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Chun Wang, David J Weiss, Zhuoran Shang
In computerized adaptive testing (CAT), a variable-length stopping rule refers to ending item administration after a pre-specified measurement precision standard has been satisfied. The goal is to provide equal measurement precision for all examinees regardless of their true latent trait level. Several stopping rules have been proposed in unidimensional CAT, such as the minimum information rule or the maximum standard error rule. These rules have also been extended to multidimensional CAT and cognitive diagnostic CAT, and they all share the same idea of monitoring measurement error...
December 3, 2018: Psychometrika
Brian D Segal, Thomas Braun, Richard Gonzalez, Michael R Elliott
Psychologists and other behavioral scientists are frequently interested in whether a questionnaire measures a latent construct. Attempts to address this issue are referred to as construct validation. We describe and extend nonparametric hypothesis testing procedures to assess matrix structures, which can be used for construct validation. These methods are based on a quadratic assignment framework and can be used either by themselves or to check the robustness of other methods. We investigate the performance of these matrix structure tests through simulations and demonstrate their use by analyzing a big five personality traits questionnaire administered as part of the Health and Retirement Study...
November 27, 2018: Psychometrika
Lars Eldén, Nickolay Trendafilov
It is well known that the classical exploratory factor analysis (EFA) of data with more observations than variables has several types of indeterminacy. We study the factor indeterminacy and show some new aspects of this problem by considering EFA as a specific data matrix decomposition. We adopt a new approach to the EFA estimation and achieve a new characterization of the factor indeterminacy problem. A new alternative model is proposed, which gives determinate factors and can be seen as a semi-sparse principal component analysis (PCA)...
November 27, 2018: Psychometrika
Quentin F Gronau, Eric-Jan Wagenmakers, Daniel W Heck, Dora Matzke
Multinomial processing trees (MPTs) are a popular class of cognitive models for categorical data. Typically, researchers compare several MPTs, each equipped with many parameters, especially when the models are implemented in a hierarchical framework. A Bayesian solution is to compute posterior model probabilities and Bayes factors. Both quantities, however, rely on the marginal likelihood, a high-dimensional integral that cannot be evaluated analytically. In this case study, we show how Warp-III bridge sampling can be used to compute the marginal likelihood for hierarchical MPTs...
November 27, 2018: Psychometrika
Steven Andrew Culpepper
Cognitive diagnosis models (CDMs) are an important psychometric framework for classifying students in terms of attribute and/or skill mastery. The [Formula: see text] matrix, which specifies the required attributes for each item, is central to implementing CDMs. The general unavailability of [Formula: see text] for most content areas and datasets poses a barrier to widespread applications of CDMs, and recent research accordingly developed fully exploratory methods to estimate Q. However, current methods do not always offer clear interpretations of the uncovered skills and existing exploratory methods do not use expert knowledge to estimate Q...
November 19, 2018: Psychometrika
Yunxiao Chen, Xiaoou Li, Siliang Zhang
Joint maximum likelihood (JML) estimation is one of the earliest approaches to fitting item response theory (IRT) models. This procedure treats both the item and person parameters as unknown but fixed model parameters and estimates them simultaneously by solving an optimization problem. However, the JML estimator is known to be asymptotically inconsistent for many IRT models, when the sample size goes to infinity and the number of items keeps fixed. Consequently, in the psychometrics literature, this estimator is less preferred to the marginal maximum likelihood (MML) estimator...
November 19, 2018: Psychometrika
Stefano Noventa, Andrea Spoto, Jürgen Heller, Augustin Kelava
Knowledge space theory (KST) structures are introduced within item response theory (IRT) as a possible way to model local dependence between items. The aim of this paper is threefold: firstly, to generalize the usual characterization of local independence without introducing new parameters; secondly, to merge the information provided by the IRT and KST perspectives; and thirdly, to contribute to the literature that bridges continuous and discrete theories of assessment. In detail, connections are established between the KST simple learning model (SLM) and the IRT General Graded Response Model, and between the KST Basic Local Independence Model and IRT models in general...
November 12, 2018: Psychometrika
Leah M Feuerstahler
The [Formula: see text] metric in item response theory is often not the most useful metric for score reporting or interpretation. In this paper, I demonstrate that the filtered monotonic polynomial (FMP) item response model, a recently proposed nonparametric item response model (Liang & Browne in J Educ Behav Stat 40:5-34, 2015), can be used to specify item response models on metrics other than the [Formula: see text] metric. Specifically, I demonstrate that any item response function (IRF) defined within the FMP framework can be re-expressed as another FMP IRF by taking monotonic transformations of the latent trait...
