British Journal of Mathematical & Statistical Psychology最新文献

{"title":"A two-step item bank calibration strategy based on 1-bit matrix completion for small-scale computerized adaptive testing","authors":"Yawei Shen,&nbsp;Shiyu Wang,&nbsp;Houping Xiao","doi":"10.1111/bmsp.12340","DOIUrl":"10.1111/bmsp.12340","url":null,"abstract":"<p>Computerized adaptive testing (CAT) is a widely embraced approach for delivering personalized educational assessments, tailoring each test to the real-time performance of individual examinees. Despite its potential advantages, CAT�s application in small-scale assessments has been limited due to the complexities associated with calibrating the item bank using sparse response data and small sample sizes. This study addresses these challenges by developing a two-step item bank calibration strategy that leverages the 1-bit matrix completion method in conjunction with two distinct incomplete pretesting designs. We introduce two novel 1-bit matrix completion-based imputation methods specifically designed to tackle the issues associated with item calibration in the presence of sparse response data and limited sample sizes. To demonstrate the effectiveness of these approaches, we conduct a comparative assessment against several established item parameter estimation methods capable of handling missing data. This evaluation is carried out through two sets of simulation studies, each featuring different pretesting designs, item bank structures, and sample sizes. Furthermore, we illustrate the practical application of the methods investigated, using empirical data collected from small-scale assessments.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12340","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140592809","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":"Sample size determination for interval estimation of the prevalence of a sensitive attribute under non-randomized response models","authors":"Shi-Fang Qiu,&nbsp;Jie Lei,&nbsp;Wai-Yin Poon,&nbsp;Man-Lai Tang,&nbsp;Ricky S. Wong,&nbsp;Ji-Ran Tao","doi":"10.1111/bmsp.12338","DOIUrl":"10.1111/bmsp.12338","url":null,"abstract":"<p>A sufficient number of participants should be included to adequately address the research interest in the surveys with sensitive questions. In this paper, sample size formulas/iterative algorithms are developed from the perspective of controlling the confidence interval width of the prevalence of a sensitive attribute under four non-randomized response models: the crosswise model, parallel model, Poisson item count technique model and negative binomial item count technique model. In contrast to the conventional approach for sample size determination, our sample size formulas/algorithms explicitly incorporate an assurance probability of controlling the width of a confidence interval within the pre-specified range. The performance of the proposed methods is evaluated with respect to the empirical coverage probability, empirical assurance probability and confidence width. Simulation results show that all formulas/algorithms are effective and hence are recommended for practical applications. A real example is used to illustrate the proposed methods.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139974734","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":"Assessment of fit of the time-varying dynamic partial credit model using the posterior predictive model checking method","authors":"Sebastian Castro-Alvarez,&nbsp;Sandip Sinharay,&nbsp;Laura F. Bringmann,&nbsp;Rob R. Meijer,&nbsp;Jorge N. Tendeiro","doi":"10.1111/bmsp.12339","DOIUrl":"10.1111/bmsp.12339","url":null,"abstract":"<p>Several new models based on item response theory have recently been suggested to analyse intensive longitudinal data. One of these new models is the time-varying dynamic partial credit model (TV-DPCM; Castro-Alvarez et al., <i>Multivariate Behavioral Research</i>, 2023, 1), which is a combination of the partial credit model and the time-varying autoregressive model. The model allows the study of the psychometric properties of the items and the modelling of nonlinear trends at the latent state level. However, there is a severe lack of tools to assess the fit of the TV-DPCM. In this paper, we propose and develop several test statistics and discrepancy measures based on the posterior predictive model checking (PPMC) method (PPMC; Rubin, <i>The Annals of Statistics</i>, 1984, 12, 1151) to assess the fit of the TV-DPCM. Simulated and empirical data are used to study the performance of and illustrate the effectiveness of the PPMC method.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139914100","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":"When and how to use set-exploratory structural equation modelling to test structural models: A tutorial using the R package lavaan","authors":"Herb Marsh,&nbsp;Abdullah Alamer","doi":"10.1111/bmsp.12336","DOIUrl":"10.1111/bmsp.12336","url":null,"abstract":"<p>Exploratory structural equation modelling (ESEM) is an alternative to the well-known method of confirmatory factor analysis (CFA). ESEM is mainly used to assess the quality of measurement models of common factors but can be efficiently extended to test structural models. However, ESEM may not be the best option in some model specifications, especially when structural models are involved, because the full flexibility of ESEM could result in technical difficulties in model estimation. Thus, set-ESEM was developed to accommodate the balance between full-ESEM and CFA. In the present paper, we show examples where set-ESEM should be used rather than full-ESEM. Rather than relying on a simulation study, we provide two applied examples using real data that are included in the OSF repository. Additionally, we provide the code needed to run set-ESEM in the free R package <i>lavaan</i> to make the paper practical. Set-ESEM structural models outperform their CFA-based counterparts in terms of goodness of fit and realistic factor correlation, and hence path coefficients in the two empirical examples. In several instances, effects that were non-significant (i.e., attenuated) in the CFA-based structural model become larger and significant in the set-ESEM structural model, suggesting that set-ESEM models may generate more accurate model parameters and, hence, lower Type II error rate.