On normal theory based inference for multilevel models with distributional violations

Data in social and behavioral sciences are often hierarchically organized though seldom normal, yet normal theory based inference procedures are routinely used for analyzing multilevel models. Based on this observation, simple adjustments to normal theory based results are proposed to minimize the consequences of violating normality assumptions. For characterizing the distribution of parameter estimates, sandwich-type covariance matrices are derived. Standard errors based on these covariance matrices remain consistent under distributional violations. Implications of various covariance estimators are also discussed. For evaluating the quality of a multilevel model, a rescaled statistic is given for both the hierarchical linear model and the hierarchical structural equation model. The rescaled statistic, improving the likelihood ratio statistic by estimating one extra parameter, approaches the same mean as its reference distribution. A simulation study with a 2-level factor model implies that the rescaled statistic is preferable.This research was supported by grants DA01070 and DA00017 from the National Institute on Drug Abuse and a University of North Texas faculty research grant. We would like to thank the Associate Editor and two reviewers for suggestions that helped to improve the paper.     

A unified approach to exploratory factor analysis with missing data,nonnormal data,and in the presence of outliers

Factor analysis is regularly used for analyzing survey data. Missing data, data with outliers and consequently nonnormal data are very common for data obtained through questionnaires. Based on covariance matrix estimates for such nonstandard samples, a unified approach for factor analysis is developed. By generalizing the approach of maximum likelihood under constraints, statistical properties of the estimates for factor loadings and error variances are obtained. A rescaled Bartlett-corrected statistic is proposed for evaluating the number of factors. Equivariance and invariance of parameter estimates and their standard errors for canonical, varimax, and normalized varimax rotations are discussed. Numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures.This project was supported by a University of North Texas Faculty Research Grant, Grant #R49/CCR610528 for Disease Control and Prevention from the National Center for Injury Prevention and Control, and Grant DA01070 from the National Institute on Drug Abuse. The results do not necessarily represent the official view of the funding agencies. The authors are grateful to three reviewers for suggestions that improved the presentation of this paper.     

Satisfiability Testing for Boolean Formulas Using Δ-trees

The tree-based data structure of -tree for propositional formulas is introduced in an improved and optimised form. The -trees allow a compact representation for negation normal forms as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfiability of the input formula. These reduction strategies are divided into two subsets (meaning- and satisfiability-preserving transformations) and can be used to decrease the size of a negation normal form A at (at most) quadratic cost. The reduction strategies are aimed at decreasing the number of required branchings and, therefore, these strategies allow to limit the size of the search space for the SAT problem.     

From case management to prevention of scientific dishonesty in Denmark

In 1992, The Danish Medical Research Council established a national committee on scientific dishonesty with the twofold task of handling cases of scientific misconduct and taking preventive initiatives. Scientific dishonesty was proven in only five cases, but in another nine cases lesser degrees of deviations from good scientific practice were found. The experiences from a total of 24 treated cases indicated that three key areas were at the basis of most of the accusations and the deviations from good practice: uncertainty about 1) authorship, about 2) rights and duties to use scientific data and about 3) agreements at the initiation of joint studies. As a consequence guidelines on good practice have been issued on these key subjects. An earlier version of this paper was presented at a symposium, Scientific Misconduct. An International Perspective, organised by The Medical University of Warsaw, 16 November, 1998.     

Tucker3 hierarchical classes analysis

This paper presents a new model for binary three-way three-mode data, called Tucker3 hierarchical classes model (Tucker3-HICLAS). This new model generalizes Leenen, Van Mechelen, De Boeck, and Rosenberg's (1999) individual differences hierarchical classes model (INDCLAS). Like the INDCLAS model, the Tucker3-HICLAS model includes a hierarchical classification of the elements of each mode, and a linking structure among the three hierarchies. Unlike INDCLAS, Tucker3-HICLAS (a) does not restrict the hierarchical classifications of the three modes to have the same rank, and (b) allows for more complex linking structures among the three hierarchies. An algorithm to fit the Tucker3-HICLAS model is described and evaluated in an extensive simulation study. An application of the model to hostility data is discussed.The first author is a Research Assistant of the Fund for Scientific Research-Flanders (Belgium). The research reported in this paper was partially supported by the Research Council of K.U. Leuven (GOA/2000/02). We are grateful to Kristof Vansteelandt for providing us with an interesting data set.     

