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1
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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Sucharew, Heidi. "Item Response Theory and Transition Models Applied to Allergen Skin Prick Testing." University of Cincinnati / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1258560557.
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Hatzinger, Reinhold. "A GLM framework for item response theory models. Reissue of 1994 Habilitation thesis." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 2008. http://epub.wu.ac.at/1384/1/document.pdf.
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The aim of the monograph is to contribute towards bridging the gap between methodological developments that have evolved in the social sciences, in particular in psychometric research, and methods of statistical modelling in a more general framework. The first part surveys certain special psychometric models (often referred to as Rasch family of models) that share common properties: separation of parameters describing qualities of the subject under investigation and parameters related to properties of the situation under which the response of a subject is observed. Using conditional maximum likelihood estimation, both types of parameters may be estimated independently from each other. In particular, the Rasch model, the rating scale model, the partial credit model, hybrid types, and linear extensions thereof are treated. The second part reviews basic ideas of generalized linear models (GLMs) as an an excellent framework for unifying different approaches and providing a natural, technical background for model formulation, estimation and testing. This is followed by a short introduction to the software package GLIM chosen to illustrate the formulation of psychometric models in the GLM framework. The third part is the main part of this monograph and shows the application of generalized linear models to psychometric approaches. It gives a unified treatment of Rasch family models in the context of log-linear models and contains some new material on log-linear longitudinal modelling. The last part of the monograph is devoted to show the usefulness of the latent variable approach in a variety of applications, such as panel, cross-over, and therapy evaluation studies, where standard statistical analysis does not necessarily lead to satisfactory results. (author´s abstract)<br>Series: Research Report Series / Department of Statistics and Mathematics
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Xin, Xin. "Using Posterior Predictive Checking of Item Response Theory Models to Study Invariance Violations." Thesis, University of North Texas, 2017. https://digital.library.unt.edu/ark:/67531/metadc984130/.
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The common practice for testing measurement invariance is to constrain parameters to be equal over groups, and then evaluate the model-data fit to reject or fail to reject the restrictive model. Posterior predictive checking (PPC) provides an alternative approach to evaluating model-data discrepancy. This paper explores the utility of PPC in estimating measurement invariance. The simulation results show that the posterior predictive p (PP p) values of item parameter estimates respond to various invariance violations, whereas the PP p values of item-fit index may fail to detect such violations. The current paper suggests comparing group estimates and restrictive model estimates with posterior predictive distributions in order to demonstrate the pattern of misfit graphically.
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Lane, Suzanne. "VALIDATING COGNITIVE SKILL SEQUENCES IN THE BEGINNING READING DOMAIN USING LATENT TRAIT MODELS." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/187541.
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The present study was a systematic investigation of hierarchical skill sequences in the beginning reading domain. The hierarchies included skills from the traditional approach to reading which reflect bottom-up processing and skills from the conceptual area of print awareness which reflect top-down processing. Researchers supporting the bottom-up approach view reading as a process in which the child extracts information from the text to gain knowledge of the print. The bottom-up processes examined were in the areas of letter recognition and letter naming, and identification of letter sounds and phonemes. The top-down processing approach views reading as a task in which the child brings his/her past experiences and knowledge about the world to gain information about print. The top-down processes examined were in the areas of print identification, inferring a word in context, and print directionality rules. Hierarchical skill sequences were developed within each of the specific areas reflecting the top-down and bottom-up processing theories. Items were developed to reflect the skill sequences based on the cognitive processes that are necessary for correct performance. This involved varying the task demands imposing various requirements of cognitive processing. The data were from 13,189 Head Start children ranging from 3 to 6 years of age. Latent trait models were constructed to reflect the viii ix hypothesized skill sequences by allowing the aj (discrimination) and bj (difficulty) parameters to be free to vary or by constraining them to be equal to other parameters. To arrive at a preferred model, each latent trait model that represented a hypothesized skill sequence was statistically compared against alternative latent trait models. The results from the present investigation supported the hierarchical skill sequences reflecting skills within the traditional area of reading. However, some of the skill sequences from the conceptual area of print awareness were not clearly supported. While the results provide a deeper understanding of beginning reading skill sequences reflecting top-down and bottom-up processing theories, future research is needed to delineate the specific skills which promote later reading ability once the child is in formal reading instruction.
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Keum, EunHee. "Applying Longitudinal IRT Models to Small Samples for Scale Evaluation." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1460996452.
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Martelli, Irene <1984>. "Multidimensional item response theory models with general and specific latent traits for ordinal data." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amsdottorato.unibo.it/6347/.
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The aim of the thesis is to propose a Bayesian estimation through Markov chain Monte Carlo of multidimensional item response theory models for graded responses with complex structures and correlated traits. In particular, this work focuses on the multiunidimensional and the additive underlying latent structures, considering that the first one is widely used and represents a classical approach in multidimensional item response analysis, while the second one is able to reflect the complexity of real interactions between items and respondents.
A simulation study is conducted to evaluate the parameter recovery for the proposed models under different conditions (sample size, test and subtest length, number of response categories, and correlation structure).
The results show that the parameter recovery is particularly sensitive to the sample size, due to the model complexity and the high number of parameters to be estimated. For a sufficiently large sample size the parameters of the multiunidimensional and additive graded response models are well reproduced. The results are also affected by the trade-off between the number of items constituting the test and the number of item categories.
An application of the proposed models on response data collected to investigate Romagna and San Marino residents' perceptions and attitudes towards the tourism industry is also presented.
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Wang, Shuo. "Joint Analysis of Social and Item Response Networks with Latent Space Models." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1571918340162685.
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Sheng, Yanyan. "Bayesian analysis of hierarchical IRT models comparing and combining the unidimensional & multi-unidimensional IRT models /." Diss., Columbia, Mo. : University of Missouri-Columbia, 2005. http://hdl.handle.net/10355/4153.
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Thesis (Ph. D.)--University of Missouri-Columbia, 2005.<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 19, 2006) Vita. Includes bibliographical references.
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O'Brien, Erin L. "DO APPLICANTS AND INCUMBENTS RESPOND TO PERSONALITY ITEMS SIMILARLY? A COMPARISON USING AN IDEAL POINT RESPONSE MODEL." Wright State University / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=wright1276703388.
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Matteucci, Mariagiulia <1980>. "Item Response Theory models for the competence evaluation: towards a multidimensional approach in the University guidance." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2007. http://amsdottorato.unibo.it/377/.
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Arabatzis, Alexandros A. "Qualitative response models theory and its application to forestry." Diss., This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-09162005-115001/.
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LaFond, Lee James. "Decision consistency and accuracy indices for the bifactor and testlet response theory models." Diss., University of Iowa, 2014. https://ir.uiowa.edu/etd/1346.
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The primary goal of this study was to develop a new procedure for estimating decision consistency and accuracy indices using the bifactor and testlet response theory (TRT) models. This study is the first to investigate decision consistency and accuracy from a multidimensional perspective, and the results have shown that the bifactor model at least behaved in way that met the author's expectations and represents a potential useful procedure. The TRT model, on the other hand, did not meet the author's expectations and generally showed poor model performance.
