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Doran, Harold – Journal of Educational and Behavioral Statistics, 2023
This article is concerned with a subset of numerically stable and scalable algorithms useful to support computationally complex psychometric models in the era of machine learning and massive data. The subset selected here is a core set of numerical methods that should be familiar to computational psychometricians and considers whitening transforms…
Descriptors: Scaling, Algorithms, Psychometrics, Computation
Fu, Jianbin – ETS Research Report Series, 2019
A maximum marginal likelihood estimation with an expectation-maximization algorithm has been developed for estimating multigroup or mixture multidimensional item response theory models using the generalized partial credit function, graded response function, and 3-parameter logistic function. The procedure includes the estimation of item…
Descriptors: Maximum Likelihood Statistics, Mathematics, Item Response Theory, Expectation
Minchen, Nathan D.; de la Torre, Jimmy; Liu, Ying – Journal of Educational and Behavioral Statistics, 2017
Nondichotomous response models have been of greater interest in recent years due to the increasing use of different scoring methods and various performance measures. As an important alternative to dichotomous scoring, the use of continuous response formats has been found in the literature. To assess finer-grained skills or attributes and to…
Descriptors: Models, Psychometrics, Test Theory, Maximum Likelihood Statistics
Carpenter, Bob; Gelman, Andrew; Hoffman, Matthew D.; Lee, Daniel; Goodrich, Ben; Betancourt, Michael; Brubaker, Marcus A.; Guo, Jiqiang; Li, Peter; Riddell, Allen – Grantee Submission, 2017
Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the…
Descriptors: Programming Languages, Probability, Bayesian Statistics, Monte Carlo Methods
Potgieter, Cornelis; Kamata, Akihito; Kara, Yusuf – Grantee Submission, 2017
This study proposes a two-part model that includes components for reading accuracy and reading speed. The speed component is a log-normal factor model, for which speed data are measured by reading time for each sentence being assessed. The accuracy component is a binomial-count factor model, where the accuracy data are measured by the number of…
Descriptors: Reading Rate, Oral Reading, Accuracy, Models
Leckie, George – Journal of Educational and Behavioral Statistics, 2018
The traditional approach to estimating the consistency of school effects across subject areas and the stability of school effects across time is to fit separate value-added multilevel models to each subject or cohort and to correlate the resulting empirical Bayes predictions. We show that this gives biased correlations and these biases cannot be…
Descriptors: Value Added Models, Reliability, Statistical Bias, Computation
Moothedath, Shana; Chaporkar, Prasanna; Belur, Madhu N. – Perspectives in Education, 2016
In recent years, the computerised adaptive test (CAT) has gained popularity over conventional exams in evaluating student capabilities with desired accuracy. However, the key limitation of CAT is that it requires a large pool of pre-calibrated questions. In the absence of such a pre-calibrated question bank, offline exams with uncalibrated…
Descriptors: Guessing (Tests), Computer Assisted Testing, Adaptive Testing, Maximum Likelihood Statistics
Andrich, David – Educational and Psychological Measurement, 2016
This article reproduces correspondence between Georg Rasch of The University of Copenhagen and Benjamin Wright of The University of Chicago in the period from January 1966 to July 1967. This correspondence reveals their struggle to operationalize a unidimensional measurement model with sufficient statistics for responses in a set of ordered…
Descriptors: Statistics, Item Response Theory, Rating Scales, Mathematical Models
an de Sande, Brett – International Educational Data Mining Society, 2016
Learning curves have proven to be a useful tool for understanding how a student learns a given skill as they progress through a curriculum. A learning curve for a given Knowledge Component (KC) is a plot of some measure of competence as a function of the number of opportunities the student has had to apply that KC. Consider the case where each…
Descriptors: Learning Processes, Knowledge Level, Problem Solving, Homework
Chiu, Chia-Yi; Köhn, Hans-Friedrich; Wu, Huey-Min – International Journal of Testing, 2016
The Reduced Reparameterized Unified Model (Reduced RUM) is a diagnostic classification model for educational assessment that has received considerable attention among psychometricians. However, the computational options for researchers and practitioners who wish to use the Reduced RUM in their work, but do not feel comfortable writing their own…
Descriptors: Educational Diagnosis, Classification, Models, Educational Assessment
Xi, Nuo; Browne, Michael W. – Journal of Educational and Behavioral Statistics, 2014
A promising "underlying bivariate normal" approach was proposed by Jöreskog and Moustaki for use in the factor analysis of ordinal data. This was a limited information approach that involved the maximization of a composite likelihood function. Its advantage over full-information maximum likelihood was that very much less computation was…
Descriptors: Factor Analysis, Maximum Likelihood Statistics, Data, Computation
Ranger, Jochen; Kuhn, Jorg-Tobias – Psychometrika, 2012
Latent trait models for response times in tests have become popular recently. One challenge for response time modeling is the fact that the distribution of response times can differ considerably even in similar tests. In order to reduce the need for tailor-made models, a model is proposed that unifies two popular approaches to response time…
Descriptors: Reaction Time, Tests, Models, Computation
Cheung, Mike
W.-L. – Structural Equation Modeling: A Multidisciplinary Journal, 2013
Structural equation modeling (SEM) is now a generic modeling framework for many multivariate techniques applied in the social and behavioral sciences. Many statistical models can be considered either as special cases of SEM or as part of the latent variable modeling framework. One popular extension is the use of SEM to conduct linear mixed-effects…
Descriptors: Structural Equation Models, Maximum Likelihood Statistics, Guidelines, Multivariate Analysis
Savalei, Victoria; Rhemtulla, Mijke – Structural Equation Modeling: A Multidisciplinary Journal, 2012
Fraction of missing information [lambda][subscript j] is a useful measure of the impact of missing data on the quality of estimation of a particular parameter. This measure can be computed for all parameters in the model, and it communicates the relative loss of efficiency in the estimation of a particular parameter due to missing data. It has…
Descriptors: Computation, Structural Equation Models, Maximum Likelihood Statistics, Data
Halpin, Peter F.; Dolan, Conor V.; Grasman, Raoul P. P. P.; De Boeck, Paul – Psychometrika, 2011
The relationship between linear factor models and latent profile models is addressed within the context of maximum likelihood estimation based on the joint distribution of the manifest variables. Although the two models are well known to imply equivalent covariance decompositions, in general they do not yield equivalent estimates of the…
Descriptors: Models, Maximum Likelihood Statistics, Computation, Goodness of Fit