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12336","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139742778","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":"Fast estimation of generalized linear latent variable models for performance and process data with ordinal, continuous, and count observed variables","authors":"Maoxin Zhang,&nbsp;Björn Andersson,&nbsp;Shaobo Jin","doi":"10.1111/bmsp.12337","DOIUrl":"10.1111/bmsp.12337","url":null,"abstract":"<p>Different data types often occur in psychological and educational measurement such as computer-based assessments that record performance and process data (e.g., response times and the number of actions). Modelling such data requires specific models for each data type and accommodating complex dependencies between multiple variables. Generalized linear latent variable models are suitable for modelling mixed data simultaneously, but estimation can be computationally demanding. A fast solution is to use Laplace approximations, but existing implementations of joint modelling of mixed data types are limited to ordinal and continuous data. To address this limitation, we derive an efficient estimation method that uses first- or second-order Laplace approximations to simultaneously model ordinal data, continuous data, and count data. We illustrate the approach with an example and conduct simulations to evaluate the performance of the method in terms of estimation efficiency, convergence, and parameter recovery. The results suggest that the second-order Laplace approximation achieves a higher convergence rate and produces accurate yet fast parameter estimates compared to the first-order Laplace approximation, while the time cost increases with higher model complexity. Additionally, models that consider the dependence of variables from the same stimulus fit the empirical data substantially better than models that disregarded the dependence.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12337","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139725087","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":"Constructing tests for skill assessment with competence-based test development","authors":"Pasquale Anselmi,&nbsp;Jürgen Heller,&nbsp;Luca Stefanutti,&nbsp;Egidio Robusto","doi":"10.1111/bmsp.12335","DOIUrl":"10.1111/bmsp.12335","url":null,"abstract":"<p>Competence-based test development is a recent and innovative method for the construction of tests that are as informative as possible about the competence state (the set of skills an individual has available) underlying the observed item responses. It finds application in different contexts, including the development of tests from scratch, and the improvement or shortening of existing tests. Given a fixed collection of competence states existing in a population of individuals and a fixed collection of competencies (each of which being the subset of skills that allow for solving an item), the competency deletion procedure results in tests that differ from each other in the competencies but are all equally informative about individuals' competence states. This work introduces a streamlined version of the competency deletion procedure that considers information necessary for test construction only, illustrates a straightforward way to incorporate test developer preferences about competencies into the test construction process, and evaluates the performance of the resulting tests in uncovering the competence states from the observed item responses.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139661345","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":"Identifiability and estimability of Bayesian linear and nonlinear crossed random effects models","authors":"Corissa T. Rohloff,&nbsp;Nidhi Kohli,&nbsp;Eric F. Lock","doi":"10.1111/bmsp.12334","DOIUrl":"10.1111/bmsp.12334","url":null,"abstract":"<p>Crossed random effects models (CREMs) are particularly useful in longitudinal data applications because they allow researchers to account for the impact of dynamic group membership on individual outcomes. However, no research has determined what data conditions need to be met to sufficiently identify these models, especially the group effects, in a longitudinal context. This is a significant gap in the current literature as future applications to real data may need to consider these conditions to yield accurate and precise model parameter estimates, specifically for the group effects on individual outcomes. Furthermore, there are no existing CREMs that can model intrinsically nonlinear growth. The goals of this study are to develop a Bayesian piecewise CREM to model intrinsically nonlinear growth and evaluate what data conditions are necessary to empirically identify both intrinsically linear and nonlinear longitudinal CREMs. This study includes an applied example that utilizes the piecewise CREM with real data and three simulation studies to assess the data conditions necessary to estimate linear, quadratic, and piecewise CREMs. Results show that the number of repeated measurements collected on groups impacts the ability to recover the group effects. Additionally, functional form complexity impacted data collection requirements for estimating longitudinal CREMs.