The multidimensional decision consistency and accuracy indices proposed in this study appear to provide good performance, at least for the bifactor model, in the case of a substantial testlet effect. For practitioners examining a test containing testlets for decision consistency and accuracy, a recommended first step is to check for dimensionality. If the testlets show a significant degree of multidimensionality, then the usage of the multidimensional indices proposed can be recommended as the simulation study showed an improved level of performance over unidimensional IRT models. However, if there is a not a significant degree of multidimensionality then the unidimensional IRT models and indices would perform as well, or even better, than the multidimensional models.
Another goal of this study was to compare methods for numerical integration used in the calculation of decision consistency and accuracy indices. This study investigated a new method (M method) that sampled ability estimates through a Monte-Carlo approach. In summary, the M method seems to be just as accurate as the other commonly used methods for numerical integration. However, it has some practical advantages over the D and P methods. As previously mentioned, it is not as nearly as computationally intensive as the D method. Also, the P method requires large sample sizes. In addition, the P method has conceptual disadvantage in that the conditioning variable, in theory, should be the true theta, not an estimated theta. The M method avoids both of these issues and seems to provide equally accurate estimates of decision consistency and accuracy indices, which makes it a strong option particularly in multidimensional cases.
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DiTrapani, John B. "IRT in SPSS: The development of a new software tool to conduct item response models." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1462378121.
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Ryan, Cari H. "Using hierarchical generalized linear modeling for detection of differential item functioning in a polytomous item response theory framework an evaluation and comparison with generalized Mantel-Haenszel /." restricted, 2008. http://etd.gsu.edu/theses/available/etd-04232008-160900/.
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Thesis (Ph. D.)--Georgia State University, 2008.<br>Title from file title page. Carolyn F. Furlow, committee chair; Phillip Gagne, T. Chris Oshima, Christopher Domaleski, committee members. Electronic text (113 p.) : digital, PDF file. Description based on contents viewed June 24, 2008. Includes bibliographical references (p. 96-101).
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Li, Caihong Rosina. "ASSESSING THE MODEL FIT OF MULTIDIMENSIONAL ITEM RESPONSE THEORY MODELS WITH POLYTOMOUS RESPONSES USING LIMITED-INFORMATION STATISTICS." UKnowledge, 2019. https://uknowledge.uky.edu/edsc_etds/45.
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Under item response theory, three types of limited information goodness-of-fit test statistics – M2, Mord, and C2 – have been proposed to assess model-data fit when data are sparse. However, the evaluation of the performance of these GOF statistics under multidimensional item response theory (MIRT) models with polytomous data is limited. The current study showed that M2 and C2 were well-calibrated under true model conditions and were powerful under misspecified model conditions. Mord were not well-calibrated when the number of response categories was more than three. RMSEA2 and RMSEAC2 are good tools to evaluate approximate fit.
The second study aimed to evaluate the psychometric properties of the Religious Commitment Inventory-10 (RCI-10; Worthington et al., 2003) within the IRT framework and estimate C2 and its RMSEA to assess global model-fit. Results showed that the RCI-10 was best represented by a bifactor model. The scores from the RCI-10 could be scored as unidimensional notwithstanding the presence of multidimensionality. Two-factor correlational solution should not be used. Study two also showed that religious commitment is a risk factor of intimate partner violence, whereas spirituality was a protecting factor from the violence. More alcohol was related with more abusive behaviors. Implications of the two studies were discussed.
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Mair, Patrick, and Horst Treiblmaier. "Partial Credit Models for Scale Construction in Hedonic Information Systems." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 2008. http://epub.wu.ac.at/1614/1/document.pdf.
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Information Systems (IS) research frequently uses survey data to measure the interplay between technological systems and human beings. Researchers have developed sophisticated procedures to build and validate multi-item scales that measure real world phenomena (latent constructs). Most studies use the so-called classical test theory (CTT), which suffers from several shortcomings. We first compare CTT to Item Response Theory (IRT) and subsequently apply a Rasch model approach to measure hedonic aspects of websites. The results not only show which attributes are best suited for scaling hedonic information systems, but also introduce IRT as a viable substitute that overcomes severall shortcomings of CTT. (author´s abstract)<br>Series: Research Report Series / Department of Statistics and Mathematics
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Kunina-Habenicht, Olga. "Theoretical and practical considerations for implementing diagnostic classification models." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2010. http://dx.doi.org/10.18452/16179.
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Kognitive Diagnosemodelle (DCMs) sind konfirmatorische probabilistische Modelle mit kategorialen latenten Variablen, die Mehrfachladungsstrukturen erlauben. Sie ermöglichen die Abbildung der Kompetenzen in mehrdimensionalen Profilen, die zur Erstellung informativer Rückmeldungen dienen können. Diese Dissertation untersucht in zwei Anwendungsstudien und einer Simulationsstudie wichtige methodische Aspekte bei der Schätzung der DCMs. In der Arbeit wurde ein neuer Mathematiktest entwickelt basierend auf theoriegeleiteten vorab definierten Q-Matrizen. In den Anwendungsstudien (a) illustrierten wir die Anwendung der DCMs für empirische Daten für den neu entwickelten Mathematiktest, (b) verglichen die DCMs mit konfirmatorischen Faktorenanalysemodellen (CFAs), (c) untersuchten die inkrementelle Validität der mehrdimensionalen Profile und (d) schlugen eine Methode zum Vergleich konkurrierender DCMs vor. Ergebnisse der Anwendungsstudien zeigten, dass die geschätzten DCMs meist einen nicht akzeptablen Modellfit aufwiesen. Zudem fanden wir nur eine vernachlässigbare inkrementelle Validität der mehrdimensionalen Profile nach der Kontrolle der Personenparameter bei der Vorhersage der Mathematiknote. Zusammengenommen sprechen diese Ergebnisse dafür, dass DCMs per se keine zusätzliche Information über die mehrdimensionalen CFA-Modelle hinaus bereitstellen. DCMs erlauben jedoch eine andere Aufbereitung der Information. In der Simulationsstudie wurde die Präzision der Parameterschätzungen in log-linearen DCMs sowie die Sensitivität ausgewählter Indizes der Modellpassung auf verschiedene Formen der Fehlspezifikation der Interaktionsterme oder der Q-Matrix untersucht. Die Ergebnisse der Simulationsstudie zeigen, dass die Parameterwerte für große Stichproben korrekt geschätzt werden, während die Akkuratheit der Parameterschätzungen bei kleineren Stichproben z. T. beeinträchtigt ist. Ein großer Teil der Personen wird in Modellen mit fehlspezifizierten Q-Matrizen falsch klassifiziert.<br>Cognitive diagnostic classification models (DCMs) have been developed to assess the cognitive processes underlying assessment responses. Current dissertation aims to provide theoretical and practical considerations for estimation of DCMs for educational applications by investigating several important underexplored issues. To avoid problems related to retrofitting of DCMs to an already existing data, test construction of the newly mathematics assessment for primary school DMA was based on a-priori defined Q-matrices. In this dissertation we compared DCMs with established psychometric models and investigated the incremental validity of DCMs profiles over traditional IRT scores. Furthermore, we addressed the issue of the verification of the Q-matrix definition. Moreover, we examined the impact of invalid Q-matrix specification on item, respondent parameter recovery, and sensitivity of selected fit measures. In order to address these issues one simulation study and two empirical studies illustrating applications of several DCMs were conducted. In the first study we have applied DCMs in general diagnostic modelling framework and compared those models to factor analysis models. In the second study we implemented a complex simulation study and investigated the implications of Q-matrix misspecification on parameter recovery and classification accuracy for DCMs in log-linear framework. In the third study we applied results of the simulation study to a practical application based on the data for 2032 students for the DMA. Presenting arguments for additional gain of DCMs over traditional psychometric models remains challenging. Furthermore, we found only a negligible incremental validity of multivariate proficiency profiles compared to the one-dimensional IRT ability estimate. Findings from the simulation study revealed that invalid Q-matrix specifications led to decreased classification accuracy. Information-based fit indices were sensitive to strong model misspecifications.
