Relevant bibliographies by topics / Item response theory – Mathematical models

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Item response theory – Mathematical models'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 February 2022

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Journal articles on the topic "Item response theory – Mathematical models"

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Kim, Jinho, and Mark Wilson. "Polytomous Item Explanatory Item Response Theory Models." Educational and Psychological Measurement 80, no. 4 (2019): 726–55. http://dx.doi.org/10.1177/0013164419892667.

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This study investigates polytomous item explanatory item response theory models under the multivariate generalized linear mixed modeling framework, using the linear logistic test model approach. Building on the original ideas of the many-facet Rasch model and the linear partial credit model, a polytomous Rasch model is extended to the item location explanatory many-facet Rasch model and the step difficulty explanatory linear partial credit model. To demonstrate the practical differences between the two polytomous item explanatory approaches, two empirical studies examine how item properties explain and predict the overall item difficulties or the step difficulties each in the Carbon Cycle assessment data and in the Verbal Aggression data. The results suggest that the two polytomous item explanatory models are methodologically and practically different in terms of (a) the target difficulty parameters of polytomous items, which are explained by item properties; (b) the types of predictors for the item properties incorporated into the design matrix; and (c) the types of item property effects. The potentials and methodological advantages of item explanatory modeling are discussed as well.
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Pacheco, Juliano Anderson, Dalton Francisco de Andrade, and Antonio Cezar Bornia. "Benchmarking by Item Response Theory (BIRTH)." Benchmarking: An International Journal 22, no. 5 (2015): 945–62. http://dx.doi.org/10.1108/bij-03-2013-0035.

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Purpose – The purpose of this paper is to present a new method for benchmarking, which allows the construction of scales of competitiveness for the comparison of products using Item Response Theory (IRT). Design/methodology/approach – Theoretically, the method combines classic benchmarking process steps with IRT steps and demonstrates through mathematical models how this technique can measure the competitiveness of products by means of a latent trait. Findings – The IRT method uses the theories of psychometrics to measure the competitiveness of products through qualitative and quantitative interpretation of the tangible and intangible characteristics of those products. To demonstrate the application of the developed method, the items were constructed for teaching staff. Research limitations/implications – The application of the developed method will increase the accuracy of assessments of the competitiveness of a product because this method uses a mathematical model of the IRT to evaluate the characteristics product that reflect market competitiveness. Items must be selected based on theories relevant to the product and/or expert opinion or customers. Practical implications – The applicability of the method results in the construction of a scale in which items identify good practice with greater difficulty because they are represented in the same units that index competitiveness. Thus, managers of companies obtain knowledge about their products and the market, which allows them to assess their performance against their competitors and to make decisions regarding the continuous improvement of their production process and expansion of product characteristics. Originality/value – This work presents a new method for benchmarking using a quantitative technique that enables measurement of the latent trait of “competitiveness” through robust mathematical models.
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Falani, Ilham, Makruf Akbar, and Dali Santun Naga. "Comparison of the Accuracy of Item Response Theory Models in Estimating Student’s Ability." Journal of Educational Science and Technology (EST) 6, no. 2 (2020): 178. http://dx.doi.org/10.26858/est.v6i2.13295.

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This study aims to determine the item response theory model which is more accurate in estimating students' mathematical abilities. The models compared in this study are Multiple Choice Model and Three-Parameter Logistic Model. Data used in this study are the responses of a mathematical test of 1704 eighth-grade junior high school students from six schools in the Depok City, West Java. The Sampling is done by using a purposive random sampling technique. The mathematics test used for research data collection consisted of 30 multiple choice format items. After the data is obtained, Research hypotheses were tested using the variance test method (F-test) to find out which model is more accurate in estimating ability parameters. The results showed that Fvalue is obtained 1.089, and Ftable is 1.087, the value of Fvalue > Ftable, so it concluded that Ho rejected. That means Multiple Choice Model is more accurate than Three-Parameter Logistic Model in estimating the parameters of students' mathematical abilities. This makes the Multiple-Choice Model a recommended model for estimating mathematical ability in MC item format tests, especially in the field of mathematics and other fields that have similar characteristics.
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Liu, Yang, Ji Seung Yang, and Alberto Maydeu-Olivares. "Restricted Recalibration of Item Response Theory Models." Psychometrika 84, no. 2 (2019): 529–53. http://dx.doi.org/10.1007/s11336-019-09667-4.