November 9, 2018: Psychometrika
Zhehan Jiang, Jonathan Templin
Fully Bayesian estimation of item response theory models with logistic link functions suffers from low computational efficiency due to posterior density functions that do not have known forms. To improve algorithmic computational efficiency, this paper proposes a Bayesian estimation method by adopting a new data-augmentation strategy in uni- and multidimensional IRT models. The strategy is based on the Pólya-Gamma family of distributions which provides a closed-form posterior distribution for logistic-based models...
October 31, 2018: Psychometrika
Marie Wiberg, James O Ramsay, Juan Li
The aim of this paper is to discuss nonparametric item response theory scores in terms of optimal scores as an alternative to parametric item response theory scores and sum scores. Optimal scores take advantage of the interaction between performance and item impact that is evident in most testing data. The theoretical arguments in favor of optimal scoring are supplemented with the results from simulation experiments, and the analysis of test data suggests that sum-scored tests would need to be longer than an optimally scored test in order to attain the same level of accuracy...
October 22, 2018: Psychometrika
Keith A Markus
No abstract text is available yet for this article.
September 25, 2018: Psychometrika
Lili Yao, Shelby J Haberman, Mo Zhang
In best linear prediction (BLP), a true test score is predicted by observed item scores and by ancillary test data. If the use of BLP rather than a more direct estimate of a true score has disparate impact for different demographic groups, then a fairness issue arises. To improve population invariance but to preserve much of the efficiency of BLP, a modified approach, penalized best linear prediction, is proposed that weights both mean square error of prediction and a quadratic measure of subgroup biases. The proposed methodology is applied to three high-stakes writing assessments...
September 21, 2018: Psychometrika
(no author information available yet)
No abstract text is available yet for this article.
December 2018: Psychometrika
Matthew J Madison, Laine P Bradshaw
A common assessment research design is the single-group pre-test/post-test design in which examinees are administered an assessment before instruction and then another assessment after instruction. In this type of study, the primary objective is to measure growth in examinees, individually and collectively. In an item response theory (IRT) framework, longitudinal IRT models can be used to assess growth in examinee ability over time. In a diagnostic classification model (DCM) framework, assessing growth translates to measuring changes in attribute mastery status over time, thereby providing a categorical, criterion-referenced interpretation of growth...
December 2018: Psychometrika
Johan Koskinen, Peng Wang, Garry Robins, Philippa Pattison
We discuss measuring and detecting influential observations and outliers in the context of exponential family random graph (ERG) models for social networks. We focus on the level of the nodes of the network and consider those nodes whose removal would result in changes to the model as extreme or "central" with respect to the structural features that "matter". We construe removal in terms of two case-deletion strategies: the tie-variables of an actor are assumed to be unobserved, or the node is removed resulting in the induced subgraph...
December 2018: Psychometrika
Minjeong Jeon, Frank Rijmen, Sophia Rabe-Hesketh
We propose a class of confirmatory factor analysis models that include multiple sets of secondary or specific factors and a general factor. The general factor accounts for the common variance among manifest variables, whereas multiple sets of secondary factors account for the remaining source-specific dependency among subsets of manifest variables. A special case of the model is further proposed which constrains the specific factor loadings to be proportional to the general factor loadings. This proportional model substantially reduces the number of model parameters while preserving the essential structure of the general model...
December 2018: Psychometrika
Joel B Greenhouse, Edward H Kennedy
No abstract text is available yet for this article.
December 2018: Psychometrika
Peter F Halpin, Yoav Bergner
The social combination theory of group problem solving is used to extend existing psychometric models to collaborative settings. A model for pairwise group work is proposed, the implications of the model for assessment design are considered, and its estimation is addressed. The results are illustrated with an empirical example in which dyads work together on a twelfth-grade level mathematics assessment. In conclusion, attention is given to avenues of research that seem most fruitful for advancing current initiatives concerning the assessment of collaboration, teamwork, and related constructs...
December 2018: Psychometrika
Daniel W Heck, Edgar Erdfelder, Pascal J Kieslich
Multinomial processing tree models assume that discrete cognitive states determine observed response frequencies. Generalized processing tree (GPT) models extend this conceptual framework to continuous variables such as response times, process-tracing measures, or neurophysiological variables. GPT models assume finite-mixture distributions, with weights determined by a processing tree structure, and continuous components modeled by parameterized distributions such as Gaussians with separate or shared parameters across states...
December 2018: Psychometrika
Marco Geraci, Alexander McLain
Missing data are a common issue in statistical analyses. Multiple imputation is a technique that has been applied in countless research studies and has a strong theoretical basis. Most of the statistical literature on multiple imputation has focused on unbounded continuous variables, with mostly ad hoc remedies for variables with bounded support. These approaches can be unsatisfactory when applied to bounded variables as they can produce misleading inferences. In this paper, we propose a flexible quantile-based imputation model suitable for distributions defined over singly or doubly bounded intervals...
December 2018: Psychometrika
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