{"title":"Item-Fit Statistic Based on Posterior Probabilities of Membership in Ability Groups.","authors":"Bartosz Kondratek","doi":"10.1177/01466216221108061","DOIUrl":"https://doi.org/10.1177/01466216221108061","url":null,"abstract":"<p><p>A novel approach to item-fit analysis based on an asymptotic test is proposed. The new test statistic, <math> <mrow><msubsup><mi>χ</mi> <mi>w</mi> <mn>2</mn></msubsup> </mrow> </math> , compares pseudo-observed and expected item mean scores over a set of ability bins. The item mean scores are computed as weighted means with weights based on test-takers' <i>a posteriori</i> density of ability within the bin. This article explores the properties of <math> <mrow><msubsup><mi>χ</mi> <mi>w</mi> <mn>2</mn></msubsup> </mrow> </math> in case of dichotomously scored items for unidimensional IRT models. Monte Carlo experiments were conducted to analyze the performance of <math> <mrow><msubsup><mi>χ</mi> <mi>w</mi> <mn>2</mn></msubsup> </mrow> </math> . Type I error of <math> <mrow><msubsup><mi>χ</mi> <mi>w</mi> <mn>2</mn></msubsup> <mo> </mo></mrow> </math> was acceptably close to the nominal level and it had greater power than Orlando and Thissen's <math><mrow><mi>S</mi> <mo>-</mo> <msup><mi>x</mi> <mn>2</mn></msup> </mrow> </math> . Under some conditions, power of <math> <mrow><msubsup><mi>χ</mi> <mi>w</mi> <mn>2</mn></msubsup> </mrow> </math> also exceeded the one reported for the computationally more demanding Stone's <math> <mrow><msup><mi>χ</mi> <mrow><mn>2</mn> <mo>∗</mo></mrow> </msup> </mrow> </math> .</p>","PeriodicalId":48300,"journal":{"name":"Applied Psychological Measurement","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9382089/pdf/10.1177_01466216221108061.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10132911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Item Response Theory True Score Equating for the Bifactor Model Under the Common-Item Nonequivalent Groups Design.","authors":"Kyung Yong Kim","doi":"10.1177/01466216221108995","DOIUrl":"10.1177/01466216221108995","url":null,"abstract":"<p><p>Applying item response theory (IRT) true score equating to multidimensional IRT models is not straightforward due to the one-to-many relationship between a true score and latent variables. Under the common-item nonequivalent groups design, the purpose of the current study was to introduce two IRT true score equating procedures that adopted different dimension reduction strategies for the bifactor model. The first procedure, which was referred to as the integration procedure, linked the latent variable scales for the bifactor model and integrated out the specific factors from the item response function of the bifactor model. Then, IRT true score equating was applied to the marginalized bifactor model. The second procedure, which was referred to as the PIRT-based procedure, projected the specific dimensions onto the general dimension to obtain a locally dependent unidimensional IRT (UIRT) model and linked the scales of the UIRT model, followed by the application of IRT true score equating to the locally dependent UIRT model. Equating results obtained with the two equating procedures along with those obtained with the unidimensional three-parameter logistic (3PL) model were compared using both simulated and real data. In general, the integration and PIRT-based procedures provided equating results that were not practically different. Furthermore, the equating results produced by the two bifactor-based procedures became more accurate than the results returned by the 3PL model as tests became more multidimensional.</p>","PeriodicalId":48300,"journal":{"name":"Applied Psychological Measurement","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9382090/pdf/10.1177_01466216221108995.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10189451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Factor Retention Using Machine Learning With Ordinal Data.","authors":"David Goretzko, Markus Bühner","doi":"10.1177/01466216221089345","DOIUrl":"https://doi.org/10.1177/01466216221089345","url":null,"abstract":"<p><p>Determining the number of factors in exploratory factor analysis is probably the most crucial decision when conducting the analysis as it clearly influences the meaningfulness of the results (i.e., factorial validity). A new method called the Factor Forest that combines data simulation and machine learning has been developed recently. This method based on simulated data reached very high accuracy for multivariate normal data, but it has not yet been tested with ordinal data. Hence, in this simulation study, we evaluated the Factor Forest with ordinal data based on different numbers of categories (2-6 categories) and compared it to common factor retention criteria. It showed higher overall accuracy for all types of ordinal data than all common factor retention criteria that were used for comparison (Parallel Analysis, Comparison Data, the Empirical Kaiser Criterion and the Kaiser Guttman Rule). The results indicate that the Factor Forest is applicable to ordinal data with at least five categories (typical scale in questionnaire research) in the majority of conditions and to binary or ordinal data based on items with less categories when the sample size is large.</p>","PeriodicalId":48300,"journal":{"name":"Applied Psychological Measurement","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ftp.ncbi.nlm.nih.gov/pub/pmc/oa_pdf/ff/4b/10.1177_01466216221089345.PMC9265486.