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Periard, David Andrew. "A Bifactor Model of Burnout? An Item Response Theory Analysis of the Maslach Burnout Inventory – Human Services Survey." Wright State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=wright1466257122.
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Burch, Melissa Price. "Validating hierarchical sequences in the design copying domain using latent trait models." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184346.
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The present study was a systematic investigation of hierarchical skill sequences in the design copying domain. The factors associated with possible variations in task difficulty were delineated. Five hierarchies were developed to reflect variations in rule usage, the structuring of responses, presence of angles, spatial orientations, and stimulus complexity. Three-hundred thirty four subjects aged five through ten years were administered a 25 item design copying test. The data were analyzed using probabilistic models. Latent trait models were developed to test the hypothesized skill sequences. Each latent trait model was statistically compared to alternate models to arrive at a preferred model that would adequately represent the data. Results suggested that items with predictable difficulty levels can be developed in this domain based on an analysis of stimulus dimensions and the use of rules for task completion. The inclusion of visual cues to guide design copying assists accurate task completion. Implications of the current findings for facilitating the construction of tests which accurately provide information about children's skill levels were discussed. The presence of hierarchical skill sequences in a variety of ability domains was supported.
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DiTrapani, John B. "Assessing the Absolute and Relative Performance of IRTrees Using Cross-Validation and the RORME Index." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1555328378474406.
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Loe, Bao Sheng. "The effectiveness of automatic item generation for the development of cognitive ability tests." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/289990.
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Research has shown that the increased use of computer-based testing has brought about new challenges. With the ease of online test administration, a large number of items are necessary to maintain the item bank and minimise the exposure rate. However, the traditional item development process is time-consuming and costly. Thus, alternative ways of creating items are necessary to improve the item development process. Automatic Item Generation (AIG) is an effective method in generating items rapidly and efficiently. AIG uses algorithms to create questions for testing purposes. However, many of these generators are in the closed form, available only to the selected few. There is a lack of open source, publicly available generators that researchers can utilise to study AIG in greater depth and to generate items for their research. Furthermore, research has indicated that AIG is far from being understood, and more research into its methodology and the psychometric properties of the items created by the generators are needed for it to be used effectively. The studies conducted in this thesis have achieved the following: 1) Five open source item generators were created, and the items were evaluated and validated. 2) Empirical evidence showed that using a weak theory approach to develop item generators was just as credible as using a strong theory approach, even though they are theoretically distinct. 3) The psychometric properties of the generated items were estimated using various IRT models to assess the impact of the template features used to create the items. 4) Joint responses and response time modelling was employed to provide new insights into cognitive processes that go beyond those obtained by typical IRT models. This thesis suggests that AIG provides a tangible solution for improving the item development process for content generation and reducing the procedural cost of generating a large number of items, with the possibility of a unified approach towards test administration (i.e. adaptive item generation). Nonetheless, this thesis focused on rule-based algorithms. The application of other forms of item generation methods and the potential for measuring the intelligence of artificial general intelligence (AGI) is discussed in the final chapter, proposing that the use of AIG techniques create new opportunities as well as challenges for researchers that will redefine the assessment of intelligence.
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Sgammato, Adrienne N. Cizek Gregory J. "An application of unfolding and cumulative item response theory models for noncognitive scaling examining the assumptions and applicability of the generalized graded unfolding model /." Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2009. http://dc.lib.unc.edu/u?/etd,2517.
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Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2009.<br>Title from electronic title page (viewed Oct. 5, 2009). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the School of Education." Discipline: Education; Department/School: Education.
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McGrane, Joshua Aaron. "Unfolding the conceptualisation and measurement of ambivalent attitudes." University of Sydney, 2009. http://hdl.handle.net/2123/5424.
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Doctor of Philosophy (PhD)<br>In the last two decades, ambivalence has emerged as one of the primary concerns of attitude researchers. The acknowledgement that individuals can simultaneously evaluate an attitude object as both positive and negative has challenged a number of the status quos of the attitude literature. This thesis utilises an unfolding approach to investigate the implications of ambivalence for the conceptualisation of attitudes and their measurement. Firstly, the assumption that ambivalence is at odds with the bipolar understanding of attitudes was investigated. The results suggested that ambivalence is consistent with bipolarity, whereby ambivalent attitudes are located at the centre of the bipolar dimension. Secondly, attitude scales for the abortion, euthanasia and Aboriginal Australians issues were constructed to reflect this bipolar understanding. The fit of these statements to Coombs’ (1964) unidimensional unfolding theory provided evidence that ambivalence is also consistent with the quantitative conceptualisation of attitudes. Together these results provided further validation of the unfolding approach to attitude measurement. These models alleviate many of the problems faced by the ubiquitous method of summated ratings, including the assessment of ambivalent evaluations. Finally, these scales were used to investigate the latent structure of attitudes and its relationship with meta-psychological judgements of ambivalence. The conclusions drawn from these analyses were limited by a number of issues, highlighting the importance of rigorously considering measurement issues for all attitude parameters. Nonetheless, they presented preliminary validation of these scales’ ability to measure ambivalent evaluations and suggested a systematic relationship between proximity to the centre of the evaluative dimension and metapsychological ambivalence. Overall, it is concluded that a number of assumptions regarding the implications of ambivalence are misplaced and the proposed solutions are even more troublesome. Suggestions for future research are made, particularly with respect to differentiating between ambivalent, indifferent and uncertain evaluative states. Furthermore, attitude researchers are encouraged to discard their operationalist biases in order to engage with the measurement issues illuminated throughout this thesis. This is necessary to account for the complexity of the attitude construct, which ambivalence is testament to.
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Pardos, Zachary Alexander. "Predictive Models of Student Learning." Digital WPI, 2012. https://digitalcommons.wpi.edu/etd-dissertations/185.
