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191.
The normal theory based maximum likelihood procedure is widely used in structural equation modeling. Three alternatives are:
the normal theory based generalized least squares, the normal theory based iteratively reweighted least squares, and the asymptotically
distribution-free procedure. When data are normally distributed and the model structure is correctly specified, the four procedures
are asymptotically equivalent. However, this equivalence is often used when models are not correctly specified. This short
paper clarifies conditions under which these procedures are not asymptotically equivalent. Analytical results indicate that,
when a model is not correct, two factors contribute to the nonequivalence of the different procedures. One is that the estimated
covariance matrices by different procedures are different, the other is that they use different scales to measure the distance
between the sample covariance matrix and the estimated covariance matrix. The results are illustrated using real as well as
simulated data. Implication of the results to model fit indices is also discussed using the comparative fit index as an example.
The work described in this paper was supported by a grant from the Research Grants Council of Hong Kong Special Administrative
Region (Project No. CUHK 4170/99M) and by NSF grant DMS04-37167. 相似文献
192.
Since data in social and behavioral sciences are often hierarchically organized, special statistical procedures for covariance
structure models have been developed to reflect such hierarchical structures. Most of these developments are based on a multivariate
normality distribution assumption, which may not be realistic for practical data. It is of interest to know whether normal
theory-based inference can still be valid with violations of the distribution condition. Various interesting results have
been obtained for conventional covariance structure analysis based on the class of elliptical distributions. This paper shows
that similar results still hold for 2-level covariance structure models. Specifically, when both the level-1 (within cluster)
and level-2 (between cluster) random components follow the same elliptical distribution, the rescaled statistic recently developed
by Yuan and Bentler asymptotically follows a chi-square distribution. When level-1 and level-2 have different elliptical distributions,
an additional rescaled statistic can be constructed that also asymptotically follows a chi-square distribution. Our results
provide a rationale for applying these rescaled statistics to general non-normal distributions, and also provide insight into
issues related to level-1 and level-2 sample sizes.
The authors thank an associate editor and three referees for their constructive comments, which led to an improved version
of the paper.
This research was supported by grants DA01070 and DA00017 from the National Institute on Drug Abuse and a University of Notre
Dame faculty research grant. 相似文献
193.
Van den Wollenberg stated a theorem specifying the conditions for a test, which is composed of two Rasch homogeneous subscales, as also behaving Rasch homogeneously. In our note, simple numerical counterexamples are given for which this theorem fails.While preparing the final version of this note, Ilse Rop passed away. The first author therefore takes sole responsibility for this final version. 相似文献
194.
H. T. Kiiveri 《Psychometrika》1987,52(4):539-554
In this paper, linear structural equation models with latent variables are considered. It is shown how many common models arise from incomplete observation of a relatively simple system. Subclasses of models with conditional independence interpretations are also discussed. Using an incomplete data point of view, the relationships between the incomplete and complete data likelihoods, assuming normality, are highlighted. For computing maximum likelihood estimates, the EM algorithm and alternatives are surveyed. For the alternative algorithms, simplified expressions for computing function values and derivatives are given. Likelihood ratio tests based on complete and incomplete data are related, and an example on using their relationship to improve the fit of a model is given.This research forms part of the author's doctoral thesis and was supported by a Commonwealth Postgraduate Research Award. The author also wishes to acknowledge the support of CSIRO during the preparation of this paper and the referees' comments which led to substantial improvements. 相似文献
195.
Equivalence of marginal likelihood of the two-parameter normal ogive model in item response theory (IRT) and factor analysis of dichotomized variables (FA) was formally proved. The basic result on the dichotomous variables was extended to multicategory cases, both ordered and unordered categorical data. Pair comparison data arising from multiple-judgment sampling were discussed as a special case of the unordered categorical data. A taxonomy of data for the IRT and FA models was also attempted.The work reported in this paper has been supported by Grant A6394 to the first author from the Natural Sciences and Engineering Research Council of Canada. 相似文献
196.
Michael W. Browne 《Psychometrika》1988,53(4):585-589
Algebraic properties of the normal theory maximum likelihood solution in factor analysis regression are investigated. Two commonly employed measures of the within sample predictive accuracy of the factor analysis regression function are considered: the variance of the regression residuals and the squared correlation coefficient between the criterion variable and the regression function. It is shown that this within sample residual variance and within sample squared correlation may be obtained directly from the factor loading and unique variance estimates, without use of the original observations or the sample covariance matrix. 相似文献
197.
Robert J. Boik 《Psychometrika》1988,53(4):469-486
Repeated measures on multivariate responses can be analyzed according to either of two models: a doubly multivariate model (DMM) or a multivariate mixed model (MMM). This paper reviews both models and gives three new results concerning the MMM. The first result is, primarily, of theoretical interest; the second and third have implications for practice. First, it is shown that, given multivariate normality, a condition called multivariate sphericity of the covariance matrix is both necessary and sufficient for the validity of the MMM analysis. To test for departure from multivariate sphericity, the likelihood ratio test can be employed. The second result is an approximation to the null distribution of the likelihood ratio test statistic, useful for moderate sample sizes. Third, for situations satisfying multivariate normality, but not multivariate sphericity, a multivariate correction factor is derived. The correction factor generalizes Box's and can be used to construct an adjusted MMM test.I am grateful to an anonymous referee for carefully attending to the mathematical details of this paper. 相似文献
198.
Two-group classification in latent trait theory: Scores with monotone likelihood ratio 总被引:1,自引:0,他引:1
D. A. Grayson 《Psychometrika》1988,53(3):383-392
This paper deals with two-group classification when a unidimensional latent trait,, is appropriate for explaining the data,X. It is shown that ifX has monotone likelihood ratio then optimal allocation rules can be based on its magnitude when allocation must be made to one of two groups related to. These groups may relate to probabilistically via a non-decreasing functionp(), or may be defined by all subjects above or below a selected value on.In the case where the data arise from dichotomous items, then only the assumption that the items have nondecreasing item characteristic functions is enough to ensure that the unweighted sum of responses (the number-right score or raw score) possesses this fundamental monotone likelihood ratio property. 相似文献
199.
A three-stage estimation procedure for structural equation models with polytomous variables 总被引:1,自引:0,他引:1
This paper is concerned with the analysis of structural equation models with polytomous variables. A computationally efficient three-stage estimator of the thresholds and the covariance structure parameters, based on partition maximum likelihood and generalized least squares estimation, is proposed. An example is presented to illustrate the method.This research was supported in part by a research grant DA01070 from the U.S. Public Health Service. The production assistance of Julie Speckart is gratefully acknowledged. 相似文献
200.
Thomas A. Warm 《Psychometrika》1989,54(3):427-450
Applications of item response theory, which depend upon its parameter invariance property, require that parameter estimates be unbiased. A new method, weighted likelihood estimation (WLE), is derived, and proved to be less biased than maximum likelihood estimation (MLE) with the same asymptotic variance and normal distribution. WLE removes the first order bias term from MLE. Two Monte Carlo studies compare WLE with MLE and Bayesian modal estimation (BME) of ability in conventional tests and tailored tests, assuming the item parameters are known constants. The Monte Carlo studies favor WLE over MLE and BME on several criteria over a wide range of the ability scale. 相似文献