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12334","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139543995","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":"Statistical inference for agreement between multiple raters on a binary scale","authors":"Sophie Vanbelle","doi":"10.1111/bmsp.12333","DOIUrl":"10.1111/bmsp.12333","url":null,"abstract":"<p>Agreement studies often involve more than two raters or repeated measurements. In the presence of two raters, the proportion of agreement and of positive agreement are simple and popular agreement measures for binary scales. These measures were generalized to agreement studies involving more than two raters with statistical inference procedures proposed on an empirical basis. We present two alternatives. The first is a Wald confidence interval using standard errors obtained by the delta method. The second involves Bayesian statistical inference not requiring any specific Bayesian software. These new procedures show better statistical behaviour than the confidence intervals initially proposed. In addition, we provide analytical formulas to determine the minimum number of persons needed for a given number of raters when planning an agreement study. All methods are implemented in the R package <i>simpleagree</i> and the Shiny app <i>simpleagree</i>.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12333","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139486878","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 cluster differences unfolding method for large datasets of preference ratings on an interval scale: Minimizing the mean squared centred residuals","authors":"Rodrigo Macías,&nbsp;J. Fernando Vera,&nbsp;Willem J. Heiser","doi":"10.1111/bmsp.12332","DOIUrl":"10.1111/bmsp.12332","url":null,"abstract":"<p>Clustering and spatial representation methods are often used in combination, to analyse preference ratings when a large number of individuals and/or object is involved. When analysed under an unfolding model, row-conditional linear transformations are usually most appropriate when the goal is to determine clusters of individuals with similar preferences. However, a significant problem with transformations that include both slope and intercept is the occurrence of degenerate solutions. In this paper, we propose a least squares unfolding method that performs clustering of individuals while simultaneously estimating the location of cluster centres and object locations in low-dimensional space. The method is based on minimising the mean squared centred residuals of the preference ratings with respect to the distances between cluster centres and object locations. At the same time, the distances are row-conditionally transformed with optimally estimated slope parameters. It is computationally efficient for large datasets, and does not suffer from the appearance of degenerate solutions. The performance of the method is analysed in an extensive Monte Carlo experiment. It is illustrated for a real data set and the results are compared with those obtained using a two-step clustering and unfolding procedure.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139426139","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":"Correcting for measurement error under meta-analysis of z-transformed correlations","authors":"Qian Zhang,&nbsp;Qi Wang","doi":"10.1111/bmsp.12328","DOIUrl":"10.1111/bmsp.12328","url":null,"abstract":"<p>This study mainly concerns correction for measurement error using the meta-analysis of Fisher's z-transformed correlations. The disattenuation formula of Spearman (American Journal of Psychology, <b>15</b>, 1904, 72) is used to correct for individual raw correlations in primary studies. The corrected raw correlations are then used to obtain the corrected z-transformed correlations. What remains little studied, however, is how to best correct for within-study sampling error variances of corrected z-transformed correlations. We focused on three within-study sampling error variance estimators corrected for measurement error that were proposed in earlier studies and is proposed in the current study: (1) the formula given by Hedges (<i>Test validity</i>, Lawrence Erlbaum, 1988) assuming a linear relationship between corrected and uncorrected z-transformed correlations (linear correction), (2) one derived by the first-order delta method based on the average of corrected z-transformed correlations (stabilized first-order correction), and (3) one derived by the second-order delta method based on the average of corrected z-transformed correlations (stabilized second-order correction). Via a simulation study, we compared performance of these estimators and the sampling error variance estimator uncorrected for measurement error in terms of estimation and inference accuracy of the mean correlation as well as the homogeneity test of effect sizes. In obtaining the corrected z-transformed correlations and within-study sampling error variances, coefficient alpha was used as a common reliability coefficient estimate. The results showed that in terms of the estimated mean correlation, sampling error variances with linear correction, the stabilized first-order and second-order corrections, and no correction performed similarly in general. Furthermore, in terms of the homogeneity test, given a relatively large average sample size and normal true scores, the stabilized first-order and second-order corrections had type I error rates that were generally controlled as well as or better than the other estimators. Overall, stabilized first-order and second-order corrections are recommended when true scores are normal, reliabilities are acceptable, the number of items per psychological scale is relatively large, and the average sample size is relatively large.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139059109","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}