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191.
Werner Stegelmann 《Psychometrika》1983,48(2):259-267
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. 相似文献
192.
Generating items during testing: Psychometric issues and models 总被引:2,自引:0,他引:2
Susan E. Embretson 《Psychometrika》1999,64(4):407-433
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 相似文献
193.
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. 相似文献
194.
R. Duncan Luce 《Psychometrika》1977,42(4):461-489
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. 相似文献
195.
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. 相似文献
196.
Bruce Bloxom 《Psychometrika》1979,44(4):473-484
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. 相似文献
197.
J. O. Ramsay 《Psychometrika》1978,43(2):145-160
Techniques are developed for surrounding each of the points in a multidimensional scaling solution with a region which will contain the population point with some level of confidence. Bayesian credibility regions are also discussed. A general theorem is proven which describes the asymptotic distribution of maximum likelihood estimates subject to identifiability constraints. This theorem is applied to a number of models to display asymptotic variance-covariance matrices for coordinate estimates under different rotational constraints. A technique is described for displaying Bayesian conditional credibility regions for any sample size.The research reported here was supported by grant number APA 320 to the author by the National Research Council of Canada. 相似文献
198.
Hiroshi Hojo 《The Japanese psychological research》1998,40(3):166-171
One probabilistic version of Coombs' unfolding model called the MMUR (Marginalization model for the Multidimensional Unfolding analysis of Ranking data) is extended to treat ranking data for groups. One favorable feature of the model is that it can both take into consideration individual differences without estimating the subject parameters and capture the differences between the groups in a systematic manner. Another advantage lies in the fact that one can see the group differences in the geometrical point configuration, since the model shows how the ideal points of the groups differ from each other in space. Four applications are provided which demonstrate that the model is useful for clarifying systematic differences in this type of data. 相似文献
199.
Data are ipsative if they are subject to a constant-sum constraint for each individual. In the present study, ordinal ipsative data (OID) are defined as the ordinal rankings across a vector of variables. It is assumed that OID are the manifestations of their underlying nonipsative vector y, which are difficult to observe directly. A two-stage estimation procedure is suggested for the analysis of structural equation models with OID. In the first stage, the partition maximum likelihood (PML) method and the generalized least squares (GLS) method are proposed for estimating the means and the covariance matrix of Acy, where Ac is a known contrast matrix. Based on the joint asymptotic distribution of the first stage estimator and an appropriate weight matrix, the generalized least squares method is used to estimate the structural parameters in the second stage. A goodness-of-fit statistic is given for testing the hypothesized covariance structure. Simulation results show that the proposed method works properly when a sufficiently large sample is available.This research was supported by National Institute on Drug Abuse Grants DA01070 and DA10017. The authors are indebted to Dr. Lee Cooper, Dr. Eric Holman, Dr. Thomas Wickens for their valuable suggestions on this study, and Dr. Fanny Cheung for allowing us to use her CPAI data set in this article. The authors would also like to acknowledge the helpful comments from the editor and the two anonymous reviewers. 相似文献
200.