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Holland, Paul W. "On the sampling theory roundations of item response theory models." Psychometrika 55, no. 4 (1990): 577–601. http://dx.doi.org/10.1007/bf02294609.

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Lipovetsky, Stan. "Handbook of Item Response Theory, Volume 1, Models." Technometrics 63, no. 3 (2021): 428–31. http://dx.doi.org/10.1080/00401706.2021.1945324.

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Sheng, Yanyan, and Christopher K. Wikle. "Comparing Multiunidimensional and Unidimensional Item Response Theory Models." Educational and Psychological Measurement 67, no. 6 (2007): 899–919. http://dx.doi.org/10.1177/0013164406296977.

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Shanmugam, Ramalingam. "Handbook of Item Response Theory: Volume one, Models." Journal of Statistical Computation and Simulation 90, no. 10 (2019): 1922. http://dx.doi.org/10.1080/00949655.2019.1628905.

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da Silva, Marcelo A., Ren Liu, Anne C. Huggins-Manley, and Jorge L. Bazán. "Incorporating the Q-Matrix Into Multidimensional Item Response Theory Models." Educational and Psychological Measurement 79, no. 4 (2018): 665–87. http://dx.doi.org/10.1177/0013164418814898.

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Multidimensional item response theory (MIRT) models use data from individual item responses to estimate multiple latent traits of interest, making them useful in educational and psychological measurement, among other areas. When MIRT models are applied in practice, it is not uncommon to see that some items are designed to measure all latent traits while other items may only measure one or two traits. In order to facilitate a clear expression of which items measure which traits and formulate such relationships as a math function in MIRT models, we applied the concept of the Q-matrix commonly used in diagnostic classification models to MIRT models. In this study, we introduced how to incorporate a Q-matrix into an existing MIRT model, and demonstrated benefits of the proposed hybrid model through two simulation studies and an applied study. In addition, we showed the relative ease in modeling educational and psychological data through a Bayesian approach via the NUTS algorithm.
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Zheng, Xiaohui, and Sophia Rabe-Hesketh. "Estimating Parameters of Dichotomous and Ordinal Item Response Models with Gllamm." Stata Journal: Promoting communications on statistics and Stata 7, no. 3 (2007): 313–33. http://dx.doi.org/10.1177/1536867x0700700302.

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Item response theory models are measurement models for categorical responses. Traditionally, the models are used in educational testing, where responses to test items can be viewed as indirect measures of latent ability. The test items are scored either dichotomously (correct–incorrect) or by using an ordinal scale (a grade from poor to excellent). Item response models also apply equally for measurement of other latent traits. Here we describe the one- and two-parameter logit models for dichotomous items, the partial-credit and rating scale models for ordinal items, and an extension of these models where the latent variable is regressed on explanatory variables. We show how these models can be expressed as generalized linear latent and mixed models and fitted by using the user-written command gllamm.
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Dissertations / Theses on the topic "Item response theory – Mathematical models"

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Lewis, Naama. "ITEM RESPONSE MODELS AND CONVEX OPTIMIZATION." OpenSIUC, 2020. https://opensiuc.lib.siu.edu/dissertations/1782.

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Item Response Theory (IRT) Models, like the one parameter, two parameters, or normal Ogive, have been discussed for many years. These models represent a rich area of investigation due to their complexity as well as the large amount of data collected in relationship to model parameter estimation. Here we propose a new way of looking at IRT models using I-projections and duality. We use convex optimization methods to derive these models. The Kullback-Leibler divergence is used as a metric and specific constraints are proposed for the various models. With this approach, the dual problem is shown to be much easier to solve than the primal problem. In particular when there are many constraints, we propose the application of a projection algorithm for solving these types of problems. We also consider re-framing the problem and utilizing a decomposition algorithm to solve for parameters as well. Both of these methods will be compared to the Rasch and 2-Parameter Logistic models using established computer software where estimation of model parameters are done under Maximum Likelihood Estimation framework. We will also compare the appropriateness of these techniques on multidimensional item response data sets and propose new models with the use of I-projections.
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Duncan, Kristin A. "Case and covariate influence implications for model assessment /." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1095357183.