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40489940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"glca: An R Package for Multiple-Group Latent Class Analysis.","authors":"Youngsun Kim, Saebom Jeon, Chi Chang, Hwan Chung","doi":"10.1177/01466216221084197","DOIUrl":"10.1177/01466216221084197","url":null,"abstract":"<p><p>Group similarities and differences may manifest themselves in a variety of ways in multiple-group latent class analysis (LCA). Sometimes, measurement models are identical across groups in LCA. In other situations, the measurement models may differ, suggesting that the latent structure itself is different between groups. Tests of measurement invariance shed light on this distinction. We created an R package glca that implements procedures for exploring differences in latent class structure between populations, taking multilevel data structure into account. The glca package deals with the fixed-effect LCA and the nonparametric random-effect LCA; the former can be applied in the situation where populations are segmented by the observed group variable itself, whereas the latter can be used when there are too many levels in the group variable to make a meaningful group comparisons by identifying a group-level latent variable. The glca package consists of functions for statistical test procedures for exploring group differences in various LCA models considering multilevel data structure.</p>","PeriodicalId":48300,"journal":{"name":"Applied Psychological Measurement","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9265491/pdf/10.1177_01466216221084197.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10091269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bridging Models of Biometric and Psychometric Assessment: A Three-Way Joint Modeling Approach of Item Responses, Response Times, and Gaze Fixation Counts.","authors":"Kaiwen Man, Jeffrey R Harring, Peida Zhan","doi":"10.1177/01466216221089344","DOIUrl":"https://doi.org/10.1177/01466216221089344","url":null,"abstract":"<p><p>Recently, joint models of item response data and response times have been proposed to better assess and understand test takers' learning processes. This article demonstrates how biometric information such as gaze fixation counts obtained from an eye-tracking machine can be integrated into the measurement model. The proposed joint modeling framework accommodates the relations among a test taker's latent ability, working speed and test engagement level via a person-side variance-covariance structure, while simultaneously permitting the modeling of item difficulty, time-intensity, and the engagement intensity through an item-side variance-covariance structure. A Bayesian estimation scheme is used to fit the proposed model to data. Posterior predictive model checking based on three discrepancy measures corresponding to various model components are introduced to assess model-data fit. Findings from a Monte Carlo simulation and results from analyzing experimental data demonstrate the utility of the model.</p>","PeriodicalId":48300,"journal":{"name":"Applied Psychological Measurement","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9265489/pdf/10.1177_01466216221089344.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10091266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bayesian Item Response Theory Models With Flexible Generalized Logit Links.","authors":"Jiwei Zhang, Ying-Ying Zhang, Jian Tao, Ming-Hui Chen","doi":"10.1177/01466216221089343","DOIUrl":"10.1177/01466216221089343","url":null,"abstract":"<p><p>In educational and psychological research, the logit and probit links are often used to fit the binary item response data. The appropriateness and importance of the choice of links within the item response theory (IRT) framework has not been investigated yet. In this paper, we present a family of IRT models with generalized logit links, which include the traditional logistic and normal ogive models as special cases. This family of models are flexible enough not only to adjust the item characteristic curve tail probability by two shape parameters but also to allow us to fit the same link or different links to different items within the IRT model framework. In addition, the proposed models are implemented in the Stan software to sample from the posterior distributions. Using readily available Stan outputs, the four Bayesian model selection criteria are computed for guiding the choice of the links within the IRT model framework. Extensive simulation studies are conducted to examine the empirical performance of the proposed models and the model fittings in terms of \"in-sample\" and \"out-of-sample\" predictions based on the deviance. Finally, a detailed analysis of the real reading assessment data is carried out to illustrate the proposed methodology.</p>","PeriodicalId":48300,"journal":{"name":"Applied Psychological Measurement","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9265488/pdf/10.1177_01466216221089343.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10091271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dual-Objective Item Selection Methods in Computerized Adaptive Test Using the Higher-Order Cognitive Diagnostic Models.","authors":"Chongqin Xi, Dongbo Tu, Yan Cai","doi":"10.1177/01466216221089342","DOIUrl":"https://doi.org/10.1177/01466216221089342","url":null,"abstract":"<p><p>To efficiently obtain information about both the general abilities and detailed cognitive profiles of examinees from a single model that uses a single-calibration process, higher-order cognitive diagnostic computerized adaptive testing (CD-CAT) that employ higher-order cognitive diagnostic models have been developed. However, the current item selection methods used in higher-order CD-CAT adaptively select items according to only the attribute profiles, which might lead to low precision regarding general abilities; hence, an appropriate method was proposed for this CAT system in this study. Under the framework of the higher-order models, the responses were affected by attribute profiles, which were governed by general abilities. It is reasonable to hold that the item responses were affected by a combination of general abilities and attribute profiles. Based on the logic of Shannon entropy and the generalized deterministic, inputs, noisy \"and\" gate (G-DINA) model discrimination index (GDI), two new item selection methods were proposed for higher-order CD-CAT by considering the above combination in this study. The simulation results demonstrated that the new methods achieved more accurate estimations of both general abilities and cognitive profiles than the existing methods and maintained distinct advantages in terms of item pool usage.