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In this dissertation, several approaches I have taken to build upon the student learning model are described. There are two focuses of this dissertation. The first focus is on improving the accuracy with which future student knowledge and performance can be predicted by individualizing the model to each student. The second focus is to predict how different educational content and tutorial strategies will influence student learning. The two focuses are complimentary but are approached from slightly different directions. I have found that Bayesian Networks, based on belief propagation, are strong at achieving the goals of both focuses. In prediction, they excel at capturing the temporal nature of data produced where student knowledge is changing over time. This concept of state change over time is very difficult to capture with classical machine learning approaches. Interpretability is also hard to come by with classical machine learning approaches; however, it is one of the strengths of Bayesian models and aids in studying the direct influence of various factors on learning. The domain in which these models are being studied is the domain of computer tutoring systems, software which uses artificial intelligence to enhance computer based tutorial instruction. These systems are growing in relevance. At their best they have been shown to achieve the same educational gain as one on one human interaction. Computer tutors have also received the attention of White House, which mentioned an tutoring platform called ASSISTments in its National Educational Technology Plan. With the fast paced adoption of these data driven systems it is important to learn how to improve the educational effectiveness of these systems by making sense of the data that is being generated from them. The studies in this proposal use data from these educational systems which primarily teach topics of Geometry and Algebra but can be applied to any domain with clearly defined sub-skills and dichotomous student response data. One of the intended impacts of this work is for these knowledge modeling contributions to facilitate the move towards computer adaptive learning in much the same way that Item Response Theory models facilitated the move towards computer adaptive testing.
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Novakovic, Ana M. "Longitudinal Models for Quantifying Disease and Therapeutic Response in Multiple Sclerosis." Doctoral thesis, Uppsala universitet, Institutionen för farmaceutisk biovetenskap, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-316562.
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Treatment of patients with multiple sclerosis (MS) and development of new therapies have been challenging due to the disease complexity and slow progression, and the limited sensitivity of available clinical outcomes. Modeling and simulation has become an increasingly important component in drug development and in post-marketing optimization of use of medication. This thesis focuses on development of pharmacometric models for characterization and quantification of the relationships between drug exposure, biomarkers and clinical endpoints in relapse-remitting MS (RRMS) following cladribine treatment. A population pharmacokinetic model of cladribine and its main metabolite, 2-chloroadenine, was developed using plasma and urine data. The renal clearance of cladribine was close to half of total elimination, and was found to be a linear function of creatinine clearance (CRCL). Exposure-response models could quantify a clear effect of cladribine tablets on absolute lymphocyte count (ALC), burden of disease (BoD), expanded disability status scale (EDSS) and relapse rate (RR) endpoints. Moreover, they gave insight into disease progression of RRMS. This thesis further demonstrates how integrated modeling framework allows an understanding of the interplay between ALC and clinical efficacy endpoints. ALC was found to be a promising predictor of RR. Moreover, ALC and BoD were identified as predictors of EDSS time-course. This enables the understanding of the behavior of the key outcomes necessary for the successful development of long-awaited MS therapies, as well as how these outcomes correlate with each other. The item response theory (IRT) methodology, an alternative approach for analysing composite scores, enabled to quantify the information content of the individual EDSS components, which could help improve this scale. In addition, IRT also proved capable of increasing the detection power of potential drug effects in clinical trials, which may enhance drug development efficiency. The developed nonlinear mixed-effects models offer a platform for the quantitative understanding of the biomarker(s)/clinical endpoint relationship, disease progression and therapeutic response in RRMS by integrating a significant amount of knowledge and data.
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Poli, Edneia Consolin. "Estudo longitudinal em matematica : possibilidades e leitura de uma realidade do ensino fundamental." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/251999.
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Orientador: Luiz Carlos de Freitas, Dalton Francisco de Andrade<br>Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Educação<br>Made available in DSpace on 2018-08-10T09:20:06Z (GMT). No. of bitstreams: 1
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Previous issue date: 2007<br>Resumo: As dificuldades encontradas no ensino e aprendizagem de Matemática têm sido marcadas por constantes buscas de entendimento de uma problemática tão atual e instigativa. O estudo é de caráter longitudinal e monitora o progresso dos alunos desde a 1ª fase do primeiro ciclo do Ensino Fundamental (7 anos) até a 2ª fase (mais ou menos 11 anos), durante quatro anos de escolaridade. Este estudo fez parte do Projeto Internacional de Aquisição Matemática, uma parceria entre a Universidade de Exeter (Inglaterra) e a Universidade Estadual de Londrina (Brasil). Participaram desta pesquisa inicialmente 600 alunos que estudavam em duas escolas estaduais e seis escolas municipais da região de Londrina. A cada ano aplicou-se um teste de Matemática que foi traduzido e validado no Brasil. O teste foi composto por conteúdos da série da qual se trata, repetindo-se algumas questões a cada ano. O conteúdo avaliado referiu-se a números, operações, geometria e medidas e tratamento da informação. Na análise quantitativa utilizou-se da teoria de resposta ao item (TRI) e para a análise qualitativa trabalhou-se com estudo de caso a partir dos resultados da TRI. No último ano da pesquisa, os alunos e professores preencheram um questionário com informações socioeconômicas e pedagógicas relacionadas ao ensino de Matemática. Pretendeu-se com esta pesquisa avaliar o rendimento dos alunos em Matemática ao longo de quatro anos de escolaridade<br>Abstract: The difficulties found within mathematical teaching-learning have been marked by constant searches for an understanding of such a current and inciting issue. This is a Longitudinal study and it has monitored the progress of students from the first phase of the first cycle of the Fundamental Grades ¿ Elementary School (7 year old students) up to the second phase (11 year old students) for four school years. This study is part of the International Project of Mathematical Attainment, a partnership between the University of Exeter (England) and the State University in Londrina (Brazil). Initially 600 students from two state and 12 county schools in the city of Londrina participated. Each year a mathematical test, that had been translated and validated in Brazil, was given to the students. The test is composed of the subject specific for each grade, and some of the questions were repeated every year. The evaluated subject involved numbers, operations, geometry and measures, and treatment of information. For the quantitative analysis the Item Response Theory (TRI) was used and for the qualitative analysis the result of the TRI was the starting point used for the case studies. In the last year of research the students and teachers filled out a form with social-economical and pedagogical information in relation to the mathematical teaching. The intention of this research was to evaluate the school attainment of the students during these four years<br>Doutorado<br>Ensino, Avaliação e Formação de Professores<br>Doutor em Educação
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Granville, Monique V. "Calibration Efficacy of Three Logistic Models to the Degrees of Reading Power Test Using Residual Analysis." Diss., Virginia Tech, 1997. http://hdl.handle.net/10919/40518.
