Optimum examinee samples for item parameter estimation in item response theory: A multi-objective programming approach

This paper proposes a multi-objective programming method for determining samples of examinees needed for estimating the parameters of a group of items. In the numerical experiments, optimum samples are compared to uniformly and normally distributed samples. The results show that the samples usually recommended in the literature are well suited for estimating the difficulty parameters. Furthermore, they are also adequate for estimating the discrimination parameters in the three-parameter model, butnot for the guessing parameters.     

Perceived social context and risk preference: A re-examination of framing effects in a life-death decision problem

This study examines the effects of perceived group context on subjects risk attitudes and their sensitivity to the framing of choice outcomes in a ‘life-death’ decision problem. It seeks to uncover the psychological mechanisms underlying decision-making biases by systematically manipulating the decision context in which the ‘life-death’ problem was described. The study revealed that subjects risk preferences varied as a function of the experimental manipulations. Previously observed reversals in preferences (framing effects) appeared in large-group contexts and disappeared in small-group and family contexts. When considering the fate of small groups, subjects unambiguously favored the probabilistic outcome, no matter how the ‘life-death’ decision problem was framed. The empirical data obtained from the present study suggest that human choice patterns are behaviorally distinguishable across large-group, small-group, and family social contexts.     

差数显著性t检验与元分析的对比研究

利用计算机构造被试总体、模拟实验研究程序进行抽样研究,探讨显著性ｔ检验方法与元分析方法在检验实验结果数据方面的差异。在模拟实验过程中,ｔ验受到显著性水平、样本容量和总体效果大小的影响,因此最终影响了统计推断的可靠性,建议：在进行显著性检验过程中,应对统计检验能力进行估计;元分析方法以样本为元素对总体进行推断,因此具有很高的准确性和可靠性,它将很有可能成为今后心理学研究的重要统计工具。     

Specifying optimum examinees for item parameter estimation in item response theory

Information functions are used to find the optimum ability levels and maximum contributions to information for estimating item parameters in three commonly used logistic item response models. For the three and two parameter logistic models, examinees who contribute maximally to the estimation of item difficulty contribute little to the estimation of item discrimination. This suggests that in applications that depend heavily upon the veracity of individual item parameter estimates (e.g. adaptive testing or text construction), better item calibration results may be obtained (for fixed sample sizes) from examinee calibration samples in which ability is widely dispersed.This work was supported by Contract No. N00014-83-C-0457, project designation NR 150-520, from Cognitive Science Program, Cognitive and Neural Sciences Division, Office of Naval Research and Educational Testing Service through the Program Research Planning Council. Reproduction in whole or in part is permitted for any purpose of the United States Government. The author wishes to acknowledge the invaluable assistance of Maxine B. Kingston in carrying out this study, and to thank Charles Lewis for his many insightful comments on earlier drafts of this paper.     

More on EM for ML factor analysis

We address several issues that are raised by Bentler and Tanaka's [1983] discussion of Rubin and Thayer [1982]. Our conclusions are: standard methods do not completely monitor the possible existence of multiple local maxima; summarizing inferential precision by the standard output based on second derivatives of the log likelihood at a maximum can be inappropriate, even if there exists a unique local maximum; EM and LISREL can be viewed as complementary, albeit not entirely adequate, tools for factor analysis.This work was partially supported by the Program Statistics Research Project at Educational Testing Service.     

Probabilistic multidimensional scaling: Complete and incomplete data

Simple procedures are described for obtaining maximum likelihood estimates of the location and uncertainty parameters of the Hefner model. This model is a probabilistic, multidimensional scaling model, which assigns a multivariate normal distribution to each stimulus point. It is shown that for such a model, standard nonmetric and metric algorithms are not appropriate. A procedure is also described for constructing incomplete data sets, by taking into consideration the degree of familiarity the subject has for each stimulus. Maximum likelihood estimates are developed both for complete and incomplete data sets. This research was supported by National Science Grant No. SOC76-20517. The first author would especially like to express his gratitude to the Netherlands Institute for Advanced Study for its very substantial help with this research.     

On Green's best linear composites with a specified structure,and oblique estimates of factor scores

Green solved the problem of least-squares estimation of several criteria subject to the constraint that the estimates have an arbitrary fixed covariance or correlation matrix. In the present paper an omission in Green's proof is discussed and resolved. Furthermore, it is shown that some recently published solutions for estimating oblique factor scores are special cases of Green's solution for the case of fixed covariance matrices.     

Determinants of pausing under variable-ratio schedules: Reinforcer magnitude, ratio size, and schedule configuration

Pigeons pecked a key under two-component multiple variable-ratio schedules that offered 8-s or 2-s access to grain. Phase 1 assessed the effects of differences in reinforcer magnitude on postreinforcement pausing, as a function of ratio size. In Phase 2, postreinforcement pausing and the first five interresponse times in each ratio were measured as a function of differences in reinforcer magnitude under equal variable-ratio schedules consisting of different configurations of individual ratios. Rates were also calculated exclusive of postreinforcement pause times in both phases. The results from Phase 1 showed that as ratio size increased, the differences in pausing educed by unequal reinforcer magnitudes also increased. The results of Phase 2 showed that the effects of reinforcer magnitude on pausing and IRT durations were a function of schedule configuration. Under one configuration, in which the smallest ratio was a fixed-ratio 1, pauses were unaffected by magnitude but the first five interresponse times were affected. Under the other configuration, in which the smallest ratio was a fixed-ratio 7, pauses were affected by reinforcer magnitude but the first five interresponse times were not. The effect of each configuration seemed to be determined by the value of the smallest individual ratio. Rates calculated exclusive of postreinforcement pause times were, in general, directly related to reinforcer magnitude, and the relation was shown to be a function of schedule configuration.     

Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models

Using the theory of pseudo maximum likelihood estimation the asymptotic covariance matrix of maximum likelihood estimates for mean and covariance structure models is given for the case where the variables are not multivariate normal. This asymptotic covariance matrix is consistently estimated without the computation of the empirical fourth order moment matrix. Using quasi-maximum likelihood theory a Hausman misspecification test is developed. This test is sensitive to misspecification caused by errors that are correlated with the independent variables. This misspecification cannot be detected by the test statistics currently used in covariance structure analysis.For helpful comments on a previous draft of the paper we are indebted to Kenneth A. Bollen, Ulrich L. Küsters, Michael E. Sobel and the anonymous reviewers of Psychometrika. For partial research support, the first author wishes to thank the Department of Sociology at the University of Arizona, where he was a visiting professor during the fall semester 1987.