</p>","PeriodicalId":48300,"journal":{"name":"Applied Psychological Measurement","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9265487/pdf/10.1177_01466216221089342.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10091270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tyler Strachan, Uk Hyun Cho, Terry Ackerman, Shyh-Huei Chen, Jimmy de la Torre, Edward H Ip
{"title":"Evaluation of the Linear Composite Conjecture for Unidimensional IRT Scale for Multidimensional Responses.","authors":"Tyler Strachan, Uk Hyun Cho, Terry Ackerman, Shyh-Huei Chen, Jimmy de la Torre, Edward H Ip","doi":"10.1177/01466216221084218","DOIUrl":"https://doi.org/10.1177/01466216221084218","url":null,"abstract":"<p><p>The linear composite direction represents, theoretically, where the unidimensional scale would lie within a multidimensional latent space. Using compensatory multidimensional IRT, the linear composite can be derived from the structure of the items and the latent distribution. The purpose of this study was to evaluate the validity of the linear composite conjecture and examine how well a fitted unidimensional IRT model approximates the linear composite direction in a multidimensional latent space. Simulation experiment results overall show that the fitted unidimensional IRT model sufficiently approximates linear composite direction when correlation between bivariate latent variables is positive. When the correlation between bivariate latent variables is negative, instability occurs when the fitted unidimensional IRT model is used to approximate linear composite direction. A real data experiment was also conducted using 20 items from a multiple-choice mathematics test from American College Testing.</p>","PeriodicalId":48300,"journal":{"name":"Applied Psychological Measurement","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9265490/pdf/10.1177_01466216221084218.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10091268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xue-Lan Qiu, Jimmy de la Torre, Sage Ro, Wen-Chung Wang
{"title":"Computerized Adaptive Testing for Ipsative Tests with Multidimensional Pairwise-Comparison Items: Algorithm Development and Applications.","authors":"Xue-Lan Qiu, Jimmy de la Torre, Sage Ro, Wen-Chung Wang","doi":"10.1177/01466216221084209","DOIUrl":"https://doi.org/10.1177/01466216221084209","url":null,"abstract":"<p><p>A computerized adaptive testing (CAT) solution for tests with multidimensional pairwise-comparison (MPC) items, aiming to measure career interest, value, and personality, is rare. This paper proposes new item selection and exposure control methods for CAT with dichotomous and polytomous MPC items and present simulation study results. The results show that the procedures are effective in selecting items and controlling within-person statement exposure with no loss of efficiency. Implications are discussed in two applications of the proposed CAT procedures: a work attitude test with dichotomous MPC items and a career interest assessment with polytomous MPC items.</p>","PeriodicalId":48300,"journal":{"name":"Applied Psychological Measurement","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9118927/pdf/10.1177_01466216221084209.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9609917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hao Luo, Daxun Wang, Zhiming Guo, Yan Cai, Dongbo Tu
{"title":"Combining Cognitive Diagnostic Computerized Adaptive Testing With Multidimensional Item Response Theory.","authors":"Hao Luo, Daxun Wang, Zhiming Guo, Yan Cai, Dongbo Tu","doi":"10.1177/01466216221084214","DOIUrl":"https://doi.org/10.1177/01466216221084214","url":null,"abstract":"<p><p>The new generation of tests not only focuses on the general ability but also the process of finer-grained skills. Under the guidance of this thought, researchers have developed a dual-purpose CD-CAT (Dual-CAT). In the existing Dual-CAT, the models used in overall ability estimation are unidimensional IRT models, which cannot apply to the multidimensional tests. This article intends to develop a multidimensional Dual-CAT to improve its applicability. To achieve this goal, this article firstly proposes some item selection methods for the multidimensional Dual-CAT, and then verifies the estimation accuracy and exposure rate of these methods through both simulation study and a real item bank study. The results show that the established multidimensional Dual-CAT is effective and the new proposed methods outperform the traditional methods. Finally, this article discusses the future direction of the Dual-CAT.</p>","PeriodicalId":48300,"journal":{"name":"Applied Psychological Measurement","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9118931/pdf/10.1177_01466216221084214.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9911725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}