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The publisher of the Degrees of Reading Power test of reading comprehension (DRP) calibrate their test using an item response model called the Rasch or one-parameter logistic model. The relationship between the use of the Rasch model in calibration of the DRP and the use of the DRP as a component of the Virginia Literacy Passport Testing Program (LPT) is addressed. Analyses concentrate on sixth grade students who were administered the DRP in 1991. The question that arises is whether the Rasch model is the appropriate model to use to calibrate the DRP in this high-stakes setting. The majority of research that has been reported by the publisher of the DRP to assess the adequacy of the Rasch model have not included direct checks on model assumptions, model features or model predictions. Instead, they have relied almost exclusively on statistical tests in assessment of model fit. This study will assess the adequacy of fitting DRP test data to the Rasch model through direct examination of the assumptions, features and predictions of the IRT model. This is accomplished by comparing the Rasch model to the less restrictive two- and three-parameter logistic models. Robust IRT-based goodness-of-fit techniques are conducted. When the DRP is used in a high stakes setting, guessing is likely for those in jeopardy of failing. Under these circumstances, we must attend to the possibility that guessing may be a factor and thereby calibrate the DRP with the three-parameter model, as this model takes guessing into account.<br>Ph. D.
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Murphy, Raegan. "Exploring a meta-theoretical framework for dynamic assessment and intelligence." Thesis, Pretoria : [s.n.], 2007. http://upetd.up.ac.za/thesis/available/etd-09302007-162044.
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Bodine, Andrew James. "A Monte Carlo Investigation of Fit Statistic Behavior in Measurement Models Assessed Using Limited-and Full-Information Estimation." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1433412282.
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Kim, Stella Yun. "Simple structure MIRT equating for multidimensional tests." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/6158.
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Equating is a statistical process used to accomplish score comparability so that the scores from the different test forms can be used interchangeably. One of the most widely used equating procedures is unidimensional item response theory (UIRT) equating, which requires a set of assumptions about the data structure. In particular, the essence of UIRT rests on the unidimensionality assumption, which requires that a test measures only a single ability. However, this assumption is not likely to be fulfilled for many real data such as mixed-format tests or tests composed of several content subdomains: failure to satisfy the assumption threatens the accuracy of the estimated equating relationships.
The main purpose of this dissertation was to contribute to the literature on multidimensional item response theory (MIRT) equating by developing a theoretical and conceptual framework for true-score equating using a simple-structure MIRT model (SS-MIRT). SS-MIRT has several advantages over other complex MIRT models such as improved efficiency in estimation and a straightforward interpretability.
In this dissertation, the performance of the SS-MIRT true-score equating procedure (SMT) was examined and evaluated through four studies using different data types: (1) real data, (2) simulated data, (3) pseudo forms data, and (4) intact single form data with identity equating. Besides SMT, four competitors were included in the analyses in order to assess the relative benefits of SMT over the other procedures: (a) equipercentile equating with presmoothing, (b) UIRT true-score equating, (c) UIRT observed-score equating, and (d) SS-MIRT observed-score equating.
In general, the proposed SMT procedure behaved similarly to the existing procedures. Also, SMT showed more accurate equating results compared to the traditional UIRT equating. Better performance of SMT over UIRT true-score equating was consistently observed across the three studies that employed different criterion relationships with different datasets, which strongly supports the benefit of a multidimensional approach to equating with multidimensional data.
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Ueckert, Sebastian. "Novel Pharmacometric Methods for Design and Analysis of Disease Progression Studies." Doctoral thesis, Uppsala universitet, Institutionen för farmaceutisk biovetenskap, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-216537.
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With societies aging all around the world, the global burden of degenerative diseases is expected to increase exponentially. From the perspective drug development, degenerative diseases represent an especially challenging class. Clinical trials, in this context often termed disease progression studies, are long, costly, require many individuals, and have low success rates. Therefore, it is crucial to use informative study designs and to analyze efficiently the obtained trial data. The development of novel approaches intended towards facilitating both the design and the analysis of disease progression studies was the aim of this thesis. This aim was pursued in three stages (i) the characterization and extension of pharmacometric software, (ii) the development of new methodology around statistical power, and (iii) the demonstration of application benefits. The optimal design software PopED was extended to simplify the application of optimal design methodology when planning a disease progression study. The performance of non-linear mixed effect estimation algorithms for trial data analysis was evaluated in terms of bias, precision, robustness with respect to initial estimates, and runtime. A novel statistic allowing for explicit optimization of study design for statistical power was derived and found to perform superior to existing methods. Monte-Carlo power studies were accelerated through application of parametric power estimation, delivering full power versus sample size curves from a few hundred Monte-Carlo samples. Optimal design and an explicit optimization for statistical power were applied to the planning of a study in Alzheimer's disease, resulting in a 30% smaller study size when targeting 80% power. The analysis of ADAS-cog score data was improved through application of item response theory, yielding a more exact description of the assessment score, an increased statistical power and an enhanced insight in the assessment properties. In conclusion, this thesis presents novel pharmacometric methods that can help addressing the challenges of designing and planning disease progression studies.
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Marques, Katia Antunes. "Análise bayesiana em modelos TRI de três parâmetros." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-02092008-214645/.
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Neste trabalho discutimos a análise bayesiana em modelos TRI (Teoria da Resposta ao Item) de três parâmetros com respostas binárias e ordinais, considerando a ligação probito. Em ambos os casos usamos técnicas baseadas em MCCM (método de Monte Carlo baseado em Cadeias de Markov) para estimação dos parâmetros dos itens. No modelo com respostas binárias, consideramos dois conjuntos de dados resultantes de provas com itens de múltipla-escolha. Para esses dados, foi feito um estudo da sensibilidade à escolha de distribuições a priori, além de uma análise das estimativas a posteriori para os parâmetros dos itens: discriminação, dificuldade e probabilidade de acerto ao acaso. Um terceiro conjunto de dados foi utilizado no estudo do modelo com respostas ordinais. Estes dados são provenientes de uma disciplina básica de estatística, onde a prova contêm itens dissertativos. As respostas foram classificadas nas categorias: certa, errada ou parcialmente certa. Utilizamos o programa WinBugs para a estimação dos parâmetros do modelo binário e a função MCMCordfactanal do programa R para estimar os parâmetros do modelo ordinal. Ambos os softwares são não proprietários e gratuitos (livres).<br>In this dissertation the bayesian analysis for three parameters IRT (Item Response Theory) models with binaries and ordinals responses, considering the probit model, was discussed. For both cases, binary and ordinal, techniques based on MCCM (Monte Carlo Markov Chain) were used to estimate the items parameters. For binary response model, was considered two data sets from tests with multipla choices items. For these two data sets, a sensibility study of the priori distributions choice was considered, and also, an analyses of a posteriori estimates of the items parameters: discrimination, difficulties and guessing. A third data set is used to ilustrate the ordinal response model. This come from an elementar statistical course, where a test with open items is considered. The responses are classified in the following categories: correct, wrong or partial correct. The WinBugs software was used to estimate the parameters for the binary model and, for the ordinal model was considered the function MCMCordfactanal from R program.
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Ferreira, Eduardo Vargas 1987. "Modelos da teoria de resposta ao item assimétricos de grupos múltiplos para respostas politômicas nominais e ordinais sob um enfoque bayesiano." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306788.
