Journal ArticleDOI
Estimating latent distributions
TLDR
In this article, the authors present maximum likelihood equations for the estimation of the population parameters directly from the observed responses; i.e., without estimating an ability parameter for each subject, and provide asymptotic standard errors and tests of fit, computing approximations, and details of four special cases: a nonparametric approximation, a normal solution, a resolution of normal components, and a beta-binomial solution.Abstract:
Consider vectors of item responses obtained from a sample of subjects from a population in which abilityθ is distributed with densityg(θ‖α), where theα are unknown parameters. Assuming the responses depend onθ through a fully specified item response model, this paper presents maximum likelihood equations for the estimation of the population parameters directly from the observed responses; i.e., without estimating an ability parameter for each subject. Also provided are asymptotic standard errors and tests of fit, computing approximations, and details of four special cases: a non-parametric approximation, a normal solution, a resolution of normal components, and a beta-binomial solution.read more
Citations
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Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 (ECLS-K): Combined User's Manual for the ECLS-K Eighth-Grade and K-8 Full Sample Data Files and Electronic Codebooks. NCES 2009-004.
TL;DR: All respondents Family Structure FSQ.020 CREATED Family type categories using both parent and sibling information CREATED Have PARENT data
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Randomization‐based inferences about latent variables from complex samples
TL;DR: Rubin's multiple imputation technique as mentioned in this paper can be used to estimate sample statistics that would have been obtained, had the variable of interest been observable, and associated variance estimates that account for uncertainty due to both the sampling of respondents and the latent nature of the variable.
Journal ArticleDOI
Estimating Population Characteristics From Sparse Matrix Samples of Item Responses
TL;DR: The concepts behind plausible values in a simplified setting are developed, their use in the National Assessment of Educational Progress (NAEP) is sketched, and the approach with data from the Scholastic Aptitude Test (SA T) is illustrated.
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Evaluation of a preliminary physical function item bank supported the expected advantages of the Patient-Reported Outcomes Measurement Information System (PROMIS).
TL;DR: The methods of the PROMIS project are likely to substantially improve measures of physical function and to increase the efficiency of their administration using CAT.
Journal ArticleDOI
Recent Developments in the Factor Analysis of Categorical Variables
TL;DR: A unified framework for exploratory factor analysis of dichotomous test items has been proposed in this paper, from a review of the classical common factor model for measured variables through generalized least squares and marginal maximum likelihood solutions for dichotomyous data.
References
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Journal ArticleDOI
Maximum likelihood from incomplete data via the EM algorithm
Book
Statistical Theories of Mental Test Scores
TL;DR: In this paper, the authors present a survey of test theory models and their application in the field of mental test analysis. But the focus of the survey is on test-score theories and models, and not the practical applications and limitations of each model studied.