British Journal of Mathematical & Statistical Psychology最新文献

{"title":"Mixtures of \u0000 \u0000 \u0000 t\u0000 \u0000 $$ t $$\u0000 factor analysers with censored responses and external covariates: An application to educational data from Peru","authors":"Wan-Lun Wang,&nbsp;Luis M. Castro,&nbsp;Huei-Jyun Li,&nbsp;Tsung-I Lin","doi":"10.1111/bmsp.12329","DOIUrl":"10.1111/bmsp.12329","url":null,"abstract":"<p>Analysing data from educational tests allows governments to make decisions for improving the quality of life of individuals in a society. One of the key responsibilities of statisticians is to develop models that provide decision-makers with pertinent information about the latent process that educational tests seek to represent. Mixtures of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation>$$ t $$</annotation>\u0000 </semantics></math> factor analysers (MtFA) have emerged as a powerful device for model-based clustering and classification of high-dimensional data containing one or several groups of observations with fatter tails or anomalous outliers. This paper considers an extension of MtFA for robust clustering of censored data, referred to as the MtFAC model, by incorporating external covariates. The enhanced flexibility of including covariates in MtFAC enables cluster-specific multivariate regression analysis of dependent variables with censored responses arising from upper and/or lower detection limits of experimental equipment. An alternating expectation conditional maximization (AECM) algorithm is developed for maximum likelihood estimation of the proposed model. Two simulation experiments are conducted to examine the effectiveness of the techniques presented. Furthermore, the proposed methodology is applied to Peruvian data from the 2007 Early Grade Reading Assessment, and the results obtained from the analysis provide new insights regarding the reading skills of Peruvian students.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138630782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Editorial acknowledgement","authors":"","doi":"10.1111/bmsp.12331","DOIUrl":"https://doi.org/10.1111/bmsp.12331","url":null,"abstract":"","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139435114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Using cross-validation methods to select time series models: Promises and pitfalls","authors":"Siwei Liu,&nbsp;Di Jody Zhou","doi":"10.1111/bmsp.12330","DOIUrl":"10.1111/bmsp.12330","url":null,"abstract":"<p>Vector autoregressive (VAR) modelling is widely employed in psychology for time series analyses of dynamic processes. However, the typically short time series in psychological studies can lead to overfitting of VAR models, impairing their predictive ability on unseen samples. Cross-validation (CV) methods are commonly recommended for assessing the predictive ability of statistical models. However, it is unclear how the performance of CV is affected by characteristics of time series data and the fitted models. In this simulation study, we examine the ability of two CV methods, namely,10-fold CV and blocked CV, in estimating the prediction errors of three time series models with increasing complexity (person-mean, AR, and VAR), and evaluate how their performance is affected by data characteristics. We then compare these CV methods to the traditional methods using the Akaike (AIC) and Bayesian (BIC) information criteria in their accuracy of selecting the most predictive models. We find that CV methods tend to underestimate prediction errors of simpler models, but overestimate prediction errors of VAR models, particularly when the number of observations is small. Nonetheless, CV methods, especially blocked CV, generally outperform the AIC and BIC. We conclude our study with a discussion on the implications of the findings and provide helpful guidelines for practice.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12330","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138500287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The effective sample size in Bayesian information criterion for level-specific fixed and random-effect selection in a two-level nested model","authors":"Sun-Joo Cho,&nbsp;Hao Wu,&nbsp;Matthew Naveiras","doi":"10.1111/bmsp.12327","DOIUrl":"10.1111/bmsp.12327","url":null,"abstract":"<p>Popular statistical software provides the Bayesian information criterion (BIC) for multi-level models or linear mixed models. However, it has been observed that the combination of statistical literature and software documentation has led to discrepancies in the formulas of the BIC and uncertainties as to the proper use of the BIC in selecting a multi-level model with respect to level-specific fixed and random effects. These discrepancies and uncertainties result from different specifications of sample size in the BIC's penalty term for multi-level models. In this study, we derive the BIC's penalty term for level-specific fixed- and random-effect selection in a two-level nested design. In this new version of BIC, called <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>BIC</mi>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </semantics></math>, this penalty term is decomposed into two parts if the random-effect variance–covariance matrix has full rank: (a) a term with the log of average sample size per cluster and (b) the total number of parameters times the log of the total number of clusters. Furthermore, we derive the new version of BIC, called <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>BIC</mi>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </semantics></math>, in the presence of redundant random effects. We show that the derived formulae, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>BIC</mi>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>BIC</mi>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </semantics></math>, adhere to empirical values via numerical demonstration and that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>BIC</mi>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </semantics></math> (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 </mrow>\u0000 </semantics></math> indicating either <span></s","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138544364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On generating plausible values for multilevel modelling with large-scale-assessment data","authors":"Xiaying Zheng","doi":"10.1111/bmsp.12326","DOIUrl":"10.1111/bmsp.12326","url":null,"abstract":"<p>Large-scale assessments (LSAs) routinely employ latent regressions to generate plausible values (PVs) for unbiased estimation of the relationship between examinees' background variables and performance. To handle the clustering effect common in LSA data, multilevel modelling is a popular choice. However, most LSAs use single-level conditioning methods, resulting in a mismatch between the imputation model and the multilevel analytic model. While some LSAs have implemented special techniques in single-level latent regressions to support random-intercept modelling, these techniques are not expected to support random-slope models. To address this gap, this study proposed two new single-level methods to support random-slope estimation. The existing and proposed methods were compared to the theoretically unbiased multilevel latent regression method in terms of their ability to support multilevel models. The findings indicate that the two existing single-level methods can support random-intercept-only models. The multilevel latent regression method provided mostly adequate estimates but was limited by computational burden and did not have the best performance across all conditions. One of our proposed single-level methods presented an efficient alternative to multilevel latent regression and was able to recover acceptable estimates for all parameters. We provide recommendations for situations where each method can be applied, with some caveats.