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Orientador: Caio Lucidius Naberezny Azevedo<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-24T12:51:18Z (GMT). No. of bitstreams: 1
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Previous issue date: 2014<br>Resumo: No presente trabalho propõem-se novos modelos da Teoria de Resposta ao Item para respostas politômicas nominais e ordinais (graduais), via dados aumentados, para grupos múltiplos. Para a modelagem das distribuições dos traços latentes de cada grupo, considera-se normais assimétricas centradas. Tal abordagem, além de acomodar a característica de assimetria aos dados, ajuda a garantir a identificabilidade dos modelos estudados, a qual é tratada tanto sob a ótica frequentista quanto bayesiana. Com relação aos métodos de estimação, desenvolveu-se procedimentos bayesianos através de algoritmos de Monte Carlo via cadeias de Markov (MCMC), utilizando o algoritmo de Gibbs (DAGS), com a verossimilhança aumentada (dados aumentados) e Metropolis-Hastings, considerando a verossimilhança original. As implementações computacionais foram escritas em linguagem C++, integradas ao ambiente computacional, gráfico e estatístico R, viabilizando rotinas gratuitas, de código aberto e alta velocidade no processamento, essenciais à difusão de tais metodologias. Para a seleção de modelos, utilizou-se o critério de informação deviance (DIC), os valores esperados do critério de informação de Akaike (EAIC) e o critério de informação bayesiano (EBIC). Em relação à verificação da qualidade do ajuste de modelos, explorou-se a checagem preditiva a posteriori, que fornece meios concretos de se avaliar a qualidade do instrumento de medida (prova, questionário etc), qualidade do ajuste do modelo de um modo global, além de indícios de violações de suposições específicas. Estudos de simulação, considerando diversas situações de interesse prático, indicam que os modelos e métodos de estimação produzem resultados bastante satisfatórios, com superioridade dos modelos assimétricos com relação ao simétrico (o qual assume simetria das distribuições das variáveis latentes). A análise de um conjunto de dados reais, referente à primeira fase do vestibular da UNICAMP de 2013, ilustra o potencial da tríade: modelagem, métodos de estimação e ferramentas de diagnósticos, desenvolvida neste trabalho<br>Abstract: In this work, we propose new Item Response Theory models for nominal and ordinal (gradual) polytomous responses through augmented data schemes considering multiple groups. For the distribution of the latent traits of each group, we consider a skew-normal distribution under the centered parametrization. This approach will allow for accommodating a possible skewness of the latent trait distribution, but is also helpful to ensure the identifiability of the models, which is studied under frequentist and Bayesian paradigms. Concerning estimation methods, we developed Bayesian methods through Markov chain Monte Carlo (MCMC) algorithms by using the Gibbs algorithm (DAGS), with augmented likelihood (augmented data) and Metropolis-Hastings algorithms, considering the original
likelihood. The computational environment was written in the C++ language and integrated with the R program (a statistical computational and graphical environment), allowing for free, open source and high-speed routines which, in turn, are essential to the dissemination of the developed methodologies. In terms of model selection, we considered the deviance information criterion (DIC), the expected Akaike information criterion (EAIC) and expected Bayesian information criterion (EBIC). Regarding model-fit assessment tools, we explore the posterior predictive model- checking which allows for assessing the quality of measurement, instruments (tests, questionnaires, and others), the model fit in a global sense,
besides providing directions toward violations of specific assumptions. Simulation studies, considering different situations of practical interest, indicate that the models and estimation methods produced reasonable results, with outperformance of skew models when compared to symmetric ones (which assumes symmetry of the latent trait distribution). Analysis of a data set which corresponds to the first phase of the 2013 written examination of UNICAMP (State University of Campinas), illustrates the potential of the following triad: modelling; estimation methods; and diagnostic tools developed in this work.<br>Mestrado<br>Estatistica<br>Mestre em Estatística
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Katsikatsou, Myrsini. "Composite Likelihood Estimation for Latent Variable Models with Ordinal and Continuous, or Ranking Variables." Doctoral thesis, Uppsala universitet, Statistiska institutionen, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-188342.
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The estimation of latent variable models with ordinal and continuous, or ranking variables is the research focus of this thesis. The existing estimation methods are discussed and a composite likelihood approach is developed. The main advantages of the new method are its low computational complexity which remains unchanged regardless of the model size, and that it yields an asymptotically unbiased, consistent, and normally distributed estimator. The thesis consists of four papers. The first one investigates the two main formulations of the unrestricted Thurstonian model for ranking data along with the corresponding identification constraints. It is found that the extra identifications constraints required in one of them lead to unreliable estimates unless the constraints coincide with the true values of the fixed parameters. In the second paper, a pairwise likelihood (PL) estimation is developed for factor analysis models with ordinal variables. The performance of PL is studied in terms of bias and mean squared error (MSE) and compared with that of the conventional estimation methods via a simulation study and through some real data examples. It is found that the PL estimates and standard errors have very small bias and MSE both decreasing with the sample size, and that the method is competitive to the conventional ones. The results of the first two papers lead to the next one where PL estimation is adjusted to the unrestricted Thurstonian ranking model. As before, the performance of the proposed approach is studied through a simulation study with respect to relative bias and relative MSE and in comparison with the conventional estimation methods. The conclusions are similar to those of the second paper. The last paper extends the PL estimation to the whole structural equation modeling framework where data may include both ordinal and continuous variables as well as covariates. The approach is demonstrated through an example run in R software. The code used has been incorporated in the R package lavaan (version 0.5-11).
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Kim, Jung-Kyung. "Tail asymptotics of queueing networks with subexponential service times." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29734.
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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2010.<br>Committee Chair: Ayhan, Hayriye; Committee Member: Foley, Robert D.; Committee Member: Goldsman, David M.; Committee Member: Reed, Joshua; Committee Member: Zwart, Bert. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Robitzsch, Alexander. "Essays zu methodischen Herausforderungen im Large-Scale Assessment." Doctoral thesis, Humboldt-Universität zu Berlin, Kultur-, Sozial- und Bildungswissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17424.
