaptive behavioural reactions—such as counterproductive work behaviour (CWB)—of volunteers. Reactions to violation feelings are, however, interrelated and may intensify over time. Extending this dynamic perspective, we introduce momentary leader–member exchange (LMX) as a buffering social resource in the relationship between violation feelings and (1) CWB and (2) the likelihood to perceive a PC breach. Using weekly diary survey data from 247 volunteers (827 observations), we conducted a moderated multilevel zero-inflated Poisson regression analysis. As hypothesized, experiencing feelings of violation during one week related positively to CWB towards the organization (CWB-O), but not to CWB towards individuals (CWB-I) during the next week. Moreover, experiencing violation feelings during one week increased the likelihood to perceive a PC breach during the subsequent week. Finally, experiencing a high-quality LMX relationship effectively mitigated the positive relationship between violation feelings during one week and (1) CWB-O, and (2) the likelihood to perceive a PC breach during the next week. Our study highlights momentary LMX as an effective redressing mechanism in the relationship between violation feelings and undesirable employee outcomes.     

Approximations to the distribution of a test statistic in covariance structure analysis: A comprehensive study

In structural equation modelling (SEM), a robust adjustment to the test statistic or to its reference distribution is needed when its null distribution deviates from a χ² distribution, which usually arises when data do not follow a multivariate normal distribution. Unfortunately, existing studies on this issue typically focus on only a few methods and neglect the majority of alternative methods in statistics. Existing simulation studies typically consider only non-normal distributions of data that either satisfy asymptotic robustness or lead to an asymptotic scaled χ² distribution. In this work we conduct a comprehensive study that involves both typical methods in SEM and less well-known methods from the statistics literature. We also propose the use of several novel non-normal data distributions that are qualitatively different from the non-normal distributions widely used in existing studies. We found that several under-studied methods give the best performance under specific conditions, but the Satorra–Bentler method remains the most viable method for most situations.