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11.
Janne V. Kujala Ulla Richardson Heikki Lyytinen 《Journal of mathematical psychology》2010,54(1):196-207
We present a simple but effective method based on Luce’s choice axiom [Luce, R.D. (1959). Individual choice behavior: A theoretical analysis. New York: John Wiley & Sons] for consistent estimation of the pairwise confusabilities of items in a multiple-choice recognition task with arbitrarily chosen choice-sets. The method combines the exact (non-asymptotic) Bayesian way of assessing uncertainty with the unbiasedness emphasized in the classical frequentist approach.We apply the method to data collected using an adaptive computer game designed for prevention of reading disability. A player’s estimated confusability of phonemes (or more accurately, phoneme-grapheme connections) and larger units of language is visualized in an easily understood way with color cues and explicit indication of the accuracy of the estimates. Visualization of learning-related changes in the player’s performance is considered.The empirical validity of the choice axiom is evaluated using the game data itself. The axiom appears to hold reasonably well although a small systematic violation is observable for the smallest choice-set sizes. 相似文献
12.
Hulya Duygu Yigit Steven Andrew Culpepper 《The British journal of mathematical and statistical psychology》2023,76(2):372-401
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. 相似文献
13.
Mixture analysis of count data has become increasingly popular among researchers of substance use, behavioral analysis, and program evaluation. However, this increase in popularity seems to have occurred along with adoption of some conventions in model specification based on arbitrary heuristics that may impact the validity of results. Findings from a systematic review of recent drug and alcohol publications suggested count variables are often dichotomized or misspecified as continuous normal indicators in mixture analysis. Prior research suggests that misspecifying skewed distributions of continuous indicators in mixture analysis introduces bias, though the consequences of this practice when applied to count indicators has not been studied. The present work describes results from a simulation study examining bias in mixture recovery when count indicators are dichotomized (median split; presence vs. absence), ordinalized, or the distribution is misspecified (continuous normal; incorrect count distribution). All distributional misspecifications and methods of categorizing resulted in greater bias in parameter estimates and recovery of class membership relative to specifying the true distribution, though dichotomization appeared to improve class enumeration accuracy relative to all other specifications. Overall, results demonstrate the importance of accurately modeling count indicators in mixture analysis, as misspecification and categorizing data can distort study outcomes. 相似文献
14.
Peida Zhan Hong Jiao Dandan Liao 《The British journal of mathematical and statistical psychology》2018,71(2):262-286
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. 相似文献
15.
Hong Jiao Yuan Zhang 《The British journal of mathematical and statistical psychology》2015,68(1):65-83
A pplications of standard item response theory models assume local independence of items and persons. This paper presents polytomous multilevel testlet models for dual dependence due to item and person clustering in testlet‐based assessments with clustered samples. Simulation and survey data were analysed with a multilevel partial credit testlet model. This model was compared with three alternative models – a testlet partial credit model (PCM), multilevel PCM, and PCM – in terms of model parameter estimation. The results indicated that the deviance information criterion was the fit index that always correctly identified the true multilevel testlet model based on the quantified evidence in model selection, while the Akaike and Bayesian information criteria could not identify the true model. In general, the estimation model and the magnitude of item and person clustering impacted the estimation accuracy of ability parameters, while only the estimation model and the magnitude of item clustering affected the item parameter estimation accuracy. Furthermore, ignoring item clustering effects produced higher total errors in item parameter estimates but did not have much impact on the accuracy of ability parameter estimates, while ignoring person clustering effects yielded higher total errors in ability parameter estimates but did not have much effect on the accuracy of item parameter estimates. When both clustering effects were ignored in the PCM, item and ability parameter estimation accuracy was reduced. 相似文献
16.
Shull, Gaynor and Grimes advanced a model for interresponse time distribution using probabilistic cycling between a higher-rate and a lower-rate response process. Both response processes are assumed to be random in time with a constant rate. The cycling between the two processes is assumed to have a constant transition probability that is independent of bout length. This report develops an analytic form of the model which has a natural parametrization for a higher-rate within-bout responding and a lower-rate visit-initiation responding. The analytic form provides a convenient basis for both a nonlinear least-squares data reduction technique to estimate the model's parameters and Monte Carlo simulations of the model. In addition, the analytic formulation is extended to both a refractory period for the rats' behavior and, separately, the strongly-banded behavior seen with pigeons. 相似文献
17.
Factor analysis is a popular statistical technique for multivariate data analysis. Developments in the structural equation modeling framework have enabled the use of hybrid confirmatory/exploratory approaches in which factor-loading structures can be explored relatively flexibly within a confirmatory factor analysis (CFA) framework. Recently, Muthén & Asparouhov proposed a Bayesian structural equation modeling (BSEM) approach to explore the presence of cross loadings in CFA models. We show that the issue of determining factor-loading patterns may be formulated as a Bayesian variable selection problem in which Muthén and Asparouhov's approach can be regarded as a BSEM approach with ridge regression prior (BSEM-RP). We propose another Bayesian approach, denoted herein as the Bayesian structural equation modeling with spike-and-slab prior (BSEM-SSP), which serves as a one-stage alternative to the BSEM-RP. We review the theoretical advantages and disadvantages of both approaches and compare their empirical performance relative to two modification indices-based approaches and exploratory factor analysis with target rotation. A teacher stress scale data set is used to demonstrate our approach. 相似文献
18.
Seventy‐three children between 6 and 7 years of age were presented with a problem having ambiguous subgoal ordering. Performance in this task showed reliable fingerprints: (a) a non‐monotonic dependence of performance as a function of the distance between the beginning and the end‐states of the problem, (b) very high levels of performance when the first move was correct, and (c) states in which accuracy of the first move was significantly below chance. These features are consistent with a non‐Markov planning agent, with an inherently inertial decision process, and that uses heuristics and partial problem knowledge to plan its actions. We applied a statistical framework to fit and test the quality of a proposed planning model (Monte Carlo Tree Search). Our framework allows us to parse out independent contributions to problem‐solving based on the construction of the value function and on general mechanisms of the search process in the tree of solutions. We show that the latter are correlated with children's performance on an independent measure of planning, while the former is highly domain specific. 相似文献
19.
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。 相似文献
20.
计算机化自适应测验(Computerized Adaptive Testing, 简称CAT)其安全性面临着新的挑战, 小题库的安全更受威胁。如何建设一个大型、优质的题库成为CAT研究中一个非常重要的课题。目前CAT题库的建设存在一些问题, 如成本高且保密性较差。尤其是等值技术较复杂且锚题重复使用容易造成泄露。如能在实施CAT过程中插入未经过参数估计的项目(原始题), 同时对原始题项目参数进行估计, 这对建设大型、优质的CAT题库来说其意义是不言而喻的。本文基于1PLM和2PLM对此进行研究, 提出了原始题在线估计的新方法以及推导出了求区分度参数a迭代初值的计算公式。研究结果表明:无论是模拟研究还是实证研究, 原始题被作答的次数对项目参数估计结果都会产生不同的影响, 并且原始题作答人数越多项目参数估计精度也越高。 相似文献