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89720647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correction to ‘a note on computing Louis' observed information matrix identity for IRT and cognitive diagnostic models’","authors":"","doi":"10.1111/bmsp.12325","DOIUrl":"10.1111/bmsp.12325","url":null,"abstract":"<p>Liu, C. W., &amp; Chalmers, R. P. (2021). A note on computing Louis' observed information matrix identity for IRT and cognitive diagnostic models. <i>British Journal of Mathematical and Statistical Psychology</i>, 74(1), 118–138. https://doi.org/10.1111/bmsp.12207</p><p>The acknowledgement of funding was included in error: the paper was received on 30 April 2020, while the mentioned grant commenced on 1 August 2020. Consequently, there is no overlap between the grant period and the received date, rendering the acknowledgment inaccurate.</p><p>We apologize for this error.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12325","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50163853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A correlated traits correlated (methods – 1) multitrait-multimethod model for augmented round-robin data","authors":"David Jendryczko,&nbsp;Fridtjof W. Nussbeck","doi":"10.1111/bmsp.12324","DOIUrl":"10.1111/bmsp.12324","url":null,"abstract":"<p>We didactically derive a correlated traits correlated (methods – 1) [CTC(M – 1)] multitrait-multimethod (MTMM) model for dyadic round-robin data augmented by self-reports. The model is an extension of the CTC(M – 1) model for cross-classified data <i>and</i> can handle dependencies between raters and targets by including reciprocity covariance parameters that are inherent in augmented round-robin designs. It can be specified as a traditional structural equation model. We present the variance decomposition as well as consistency and reliability coefficients. Moreover, we explain how to evaluate fit of a CTC(M – 1) model for augmented round-robin data. In a simulation study, we explore the properties of the full information maximum likelihood estimation of the model. Model (mis)fit can be quite accurately detected with the test of not close fit and dynamic root mean square errors of approximation. Even with few small round-robin groups, relative parameter estimation bias and coverage rates are satisfactory, but several larger round-robin groups are needed to minimize relative parameter estimation inaccuracy. Further, neglecting the reciprocity covariance-structure of the augmented round-robin data does not severely bias the remaining parameter estimates. All analyses (including data, R scripts, and results) and the simulation study are provided in the Supporting Information. Implications and limitations are discussed.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12324","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41241136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Gibbs-INLA algorithm for multidimensional graded response model analysis","authors":"Xiaofan Lin,&nbsp;Siliang Zhang,&nbsp;Yincai Tang,&nbsp;Xuan Li","doi":"10.1111/bmsp.12321","DOIUrl":"10.1111/bmsp.12321","url":null,"abstract":"<p>In this paper, we propose a novel Gibbs-INLA algorithm for the Bayesian inference of graded response models with ordinal response based on multidimensional item response theory. With the combination of the Gibbs sampling and the integrated nested Laplace approximation (INLA), the new framework avoids the cumbersome tuning which is inevitable in classical Markov chain Monte Carlo (MCMC) algorithm, and has low computing memory, high computational efficiency with much fewer iterations, and still achieve higher estimation accuracy. Therefore, it has the ability to handle large amount of multidimensional response data with different item responses. Simulation studies are conducted to compare with the Metroplis-Hastings Robbins-Monro (MH-RM) algorithm and an application to the study of the IPIP-NEO personality inventory data is given to assess the performance of the new algorithm. Extensions of the proposed algorithm for application on more complicated models and different data types are also discussed.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41158559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Bayesian nonparametric approach for handling item and examinee heterogeneity in assessment data","authors":"Tianyu Pan,&nbsp;Weining Shen,&nbsp;Clintin P. Davis-Stober,&nbsp;Guanyu Hu","doi":"10.1111/bmsp.12322","DOIUrl":"10.1111/bmsp.12322","url":null,"abstract":"<p>We propose a novel nonparametric Bayesian item response theory model that estimates clusters at the question level, while simultaneously allowing for heterogeneity at the examinee level under each question cluster, characterized by a mixture of binomial distributions. The main contribution of this work is threefold. First, we present our new model and demonstrate that it is identifiable under a set of conditions. Second, we show that our model can correctly identify question-level clusters asymptotically, and the parameters of interest that measure the proficiency of examinees in solving certain questions can be estimated at a <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msqrt>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msqrt>\u0000 </mrow>\u0000 </semantics></math> rate (up to a log term). Third, we present a tractable sampling algorithm to obtain valid posterior samples from our proposed model. Compared to the existing methods, our model manages to reveal the multi-dimensionality of the examinees' proficiency level in handling different types of questions parsimoniously by imposing a nested clustering structure. The proposed model is evaluated via a series of simulations as well as apply it to an English proficiency assessment data set. This data analysis example nicely illustrates how our model can be used by test makers to distinguish different types of students and aid in the design of future tests.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41174590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Replies to comments on \"Which method delivers greater signal-to-noise ratio: Structural equation modelling or regression analysis with weighted composites?\" by Yuan and Fang (2023)","authors":"Ke-Hai Yuan,&nbsp;Yongfei Fang","doi":"10.1111/bmsp.12323","DOIUrl":"10.1111/bmsp.12323","url":null,"abstract":"","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10243790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}