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A new person-fit method based on machine learning in CDM in education. 教育CDM中基于机器学习的人-拟合新方法。
The British journal of mathematical and statistical psychology Pub Date : 2022-03-27 DOI: 10.1111/bmsp.12270
Zhemin Zhu, D. Arthur, Hua-Hua Chang
{"title":"A new person-fit method based on machine learning in CDM in education.","authors":"Zhemin Zhu, D. Arthur, Hua-Hua Chang","doi":"10.1111/bmsp.12270","DOIUrl":"https://doi.org/10.1111/bmsp.12270","url":null,"abstract":"Cognitive diagnosis models have become popular in educational assessment and are used to provide more individualized feedback about a student's specific strengths and weaknesses than traditional total scores. However, if the testing data are contaminated by certain biases or aberrant response patterns, such predictions may not be accurate. The current research objective is to develop a new person-fit method that is based on machine learning and improves the functionality of existing person-fit methods. Various simulations were designed under three aberrant conditions: cheating, sleeping and random guessing. Simulation results showed that the new method was more powerful and effective than previous methods, especially for short-length tests.","PeriodicalId":272649,"journal":{"name":"The British journal of mathematical and statistical psychology","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"119379894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Marginalized maximum a posteriori estimation for the four-parameter logistic model under a mixture modelling framework. 混合建模框架下四参数logistic模型的边缘极大后验估计。
The British journal of mathematical and statistical psychology Pub Date : 2020-11-01 DOI: 10.1111/bmsp.12185
Xiangbin Meng, Gongjun Xu, Jiwei Zhang, Jian Tao
{"title":"Marginalized maximum a posteriori estimation for the four-parameter logistic model under a mixture modelling framework.","authors":"Xiangbin Meng, Gongjun Xu, Jiwei Zhang, Jian Tao","doi":"10.1111/bmsp.12185","DOIUrl":"https://doi.org/10.1111/bmsp.12185","url":null,"abstract":"The four-parameter logistic model (4PLM) has recently attracted much interest in various applications. Motivated by recent studies that re-express the four-parameter model as a mixture model with two levels of latent variables, this paper develops a new expectation-maximization (EM) algorithm for marginalized maximum a posteriori estimation of the 4PLM parameters. The mixture modelling framework of the 4PLM not only makes the proposed EM algorithm easier to implement in practice, but also provides a natural connection with popular cognitive diagnosis models. Simulation studies were conducted to show the good performance of the proposed estimation method and to investigate the impact of the additional upper asymptote parameter on the estimation of other parameters. Moreover, a real data set was analysed using the 4PLM to show its improved performance over the three-parameter logistic model.","PeriodicalId":272649,"journal":{"name":"The British journal of mathematical and statistical psychology","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130979225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
Corrigendum. 有待纠正。
IF 2.6
The British journal of mathematical and statistical psychology Pub Date : 2020-11-01 DOI: 10.1111/bmsp.12225
{"title":"Corrigendum.","authors":"","doi":"10.1111/bmsp.12225","DOIUrl":"https://doi.org/10.1111/bmsp.12225","url":null,"abstract":"","PeriodicalId":272649,"journal":{"name":"The British journal of mathematical and statistical psychology","volume":"73 3","pages":"556"},"PeriodicalIF":2.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/bmsp.12225","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38596604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A latent topic model with Markov transition for process data. 过程数据的马尔可夫转换潜主题模型。
IF 2.6
The British journal of mathematical and statistical psychology Pub Date : 2020-11-01 Epub Date: 2020-01-08 DOI: 10.1111/bmsp.12197
Haochen Xu, Guanhua Fang, Zhiliang Ying
{"title":"A latent topic model with Markov transition for process data.","authors":"Haochen Xu,&nbsp;Guanhua Fang,&nbsp;Zhiliang Ying","doi":"10.1111/bmsp.12197","DOIUrl":"https://doi.org/10.1111/bmsp.12197","url":null,"abstract":"<p><p>We propose a latent topic model with a Markov transition for process data, which consists of time-stamped events recorded in a log file. Such data are becoming more widely available in computer-based educational assessment with complex problem-solving items. The proposed model can be viewed as an extension of the hierarchical Bayesian topic model with a hidden Markov structure to accommodate the underlying evolution of an examinee's latent state. Using topic transition probabilities along with response times enables us to capture examinees' learning trajectories, making clustering/classification more efficient. A forward-backward variational expectation-maximization (FB-VEM) algorithm is developed to tackle the challenging computational problem. Useful theoretical properties are established under certain asymptotic regimes. The proposed method is applied to a complex problem-solving item in the 2012 version of the Programme for International Student Assessment (PISA).</p>","PeriodicalId":272649,"journal":{"name":"The British journal of mathematical and statistical psychology","volume":"73 3","pages":"474-505"},"PeriodicalIF":2.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/bmsp.12197","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37521642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
D-optimal design for the Rasch counts model with multiple binary predictors. 具有多个二元预测因子的Rasch计数模型的d -最优设计。
IF 2.6
The British journal of mathematical and statistical psychology Pub Date : 2020-11-01 Epub Date: 2020-05-14 DOI: 10.1111/bmsp.12204
Ulrike Graßhoff, Heinz Holling, Rainer Schwabe
