对变化/分割模型的检验(I)

用两个实验对变化／分割模型进行了检验。实验１控制目标时距和该时距内的填充数字系列,操纵数字系列的分割段数;实验２控制目标时距内的填充数字系列的间距,操纵目标时距及其中填充数字系列的分割段数,要求被试用再现法和多数估计法分别复制目标时距,并进行立即估计和延迟估计。结果显示：与存储容量模型和加工时间模型相比较,变化／分割模型对时间估计的解释具有更高的预测效度     

Estimating latent distributions

Consider vectors of item responses obtained from a sample of subjects from a population in which ability is distributed with densityg(), where the are unknown parameters. Assuming the responses depend on through a fully specified item response model, this paper presents maximum likelihood equations for the estimation of the population parameters directly from the observed responses; i.e., without estimating an ability parameter for each subject. Also provided are asymptotic standard errors and tests of fit, computing approximations, and details of four special cases: a non-parametric approximation, a normal solution, a resolution of normal components, and a beta-binomial solution.The author would like to thank R. Darrell Bock for his comments, suggestions, and encouragement during the course of this work.     

Sequential estimation in multidimensional scaling

The concept of sequential estimation is introduced in multidimensional scaling (MDS). The sequential estimation method developed in this paper refers to continually updating estimates of a configuration as new observations are added. This method has a number of advantages, such as a locally optimal design of the experiment can be easily constructed, and dynamic experimentation is made possible. Using artificial data, the performance of our sequential method is illustrated.We are indebted to anonymous reviewers for their suggestions. In addition, we thank Dr. Frank Critchley for his helpful comments on our Q/S algorithm.     

Reliability estimation for a test with parts of unknown lengths

The separate questions on an essay test or the individual judges on a rater panel may constitute congeneric parts rather than tau-equivalent parts. Also, it may be necessary to infer the lengths of the congeneric parts from their variances and covariances, rather than from some obvious feature of each part, such as the range of possible scores. Cronbach's alpha coefficient applied to such part-tests data will underestimate total score reliability. Several reliability coefficients are developed for such instruments. They may be regarded as extensions of the coefficient developed by Kristof for a three-part test.     

Expanding the rasch model to a general model having more than one dimension

The well-known Rasch model is generalized to a multicomponent model, so that observations of component events are not needed to apply the model. It is shown that the generalized model has retained the property of the specific objectivity of the Rasch model. For a restricted variant of the model, maximum likelihood estimates of its parameters and a statistical test of the model are given. The results of an application to a mathematics test involving six components are described.     

Generating items during testing: Psychometric issues and models

On-line item generation is becoming increasingly feasible for many cognitive tests. Item generation seemingly conflicts with the well established principle of measuring persons from items with known psychometric properties. This paper examines psychometric principles and models required for measurement from on-line item generation. Three psychometric issues are elaborated for item generation. First, design principles to generate items are considered. A cognitive design system approach is elaborated and then illustrated with an application to a test of abstract reasoning. Second, psychometric models for calibrating generating principles, rather than specific items, are required. Existing item response theory (IRT) models are reviewed and a new IRT model that includes the impact on item discrimination, as well as difficulty, is developed. Third, the impact of item parameter uncertainty on person estimates is considered. Results from both fixed content and adaptive testing are presented.This article is based on the Presidential Address Susan E. Embretson gave on June 26, 1999 at the 1999 Annual Meeting of the Psychometric Society held at the University of Kansas in Lawrence, Kansas. —Editor     

Comparing the predictive powers of alternative multiple regression models

Mean squared error of prediction is used as the criterion for determining which of two multiple regression models (not necessarily nested) is more predictive. We show that an unrestricted (or true) model witht parameters should be chosen over a restricted (or misspecified) model withm parameters if (P _t ² ?P _m ² )>(1?P _t ² )(t?m)/n, whereP _t ² andP _m ² are the population coefficients of determination of the unrestricted and restricted models, respectively, andn is the sample size. The left-hand side of the above inequality represents the squared bias in prediction by using the restricted model, and the right-hand side gives the reduction in variance of prediction error by using the restricted model. Thus, model choice amounts to the classical statistical tradeoff of bias against variance. In practical applications, we recommend thatP ² be estimated by adjustedR ² . Our recommendation is equivalent to performing theF-test for model comparison, and using a critical value of 2?(m/n); that is, ifF>2?(m/n), the unrestricted model is recommended; otherwise, the restricted model is recommended.     

Thurstone's discriminal processes fifty years later

Four issues are discussed concerning Thurstone's discriminal processes: the distributions governing the representation, the nature of the response decision rules, the relation of the mean representation to physical characteristics of the stimulus, and factors affecting the variance of the representation. A neural schema underlying the representation is proposed which involves samples in time of pulse trains on individual neural fibers, estimators of parameters of the several pulse trains, samples of neural fibers, and an aggregation of the estimates over the sample. The resulting aggregated estimate is the Thurstonian representation. Two estimators of pulse rate, which is monotonic with signal intensity, are timing and counting ratios and two methods of aggregation are averaging and maximizing. These lead to very different predictions in a speed-accuracy experiment; data indicate that both estimators are available and the aggregation is by averaging. Magnitude estimation data are then used both to illustrate an unusual response rule and to study the psychophysical law. In addition, the pattern of variability and correlation of magnitude estimates on successive trials is interpreted in terms of the sample size over which the aggregation takes place. Neural sample size is equated with selective attention, and is an important factor affecting the variability of the representation. It accounts for the magical number seven phenomenon in absolute identification and predicts the impact of nonuniform distributions of intensities on the absolute identification of two frequencies. 1977 Psychometric Society Presidential Address. This work was supported in part by a grant of the National Science Foundation to Harvard University. I wish to express my appreciation to S. Burbeck, D. M. Green, M. Shaw, and B. Wandell for their useful comments on an earlier draft of this paper.     

Bayesian estimation of item response curves

Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. The procedure is illustrated by data from a mathematics test.This work was supported under Contract No. N00014-85-K-0113, NR 150-535, from Personnel and Training Research Programs, Psychological Sciences Division, Office of Naval Research. The authors wish to thank Mark D. Reckase for providing the ACT data used in the illustration and Michael J. Soltys for computational assistance. They also wish to thank the editor and four anonymous reviewers for many valuable suggestions.     

Estimating an unobserved component of a serial response time model

A method is developed for estimating the response time distribution of an unobserved component in a two-component serial model, assuming the components are stochastically independent. The estimate of the component's density function is constrained only to be unimodal and non-negative. Numerical examples suggest that the method can yield reasonably accurate estimates with sample sizes of 300 and, in some cases, with sample sizes as small as 100.The author wishes to thank David Kohfeld, Jim Ramsay, Jim Townsend and two anonymous referees for a number of useful and stimulating comments on an earlier version of this paper.