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Mit der wachsenden Verbreitung empirischer Schulleistungsleistungen im Large-Scale Assessment gehen eine Reihe methodischer Herausforderungen einher. Die vorliegende Arbeit untersucht, welche Konsequenzen Modellverletzungen in eindimensionalen Item-Response-Modellen (besonders im Rasch-Modell) besitzen. Insbesondere liegt der Fokus auf vier methodischen Herausforderungen von Modellverletzungen. Erstens, implizieren Positions- und Kontexteffekte, dass gegenüber einem eindimensionalen IRT-Modell Itemschwierigkeiten nicht unabhängig von der Position im Testheft und der Zusammenstellung des Testheftes ausgeprägt sind und Schülerfähigkeiten im Verlauf eines Tests variieren können. Zweitens, verursacht die Vorlage von Items innerhalb von Testlets lokale Abhängigkeiten, wobei unklar ist, ob und wie diese in der Skalierung berücksichtigt werden sollen. Drittens, können Itemschwierigkeiten aufgrund verschiedener Lerngelegenheiten zwischen Schulklassen variieren. Viertens, sind insbesondere in low stakes Tests nicht bearbeitete Items vorzufinden. In der Arbeit wird argumentiert, dass trotz Modellverletzungen nicht zwingend von verzerrten Schätzungen von Itemschwierigkeiten, Personenfähigkeiten und Reliabilitäten ausgegangen werden muss. Außerdem wird hervorgehoben, dass man psychometrisch häufig nicht entscheiden kann und entscheiden sollte, welches IRT-Modell vorzuziehen ist. Dies trifft auch auf die Fragestellung zu, wie nicht bearbeitete Items zu bewerten sind. Ausschließlich Validitätsüberlegungen können dafür Hinweise geben. Modellverletzungen in IRT-Modellen lassen sich konzeptuell plausibel in den Ansatz des Domain Samplings (Item Sampling; Generalisierbarkeitstheorie) einordnen. In dieser Arbeit wird gezeigt, dass die statistische Unsicherheit in der Modellierung von Kompetenzen nicht nur von der Stichprobe der Personen, sondern auch von der Stichprobe der Items und der Wahl statistischer Modelle verursacht wird.<br>Several methodological challenges emerge in large-scale student assessment studies like PISA and TIMSS. Item response models (IRT models) are essential for scaling student abilities within these studies. This thesis investigates the consequences of several model violations in unidimensional IRT models (especially in the Rasch model). In particular, this thesis focuses on the following four methodological challenges of model violations. First, position effects and contextual effects imply (in comparison to unidimensional IRT models) that item difficulties depend on the item position in a test booklet as well as on the composition of a test booklet. Furthermore, student abilities are allowed to vary among test positions. Second, the administration of items within testlets causes local dependencies, but it is unclear whether and how these dependencies should be taken into account for the scaling of student abilities. Third, item difficulties can vary among different school classes due to different opportunities to learn. Fourth, the amount of omitted items is in general non-negligible in low stakes tests. In this thesis it is argued that estimates of item difficulties, student abilities and reliabilities can be unbiased despite model violations. Furthermore, it is argued that the choice of an IRT model cannot and should not be made (solely) from a psychometric perspective. This also holds true for the problem of how to score omitted items. Only validity considerations provide reasons for choosing an adequate scoring procedure. Model violations in IRT models can be conceptually classified within the approach of domain sampling (item sampling; generalizability theory). In this approach, the existence of latent variables need not be posed. It is argued that statistical uncertainty in modelling competencies does not only depend on the sampling of persons, but also on the sampling of items and on the choice of statistical models.
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Gurkan, Gulsah. "From OLS to Multilevel Multidimensional Mixture IRT: A Model Refinement Approach to Investigating Patterns of Relationships in PISA 2012 Data." Thesis, Boston College, 2021. http://hdl.handle.net/2345/bc-ir:109191.
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Thesis advisor: Henry I. Braun<br>Secondary analyses of international large-scale assessments (ILSA) commonly characterize relationships between variables of interest using correlations. However, the accuracy of correlation estimates is impaired by artefacts such as measurement error and clustering. Despite advancements in methodology, conventional correlation estimates or statistical models not addressing this problem are still commonly used when analyzing ILSA data. This dissertation examines the impact of both the clustered nature of the data and heterogeneous measurement error on the correlations reported between background data and proficiency scales across countries participating in ILSA. In this regard, the operating characteristics of competing modeling techniques are explored by means of applications to data from PISA 2012. Specifically, the estimates of correlations between math self-efficacy and math achievement across countries are the principal focus of this study. Sequentially employing four different statistical techniques, a step-wise model refinement approach is used. After each step, the changes in the within-country correlation estimates are examined in relation to (i) the heterogeneity of distributions, (ii) the amount of measurement error, (iii) the degree of clustering, and (iv) country-level math performance. The results show that correlation estimates gathered from two-dimensional IRT models are more similar across countries in comparison to conventional and multilevel linear modeling estimates. The strength of the relationship between math proficiency and math self-efficacy is moderated by country mean math proficiency and this was found to be consistent across all four models even when measurement error and clustering were taken into account. Multilevel multidimensional mixture IRT modeling results support the hypothesis that low-performing groups within countries have a lower correlation between math self-efficacy and math proficiency. A weaker association between math self-efficacy and math proficiency in lower achieving groups is consistently seen across countries. A multilevel mixture IRT modeling approach sheds light on how this pattern emerges from greater randomness in the responses of lower performing groups. The findings from this study demonstrate that advanced modeling techniques not only are more appropriate given the characteristics of the data, but also provide greater insight about the patterns of relationships across countries<br>Thesis (PhD) — Boston College, 2021<br>Submitted to: Boston College. Lynch School of Education<br>Discipline: Educational Research, Measurement and Evaluation
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Azevedo, Caio Lucidius Naberezny. "Modelos longitudinais de grupos múltiplos multiníveis na teoria da resposta ao item: métodos de estimação e seleção estrutural sob uma perspectiva bayesiana." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-15042008-165256/.
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No presente trabalho propomos uma estrutura bayesiana, através de um esquema de dados aumentados, para analisar modelos longitudinais com grupos mútiplos (MLGMTRI) na Teoria da Resposta ao Item (TRI). Tal estrutura consiste na tríade : modelagem, métodos de estimação e métodos de diagnóstico para a classe de MLGMTRI. Na parte de modelagem, explorou-se as estruturas multivariada e multinível, com o intuito de representar a hierarquia existente em dados longitudinais com grupos múltiplos. Esta abordagem permite considerar várias classes de submodelos como: modelos de grupos múltiplos e modelos longitudinais de um único grupo. Estudamos alguns aspectos positivos e negativos de cada uma das supracitadas abordagens. A modelagem multivariada permite representar de forma direta estruturas de dependência, além de possibilitar que várias delas sejam facilmente incorporadas no processo de estimação. Isso permite considerar, por exemplo, uma matriz não estruturada e assim, obter indícios da forma mais apropriada para a estrutura de dependência. Por outro lado, a modelagem multinível propicia uma interpretação mais direta, obtenção de condicionais completas univariadas, fácil inclusão de informações adicionais, incorporação de fontes de dependência intra e entre unidades amostrais, dentre outras. Com relação aos métodos de estimação, desenvolvemos um procedimento baseado nas simulações de Monte Carlo via cadeias de Markov (MCMC). Mostramos que as distribuições condicionais completas possuem forma analítica conhecida e, além disso, são fáceis de se amostrar. Tal abordagem, apesar de demandar grande esforço computacional, contorna diversos problemas encontrados em outros procedimentos como: limitação no número de grupos envolvidos, quantidade de condições de avaliação, escolha de estruturas de dependência, assimetria dos traços latentes, imputação de dados, dentre outras. Além disso, através da metodologia MCMC, desenvolvemos uma estrutura de seleção de matrizes de covariâncias, através de um esquema de Monte Carlo via Cadeias de Markov de Saltos Reversíveis (RJMCMC). Estudos de simulação indicam que o modelo, o método de estimação e o método de seleção produzem resultados bastante satisfatórios. Também, robustez à escolha de prioris e valores iniciais foi observada. Os métodos de estimação desenvolvidos podem ser estendidos para diversas situações de interesse de um modo bem direto. Algumas das técnicas de diagnóstico estudadas permitem avaliar a qualidade do ajuste do modelo de um modo global. Outras medidas fornecem indícios de violação de suposições específicas, como ausência de normalidade para os traços latentes. Tal metodologia fornece meios concretos de se avaliar a qualidade do instrumento de medida (prova, questionário etc). Finalmente, a análise de um conjunto de dados real, utilizando-se alguns dos modelos abordados no presente trabalho, ilustra o potencial da tríade desenvolvida além de indicar um ganho na utilização dos modelos longitudinais da TRI na análise de ensaios educacionais com medidas repetidas em deterimento a suposição de independência.