Nonconvergence,improper solutions,and starting values in lisrel maximum likelihood estimation

In the framework of a robustness study on maximum likelihood estimation with LISREL three types of problems are dealt with: nonconvergence, improper solutions, and choice of starting values. The purpose of the paper is to illustrate why and to what extent these problems are of importance for users of LISREL. The ways in which these issues may affect the design and conclusions of robustness research is also discussed.     

Extending exploratory diagnostic classification models: Inferring the effect of covariates

Diagnostic models provide a statistical framework for designing formative assessments by classifying student knowledge profiles according to a collection of fine-grained attributes. The context and ecosystem in which students learn may play an important role in skill mastery, and it is therefore important to develop methods for incorporating student covariates into diagnostic models. Including covariates may provide researchers and practitioners with the ability to evaluate novel interventions or understand the role of background knowledge in attribute mastery. Existing research is designed to include covariates in confirmatory diagnostic models, which are also known as restricted latent class models. We propose new methods for including covariates in exploratory RLCMs that jointly infer the latent structure and evaluate the role of covariates on performance and skill mastery. We present a novel Bayesian formulation and report a Markov chain Monte Carlo algorithm using a Metropolis-within-Gibbs algorithm for approximating the model parameter posterior distribution. We report Monte Carlo simulation evidence regarding the accuracy of our new methods and present results from an application that examines the role of student background knowledge on the mastery of a probability data set.     

Application of the bootstrap methods in factor analysis

A Monte Carlo experiment is conducted to investigate the performance of the bootstrap methods in normal theory maximum likelihood factor analysis both when the distributional assumption is satisfied and unsatisfied. The parameters and their functions of interest include unrotated loadings, analytically rotated loadings, and unique variances. The results reveal that (a) bootstrap bias estimation performs sometimes poorly for factor loadings and nonstandardized unique variances; (b) bootstrap variance estimation performs well even when the distributional assumption is violated; (c) bootstrap confidence intervals based on the Studentized statistics are recommended; (d) if structural hypothesis about the population covariance matrix is taken into account then the bootstrap distribution of the normal theory likelihood ratio test statistic is close to the corresponding sampling distribution with slightly heavier right tail.This study was carried out in part under the ISM cooperative research program (91-ISM · CRP-85, 92-ISM · CRP-102). The authors would like to thank the editor and three reviewers for their helpful comments and suggestions which improved the quality of this paper considerably.     

A method for simulating non-normal distributions

A method of introducing a controlled degree of skew and kurtosis for Monte Carlo studies was derived. The form of such a transformation on normal deviates [X N(0, 1)] isY =a +bX +cX ² +dX ³. Analytic and empirical validation of the method is demonstrated.This work was done while the author was at the University of Illinois at Champaign-Urbana.     

An examination of the effect of six types of error perturbation on fifteen clustering algorithms

An evaluation of several clustering methods was conducted. Artificial clusters which exhibited the properties of internal cohesion and external isolation were constructed. The true cluster structure was subsequently hidden by six types of error-perturbation. The results indicated that the hierarchical methods were differentially sensitive to the type of error perturbation. In addition, generally poor recovery performance was obtained when random seed points were used to start theK-means algorithms. However, two alternative starting procedures for the nonhierarchical methods produced greatly enhanced cluster recovery and were found to be robust with respect to all of the types of error examined.     

Selective deficit of conceptual structures in aphasia: Class versus thematic relations

Conceptual structures in aphasia were investigated by means of a nonverbal test. The understanding of class and thematic relationships was demonstrated to be selectively impaired according to varieties of aphasic deficit. Broca's aphasics showed difficulty evaluating a thematic relationship and did not differ from normal controls as far as class relationships were concerned. The opposite happened for Wernicke's aphasics whose defect seems to be selectively restricted to class relationships.     

Problems with bootstrapping pearson correlations in very small bivariate samples

Efron'sMonte Carlo bootstrap algorithm is shown to cause degeneracies in Pearson'sr for sufficiently small samples. Two ways of preventing this problem when programming the bootstrap ofr are considered.     

Global and local covert visual attention: Evidence from a bayesian hidden markov model

Psychological, psychophysical and physiological research indicates that people switch between two covert attention states, local and global attention, while visually exploring complex scenes. The focus in the local attention state is on specific aspects and details of the scene, and on examining its content with greater visual detail. The focus in the global attention state is on exploring the informative and perceptually salient areas of the scene, and possibly on integrating the information contained therein. The existence of these two visual attention states, their relative prevalence and sequence in time has remained empirically untested to date. To fill this gap, we develop a psychometric model of visual covert attention that extends recent work on hidden Markov models, and we test it using eye-movement data. The model aims to describe the observed time series of saccades typically collected in eye-movement research by assuming a latent Markov process, indicative of the brain switching between global and local covert attention. We allow subjects to be in either state while exploring a stimulus visually, and to switch between them an arbitrary number of times. We relax the no-memory-property of the Markov chain. The model that we develop is estimated with MCMC methodology and calibrated on eye-movement data collected in a study of consumers' attention to print advertisements in magazines.We thank Dominique Claessens of Verify International for making the data available to us.     

Cognitive diagnosis modelling incorporating item response times

To provide more refined diagnostic feedback with collateral information in item response times (RTs), this study proposed joint modelling of attributes and response speed using item responses and RTs simultaneously for cognitive diagnosis. For illustration, an extended deterministic input, noisy ‘and’ gate (DINA) model was proposed for joint modelling of responses and RTs. Model parameter estimation was explored using the Bayesian Markov chain Monte Carlo (MCMC) method. The PISA 2012 computer-based mathematics data were analysed first. These real data estimates were treated as true values in a subsequent simulation study. A follow-up simulation study with ideal testing conditions was conducted as well to further evaluate model parameter recovery. The results indicated that model parameters could be well recovered using the MCMC approach. Further, incorporating RTs into the DINA model would improve attribute and profile correct classification rates and result in more accurate and precise estimation of the model parameters.     

抑郁在青少年核心自我评价与自杀意念间的中介作用:基于Bootstrap法和MCMC法的实证研究

考察抑郁在青少年核心自我评价与自杀意念间的中介作用。对502名高中生进行量表测评。通过偏差校正的Bootstrap法和有先验信息的MCMC法求出中介效应值的95%置信区间分别为[-.030,-.011]和[-.024,-.014],提示抑郁的中介效应显著。效应量k2、R2med分别为.124、.104,偏差校正的Bootstrap法抽样5000次后,构建的效应量的95%置信区间分别为[.070,.178]、[.063,.156],两种指标共同验证效应量为中等。研究结果说明抑郁在核心自我评价与自杀意念间起部分中介作用,效应量中等。