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Thesis (Ph. D.)--Ohio State University, 2004.<br>Title from first page of PDF file. Document formatted into pages; contains xi, 123 p.; also includes graphics (some col.). Includes bibliographical references (p. 120-123).
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Stanley, Leanne M. "Flexible Multidimensional Item Response Theory Models Incorporating Response Styles." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1494316298549437.

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Morey, Richard D. "Item response models for the measurement of thresholds." Diss., Columbia, Mo. : University of Missouri-Columbia, 2008. http://hdl.handle.net/10355/5500.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2008.<br>The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on July 28, 2009 Includes bibliographical references.
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Toribio, Sherwin G. "Bayesian Model Checking Strategies for Dichotomous Item Response Theory Models." Bowling Green State University / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1150425606.

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Wang, Yixi. "Application of Item Response Tree (IRTree) Models on Testing Data: Comparing Its Performance with Binary and Polytomous Item Response Models." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587481533999313.

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Si, Ching-Fung B. "Ability Estimation Under Different Item Parameterization and Scoring Models." Thesis, University of North Texas, 2002. https://digital.library.unt.edu/ark:/67531/metadc3116/.

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A Monte Carlo simulation study investigated the effect of scoring format, item parameterization, threshold configuration, and prior ability distribution on the accuracy of ability estimation given various IRT models. Item response data on 30 items from 1,000 examinees was simulated using known item parameters and ability estimates. The item response data sets were submitted to seven dichotomous or polytomous IRT models with different item parameterization to estimate examinee ability. The accuracy of the ability estimation for a given IRT model was assessed by the recovery rate and the root mean square errors. The results indicated that polytomous models produced more accurate ability estimates than the dichotomous models, under all combinations of research conditions, as indicated by higher recovery rates and lower root mean square errors. For the item parameterization models, the one-parameter model out-performed the two-parameter and three-parameter models under all research conditions. Among the polytomous models, the partial credit model had more accurate ability estimation than the other three polytomous models. The nominal categories model performed better than the general partial credit model and the multiple-choice model with the multiple-choice model the least accurate. The results further indicated that certain prior ability distributions had an effect on the accuracy of ability estimation; however, no clear order of accuracy among the four prior distribution groups was identified due to an interaction between prior ability distribution and threshold configuration. The recovery rate was lower when the test items had categories with unequal threshold distances, were close at one end of the ability/difficulty continuum, and were administered to a sample of examinees whose population ability distribution was skewed to the same end of the ability continuum.
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Patsias, Kyriakos. "A HIGH PERFORMANCE GIBBS-SAMPLING ALGORITHM FOR ITEM RESPONSE THEORY MODELS." Available to subscribers only, 2009. http://proquest.umi.com/pqdweb?did=1796121011&sid=3&Fmt=2&clientId=1509&RQT=309&VName=PQD.

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Schröder, Nadine. "Using Multidimensional Item Response Theory Models to Explain Multi-Category Purchases." Vahlen, 2017. http://epub.wu.ac.at/6538/1/0344%2D1369%2D2017%2D2%2D27.pdf.

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We apply multidimensional item response theory models (MIRT) to analyse multi-category purchase decisions. We further compare their performance to benchmark models by means of topic models. Estimation is based on two types of data sets. One contains only binary the other polytomous purchase decisions. We show that MIRT are superior w. r. t. our chosen benchmark models. In particular, MIRT are able to reveal intuitive latent traits that can be interpreted as characteristics of households relevant for multi-category purchase decisions. With the help of latent traits marketers are able to predict future purchase behaviour for various types of households. These information may guide shop managers for cross selling activities and product recommendations.
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Combs, Adam. "Bayesian Model Checking Methods for Dichotomous Item Response Theory and Testlet Models." Bowling Green State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1394808820.

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Books on the topic "Item response theory – Mathematical models"

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L, Nering Michael, ed. Polytomous item response theory models. Sage Publications, 2006.

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Ostini, Remo. Polytomous item response theory models. Sage Publications, 2005.

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Handbook of item response theory. CRC Press, 2015.

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K, Hambleton Ronald, ed. Handbook of modern item response theory. Springer, 1997.

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The theory and practice of item response theory. Guildord Press, 2009.