{"title":"D-optimal design for the Rasch counts model with multiple binary predictors.","authors":"Ulrike Graßhoff,&nbsp;Heinz Holling,&nbsp;Rainer Schwabe","doi":"10.1111/bmsp.12204","DOIUrl":"https://doi.org/10.1111/bmsp.12204","url":null,"abstract":"<p><p>In this paper we derive optimal designs for the Rasch Poisson counts model and its extended version of the (generalized) negative binomial counts model incorporating several binary predictors for the difficulty parameter. To efficiently estimate the regression coefficients of the predictors, locally D-optimal designs are developed. After an introduction to the Rasch Poisson counts model and its extension, we will specify these models as particular generalized linear models. Based on this embedding, optimal designs for both models including several binary explanatory variables will be presented. Therefore, we will derive conditions on the effect sizes for certain designs to be locally D-optimal. Finally, it is pointed out that the results derived for the Rasch Poisson models can be applied for more general Poisson regression models which should receive more attention in future psychological research.</p>","PeriodicalId":272649,"journal":{"name":"The British journal of mathematical and statistical psychology","volume":"73 3","pages":"541-555"},"PeriodicalIF":2.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/bmsp.12204","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37935111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Modelling inter-individual differences in latent within-person variation: The confirmatory factor level variability model. 模拟潜在的人内变异的个体间差异:验证性因素水平变异模型。
IF 2.6
The British journal of mathematical and statistical psychology Pub Date : 2020-11-01 Epub Date: 2020-01-08 DOI: 10.1111/bmsp.12196
Steffen Nestler
{"title":"Modelling inter-individual differences in latent within-person variation: The confirmatory factor level variability model.","authors":"Steffen Nestler","doi":"10.1111/bmsp.12196","DOIUrl":"https://doi.org/10.1111/bmsp.12196","url":null,"abstract":"<p><p>Psychological theories often produce hypotheses that pertain to individual differences in within-person variability. To empirically test the predictions entailed by such hypotheses with longitudinal data, researchers often use multilevel approaches that allow them to model between-person differences in the mean level of a certain variable and the residual within-person variance. Currently, these approaches can be applied only when the data stem from a single variable. However, it is common practice in psychology to assess not just a single measure but rather several measures of a construct. In this paper we describe a model in which we combine the single-indicator model with confirmatory factor analysis. The new model allows individual differences in latent mean-level factors and latent within-person variability factors to be estimated. Furthermore, we show how the model's parameters can be estimated with a maximum likelihood estimator, and we illustrate the approach using an example that involves intensive longitudinal data.</p>","PeriodicalId":272649,"journal":{"name":"The British journal of mathematical and statistical psychology","volume":"73 3","pages":"452-473"},"PeriodicalIF":2.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/bmsp.12196","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37522167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 14
A new quantile estimator with weights based on a subsampling approach. 一种新的基于子抽样方法的权重分位数估计器。
IF 2.6
The British journal of mathematical and statistical psychology Pub Date : 2020-11-01 Epub Date: 2020-01-16 DOI: 10.1111/bmsp.12198
Gözde Navruz, A Fırat Özdemir
{"title":"A new quantile estimator with weights based on a subsampling approach.","authors":"Gözde Navruz,&nbsp;A Fırat Özdemir","doi":"10.1111/bmsp.12198","DOIUrl":"https://doi.org/10.1111/bmsp.12198","url":null,"abstract":"<p><p>Quantiles are widely used in both theoretical and applied statistics, and it is important to be able to deploy appropriate quantile estimators. To improve performance in the lower and upper quantiles, especially with small sample sizes, a new quantile estimator is introduced which is a weighted average of all order statistics. The new estimator, denoted NO, has desirable asymptotic properties. Moreover, it offers practical advantages over four estimators in terms of efficiency in most experimental settings. The Harrell-Davis quantile estimator, the default quantile estimator of the R programming language, the Sfakianakis-Verginis SV2 quantile estimator and a kernel quantile estimator. The NO quantile estimator is also utilized in comparing two independent groups with a percentile bootstrap method and, as expected, it is more successful than other estimators in controlling Type I error rates.</p>","PeriodicalId":272649,"journal":{"name":"The British journal of mathematical and statistical psychology","volume":"73 3","pages":"506-521"},"PeriodicalIF":2.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/bmsp.12198","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37547475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Modelling monotonic effects of ordinal predictors in Bayesian regression models. 贝叶斯回归模型中有序预测因子单调效应的建模。
IF 2.6
The British journal of mathematical and statistical psychology Pub Date : 2020-11-01 Epub Date: 2020-01-13 DOI: 10.1111/bmsp.12195
Paul-Christian Bürkner, Emmanuel Charpentier