Shackling the shoulders of giants

This paper informally summarizes a two-day symposium held at the U.S. National Academy of Sciences in Washington, D.C., September 5–6, 2002. The issue was to what extent the progress of science and societal capacity for continued technological innovation are threatened by excessive protection of intellectual property. Excessive protection creates disadvantages not only for scientists and inventors but also for educators/students and for librarians/clientele. Speakers from a variety of disciplines and institutions agreed unanimously that scientific and technological progress is, indeed, under serious threat. Various opinions were expressed about the degree of threat, currently and prospectively, as well as what counter-measures are best suited to resist undue restrictions on creative uses of scientific and technical data and information. This summary is based entirely on the author’s notes from the symposium, and the commentary offered is his alone. My apologies to the speakers if this paper does not accurately reflect the primary intent of their presentations. The “Suggested Readings” offered at the end are not specific to the speakers’ statements but rather are offered as a general resource to aid further research. The definitive record of the symposium is planned to be available from the National Academies Press as a Proceedings publication in the summer of 2003. John Gardenier is an independent researcher, ethicist and science writer.     

Constrained maximum likelihood estimation of two-level covariance structure model via EM type algorithms

In this paper, the constrained maximum likelihood estimation of a two-level covariance structure model with unbalanced designs is considered. The two-level model is reformulated as a single-level model by treating the group level latent random vectors as hypothetical missing-data. Then, the popular EM algorithm is extended to obtain the constrained maximum likelihood estimates. For general nonlinear constraints, the multiplier method is used at theM-step to find the constrained minimum of the conditional expectation. An accelerated EM gradient procedure is derived to handle linear constraints. The empirical performance of the proposed EM type algorithms is illustrated by some artifical and real examples.This research was supported by a Hong Kong UCG Earmarked Grant, CUHK 4026/97H. We are greatly indebted to D.E. Morisky and J.A. Stein for the use of their AIDS data in our example. We also thank the Editor, two anonymous reviewers, W.Y. Poon and H.T. Zhu for constructive suggestions and comments in improving the paper. The assistance of Michael K.H. Leung and Esther L.S. Tam is gratefully acknowledged.     

Evaluation of antecedent stimulus parameters for the treatment of escape-maintained aberrant behavior

We evaluated a methodology for identifying the range of stimulus features of antecedent stimuli associated with aberrant behavior in demand contexts in natural settings. For each participant, an experimental analysis of antecedents (Phase 1) was conducted to confirm the hypothesis that task instructions occasioned increases in aberrant behavior. During Phase 2, specific stimulus features associated with the presentation of task instructions were assessed by evaluating the child's behavior across two distinct settings, therapists, and types of tasks in a sequential fashion. Aberrant behavior occurred immediately across settings and therapists, presumably because the presence of a discriminative stimulus for escape-maintained behavior (the delivery of a task instruction) occasioned aberrant behavior. However, aberrant behavior decreased initially across tasks, suggesting that familiarity with the task might be a variable. During Phase 3, an experimental (functional) analysis of consequences was conducted with 2 participants to verify that aberrant behavior was maintained by negative reinforcement. During Phase 4, a treatment package that interspersed play with task instructions was conducted to disrupt the ongoing occurrence of aberrant behavior. Immediate and durable treatment effects occurred for 2 of the 3 participants.     

Predicting elections from the most important issue: A test of the take‐the‐best heuristic

We used the take‐the‐best heuristic to develop a model to forecast the popular two‐party vote shares in U.S. presidential elections. The model draws upon information about how voters expect the candidates to deal with the most important issue facing the country. We used cross‐validation to calculate a total of 1000 out‐of‐sample forecasts, one for each of the last 100 days of the ten U.S. presidential elections from 1972 to 2008. Ninety‐seven per cent of forecasts correctly predicted the winner of the popular vote. The model forecasts were competitive compared to forecasts from methods that incorporate substantially more information (e.g., econometric models and the Iowa Electronic Markets). The purpose of the model is to provide fast advice on which issues candidates should stress in their campaign. Copyright © 2010 John Wiley & Sons, Ltd.     

Commentary on “Mediation analysis and categorical variables: The final frontier” by Dawn Iacobucci

The commentary discusses several topics in Dr. Iacobucci's article on mediation analysis with categorical variables including the lack of equivalency of mediated effect measures, ab, and c–c′, that are algebraically equivalent in ordinary least squares regression models. The commentary raises the issue of correlated mediation coefficients and presents formulas to include the correlation in the test of significance. References to new developments in causal mediation analysis for categorical variables are given and the importance of programs of research to establish a mediation theory is emphasized.