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Ackerman, Terry A. The robustness of LOGIST and BILOG IRT estimation programs to violations of local independence. American College Testing Program, 1988.

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Woodruff, David. Estimation of item response models using the EM algorithm for finite mixtures. American College Testing Program, 1996.

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Zeng, Lingjia. An IRT scale transformation method for parameters calibrated from multiple samples of subjects. American College Testing Program, 1996.

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Russell, Waugh, ed. Applications of Rasch measurement in education. Nova Science Publishers, 2009.

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Ban, Jae-Chun. Data sparseness and online pretest item calibration/scaling methods in CAT. ACT, Inc., 2002.

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Book chapters on the topic "Item response theory – Mathematical models"

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An, Xinming, and Yiu-Fai Yung. "Notes on the Estimation of Item Response Theory Models." In Springer Proceedings in Mathematics & Statistics. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9348-8_19.

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Embretson, Susan. "Explanatory Item Response Theory Models: Impact on Validity and Test Development?" In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-01310-3_1.

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Hambleton, Ronald K., and Hariharan Swaminathan. "Item Response Models." In Item Response Theory. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-017-1988-9_3.

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Hambleton, Ronald K., and Hariharan Swaminathan. "Practical Considerations in Using IRT Models." In Item Response Theory. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-017-1988-9_14.

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Reckase, Mark D. "Unidimensional Item Response Theory Models." In Multidimensional Item Response Theory. Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-89976-3_2.

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Reckase, Mark D. "Multidimensional Item Response Theory Models." In Multidimensional Item Response Theory. Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-89976-3_4.

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Fox, Jean-Paul. "Multilevel Item Response Theory Models." In Bayesian Item Response Modeling. Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-0742-4_6.

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Embretson, Susan E. "Multicomponent Response Models." In Handbook of Modern Item Response Theory. Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4757-2691-6_18.

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San Martín, Ernesto. "Identification of Item Response Theory Models." In Handbook of Item Response Theory. Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/b19166-8.

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Moses, Tim. "Loglinear Models for Observed-Score Distributions." In Handbook of Item Response Theory. Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/b19166-5.

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Conference papers on the topic "Item response theory – Mathematical models"

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Mori, Kazumasa, and Takuya Ohmori. "The Bayesian estimators of polytomous item response theory models with approximated conditional likelihood and their mathematical optimalities." In 2016 IEEE International Conference on Big Data (Big Data). IEEE, 2016. http://dx.doi.org/10.1109/bigdata.2016.7841046.

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Parmaningsih, Triwik Jatu, and Dewi Retno Sari Saputro. "Rasch analysis on item response theory: Review of model suitability." In THE THIRD INTERNATIONAL CONFERENCE ON MATHEMATICS: Education, Theory and Application. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0040305.

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Ye, Ziwen, and Jianan Sun. "Comparing Item Selection Criteria in Multidimensional Computerized Adaptive Testing for Two Item Response Theory Models." In 2018 3rd International Conference on Computational Intelligence and Applications (ICCIA). IEEE, 2018. http://dx.doi.org/10.1109/iccia.2018.00008.

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Nussbaum, Frank, and Joachim Giesen. "Disentangling Direct and Indirect Interactions in Polytomous Item Response Theory Models." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/310.

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Measurement is at the core of scientific discovery. However, some quantities, such as economic behavior or intelligence, do not allow for direct measurement. They represent latent constructs that require surrogate measurements. In other scenarios, non-observed quantities can influence the variables of interest. In either case, models with latent variables are needed. Here, we investigate fused latent and graphical models that exhibit continuous latent variables and discrete observed variables. These models are characterized by a decomposition of the pairwise interaction parameter matrix into a group-sparse component of direct interactions and a low-rank component of indirect interactions due to the latent variables. We first investigate when such a decomposition is identifiable. Then, we show that fused latent and graphical models can be recovered consistently from data in the high-dimensional setting. We support our theoretical findings with experiments on synthetic and real-world data from polytomous item response theory studies.
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Wang, Hua, Cuiqin Ma, and Ningning Chen. "A brief review on Item Response Theory models-based parameter estimation methods." In Education (ICCSE 2010). IEEE, 2010. http://dx.doi.org/10.1109/iccse.2010.5593443.