<br>In this work we proposed a bayesian framework, by using an augmented data scheme, to analyze longitudinal multiple groups models (LMGMIRT) in the Item Response Theory (IRT). Such framework consists in the following set : modelling, estimation methods and diagnostic tools to the LMGMIRT. Concerning the modelling, we exploited multivariate and multilevel structures in order to represent the hierarchical nature of the longitudinal multiple groupos model. This approach allows to consider several submodels such that: multiple groups and longitudinal one group models. We studied some positive and negative aspects of both above mentioned approches. The multivariate modelling allows to represent, in a straightforward way, many dependence structures. Furthermore it possibilities that many of them can be easily considered in the estimation process. This allows, for example, to consider an unstructured covariance matrix and, then, it allows to obtain information about the most appropritate dependece structure. On the other hand, the multilevel modelling permits to obtain: more straightforward interpretations of the model, the construction of univariate full conditional distributions, an easy way to include auxiliary information, the incorporation of within and between subjects (groups) sources of variability, among others. Concerning the estimation methods, we developed a procedure based on Monte Carlo Markov Chain (MCMC) simulation. We showed that the full conditional distributions are known and easy to sample from. Even though such approach demands a considerable amount of time it circumvents many problems such that: limitation in the number of groups that can be considered, the limitation in the number of instants of observation, the choice of covariance matrices, latent trait asymmetry, data imputation, among others. Furthermore, within the MCMC metodology, we developed a procedure to select covariance matrices, by using the so called Reversible Jump MCMC (RJMCMC). Simulation studies show that the model, the estimation method and the model selection procedure produce reasonable results. Also, the studies indicate that the developed metodology presents robustness concerning prior choice and different initial values choice. It is possible to extent the developed estimation methods to other situations in a straightforward way. Some diagnostics techniques that were studied allow to assess the model fit, in a global sense. Others techniques give directions toward the departing from some specific assumptions as the latent trait normality. Such methodology also provides ways to assess the quality of the test or questionaire used to measure the latent traits. Finally, by analyzing a real data set, using some of the models that were developed, it was possible to verify the potential of the methodology considered in this work. Furthermore, the results of this analysis indicate advantages in using longitudinal IRT models to model educational repeated measurement data instead of to assume independence.
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Fujii, Tânia Robaskiewicz Coneglian. "Estudo sobre construção de escalas com base na Teoria da Resposta ao Item : avaliação de proficiência em conteúdos matemáticos básicos /." Universidade Estadual Paulista (UNESP), 2018. http://hdl.handle.net/11449/154453.
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Previous issue date: 2018-05-07<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>Neste trabalho realizou-se um estudo sobre construção de escalas, com base na Teoria da Resposta ao Item (TRI), resultando na construção e interpretação pedagógica de uma escala de conhecimento para medir a proficiência em conteúdos matemáticos, necessários para o acompanhamento das disciplinas de cálculo e similares dos ingressantes nos cursos da área de exatas. O modelo matemático adotado nesta pesquisa foi o logístico unidimensional de três parâmetros. A estimação dos parâmetros dos itens e das proficiências dos respondentes foi feita sob enfoque bayesiano, utilizando-se o amostrador de Gibbs, algoritmo da classe dos Métodos de Monte Carlo via Cadeia de Markov (MCMC), implementado via software OpenBUGS (Bayesian inference Using Gibbs Sampling), direcionado para análise bayesiana de modelos complexos. O software BILOG-MG também foi utilizado para comparação dos resultados. O instrumento utilizado para a medida do conhecimento consistiu em uma prova composta por trinta e seis itens de múltipla escolha, cada um com cinco alternativas, sendo somente uma a correta. Os itens foram elaborados com base em uma matriz de referência construída para este fim, dividida em três temas, sendo estes “espaço e forma”, “grandezas e medidas” e “números e operações/álgebra e funções”. Cada tema é composto por competências e cada competência descreve uma habilidade que se deseja medir. Para a construção da escala proposta, optou-se por adotar uma escala com média 250 e desvio padrão 50. Nesta escala foram selecionados níveis para serem interpretados em um intervalo de 75 a 425. Para interpretação da escala proposta, foram comparados alguns métodos de posicionamento de itens âncora nos níveis selecionados. Buscando a interpretação da escala, em toda a sua amplitude, optou-se por utilizar a análise de agrupamentos hierárquicos para segmentar a escala em grupos, ou seja, em faixas de proficiência. A escala foi dividida em cinco grupos, cada grupo caracterizado com base nos itens posicionados como âncora, a partir de suas probabilidades de resposta correta e de seus valores para o parâmetro de discriminação. Embora os resultados sejam consistentes, apontam para a necessidade de um processo contínuo de aprimoramento do banco de questões e da escala de proficiência.<br>In this work, a study was carried out on the construction of scales, based on the Item Response Theory (IRT), resulting in the construction and pedagogical interpretation of a scale of knowledge to measure the proficiency in mathematical contents, necessary for the follow-up of Calculus and similar subjects of the students in the courses of the Exact Sciences Area. The mathematical model adopted in this research was the three parameters one-dimensional logistic. The parameters estimation of the items and proficiencies of the respondents was done using a Bayesian approach using the Gibbs sampler, Monte Carlo Methods via Markov Chain algorithm (MCMC), implemented using OpenBUGS software (Bayesian inference Using Gibbs Sampling), directed to Bayesian analysis of complex models. The BILOG-MG software was also used to compare the results. The instrument used for the measurement of knowledge consisted of a test composed of thirty-six multiple choice items, each with five alternatives, with only one correct. The items were elaborated based on a reference matrix constructed for this purpose, divided in three themes, being these “space and form”, “quantities and measures” and “numbers and operations/ algebra and functions". Each subject is composed of competencies and each competency describes a skill that one wishes to measure. In order to construct the proposed scale, we chose to adopt a scale with a mean of 250 and standard deviation of 50. In this scale, we selected levels to be interpreted in a range of 75 to 425. For the interpretation of the proposed scale, some methods of positioning anchor items at the selected levels were compared. In order to interpret the scale in all its amplitude, it was decided to use hierarchical groupings analysis to segment the scale into groups, that is, in skill bands. The scale was divided into five groups, each group was characterized based on the items positioned as anchor, from their correct response probabilities and their values for the discrimination parameter. Although the results are consistent, they point to the need for an ongoing upgrading process of questions bank and proficiency scale.
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Broadfoot, Alison Ann. "Comparing the Dominance Approach to the Ideal-Point Approach in the Measurement and Predictability of Personality." Bowling Green State University / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1211913274.
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