{"title":"Modelling monotonic effects of ordinal predictors in Bayesian regression models.","authors":"Paul-Christian Bürkner,&nbsp;Emmanuel Charpentier","doi":"10.1111/bmsp.12195","DOIUrl":"https://doi.org/10.1111/bmsp.12195","url":null,"abstract":"<p><p>Ordinal predictors are commonly used in regression models. They are often incorrectly treated as either nominal or metric, thus under- or overestimating the information contained. Such practices may lead to worse inference and predictions compared to methods which are specifically designed for this purpose. We propose a new method for modelling ordinal predictors that applies in situations in which it is reasonable to assume their effects to be monotonic. The parameterization of such monotonic effects is realized in terms of a scale parameter b representing the direction and size of the effect and a simplex parameter <math><mi>ς</mi></math> modelling the normalized differences between categories. This ensures that predictions increase or decrease monotonically, while changes between adjacent categories may vary across categories. This formulation generalizes to interaction terms as well as multilevel structures. Monotonic effects may be applied not only to ordinal predictors, but also to other discrete variables for which a monotonic relationship is plausible. In simulation studies we show that the model is well calibrated and, if there is monotonicity present, exhibits predictive performance similar to or even better than other approaches designed to handle ordinal predictors. Using Stan, we developed a Bayesian estimation method for monotonic effects which allows us to incorporate prior information and to check the assumption of monotonicity. We have implemented this method in the R package brms, so that fitting monotonic effects in a fully Bayesian framework is now straightforward.</p>","PeriodicalId":272649,"journal":{"name":"The British journal of mathematical and statistical psychology","volume":"73 3","pages":"420-451"},"PeriodicalIF":2.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/bmsp.12195","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37547797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 70
Curiosity-driven recommendation strategy for adaptive learning via deep reinforcement learning. 基于深度强化学习的自适应学习的好奇心驱动推荐策略。
IF 2.6
The British journal of mathematical and statistical psychology Pub Date : 2020-11-01 Epub Date: 2020-02-21 DOI: 10.1111/bmsp.12199
Ruijian Han, Kani Chen, Chunxi Tan
{"title":"Curiosity-driven recommendation strategy for adaptive learning via deep reinforcement learning.","authors":"Ruijian Han,&nbsp;Kani Chen,&nbsp;Chunxi Tan","doi":"10.1111/bmsp.12199","DOIUrl":"https://doi.org/10.1111/bmsp.12199","url":null,"abstract":"<p><p>The design of recommendation strategies in the adaptive learning systems focuses on utilizing currently available information to provide learners with individual-specific learning instructions. As a critical motivate for human behaviours, curiosity is essentially the drive to explore knowledge and seek information. In a psychologically inspired view, we propose a curiosity-driven recommendation policy within the reinforcement learning framework, allowing for an efficient and enjoyable personalized learning path. Specifically, a curiosity reward from a well-designed predictive model is generated to model one's familiarity with the knowledge space. Given such curiosity rewards, we apply the actor-critic method to approximate the policy directly through neural networks. Numerical analyses with a large continuous knowledge state space and concrete learning scenarios are provided to further demonstrate the efficiency of the proposed method.</p>","PeriodicalId":272649,"journal":{"name":"The British journal of mathematical and statistical psychology","volume":"73 3","pages":"522-540"},"PeriodicalIF":2.6,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/bmsp.12199","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37661803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Combining diversity and dispersion criteria for anticlustering: A bicriterion approach. 结合多样性和分散准则的反聚类:双准则方法。
The British journal of mathematical and statistical psychology Pub Date : 2020-11-01 DOI: 10.1111/bmsp.12186
M. Brusco, J. Cradit, D. Steinley
{"title":"Combining diversity and dispersion criteria for anticlustering: A bicriterion approach.","authors":"M. Brusco, J. Cradit, D. Steinley","doi":"10.1111/bmsp.12186","DOIUrl":"https://doi.org/10.1111/bmsp.12186","url":null,"abstract":"Most partitioning methods used in psychological research seek to produce homogeneous groups (i.e., groups with low intra-group dissimilarity). However, there are also applications where the goal is to provide heterogeneous groups (i.e., groups with high intra-group dissimilarity). Examples of these anticlustering contexts include construction of stimulus sets, formation of student groups, assignment of employees to project work teams, and assembly of test forms from a bank of items. Unfortunately, most commercial software packages are not equipped to accommodate the objective criteria and constraints that commonly arise for anticlustering problems. Two important objective criteria for anticlustering based on information in a dissimilarity matrix are: a diversity measure based on within-cluster sums of dissimilarities; and a dispersion measure based on the within-cluster minimum dissimilarities. In many instances, it is possible to find a partition that provides a large improvement in one of these two criteria with little (or no) sacrifice in the other criterion. For this reason, it is of significant value to explore the trade-offs that arise between these two criteria. Accordingly, the key contribution of this paper is the formulation of a bicriterion optimization problem for anticlustering based on the diversity and dispersion criteria, along with heuristics to approximate the Pareto efficient set of partitions. A motivating example and computational study are provided within the framework of test assembly.","PeriodicalId":272649,"journal":{"name":"The British journal of mathematical and statistical psychology","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130890615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
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