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Li, Fang, Fengxuan Jing, Xiaoyao Xie, et al. "Estimation of multidimensional item response theory models in person parameter base on genetic algorithm." In 2010 International Conference on Anti-Counterfeiting, Security and Identification (2010 ASID). IEEE, 2010. http://dx.doi.org/10.1109/icasid.2010.5551499.

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Tong, Shiwei, Qi Liu, Runlong Yu, et al. "Item Response Ranking for Cognitive Diagnosis." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/241.

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Cognitive diagnosis, a fundamental task in education area, aims at providing an approach to reveal the proficiency level of students on knowledge concepts. Actually, monotonicity is one of the basic conditions in cognitive diagnosis theory, which assumes that student's proficiency is monotonic with the probability of giving the right response to a test item. However, few of previous methods consider the monotonicity during optimization. To this end, we propose Item Response Ranking framework (IRR), aiming at introducing pairwise learning into cognitive diagnosis to well model the monotonicity between item responses. Specifically, we first use an item specific sampling method to sample item responses and construct response pairs based on their partial order, where we propose the two-branch sampling methods to handle the unobserved responses. After that, we use a pairwise objective function to exploit the monotonicity in the pair formulation. In fact, IRR is a general framework which can be applied to most of contemporary cognitive diagnosis models. Extensive experiments demonstrate the effectiveness and interpretability of our method.
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Sayeed, Tanvir Mehedi, Leonard M. Lye, and Heather Peng. "Response Surface Models for Analyzing Planing Hull Motions in a Vertical Plane." In ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/omae2014-23489.

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A non-linear mathematical model, Planing Hull Motion Program (PHMP) has been developed based on strip theory to predict the heave and pitch motions of planing hull at high speed in head seas. PHMP has been validated against published model test data. For various combinations of design parameters, PHMP can predict the heave and pitch motions and bow and center of gravity accelerations with reasonable accuracy at planing and semi-planing speeds. This paper illustrates an application of modern statistical design of experiment (DOE) methodology to develop simple surrogate models to assess planing hull motions in a vertical plane (surge, heave and pitch) in calm water and in head seas. Responses for running attitude (sinkage and trim) in calm water, and for heave and pitch motions and bow and center of gravity accelerations in head seas were obtained from PHMP based on a multifactor uniform design scheme. Regression surrogate models were developed for both calm water and in head seas for each of the relevant responses. Results showed that the simple one line regression models provided adequate fit to the generated responses and provided valuable insights into the behaviour of planing hull motions in a vertical plane. The simple surrogate models can be a quick and useful tool for the designers during the preliminary design stages.
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Taghipour, Reza, Tristan Perez, and Torgeir Moan. "Time Domain Hydroelastic Analysis of a Flexible Marine Structure Using State-Space Models." In ASME 2007 26th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2007. http://dx.doi.org/10.1115/omae2007-29272.

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This article deals with time-domain hydroelastic analysis of a marine structure. The convolution terms in the mathematical model are replaced by their alternative state-space representations whose parameters are obtained by using the realization theory. The mathematical model is validated by comparison to experimental results of a very flexible barge. Two types of time-domain simulations are performed: dynamic response of the initially inert structure to incident regular waves and transient response of the structure after it is released from a displaced condition in still water. The accuracy and the efficiency of the simulations based on the state-space model representations are compared to those that integrate the convolutions.
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Ghosh, Aritra, and Andrew Lan. "BOBCAT: Bilevel Optimization-Based Computerized Adaptive Testing." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/332.

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Computerized adaptive testing (CAT) refers to a form of tests that are personalized to every student/test taker. CAT methods adaptively select the next most informative question/item for each student given their responses to previous questions, effectively reducing test length. Existing CAT methods use item response theory (IRT) models to relate student ability to their responses to questions and static question selection algorithms designed to reduce the ability estimation error as quickly as possible; therefore, these algorithms cannot improve by learning from large-scale student response data. In this paper, we propose BOBCAT, a Bilevel Optimization-Based framework for CAT to directly learn a data-driven question selection algorithm from training data. BOBCAT is agnostic to the underlying student response model and is computationally efficient during the adaptive testing process. Through extensive experiments on five real-world student response datasets, we show that BOBCAT outperforms existing CAT methods (sometimes significantly) at reducing test length.
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