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Principal Component Analysis on the Covariance Matrix for Data Reduction in Large-Scale Assessments
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Paul A. Jewsbury; Matthew S. Johnson – Large-scale Assessments in Education, 2025
The standard methodology for many large-scale assessments in education involves regressing latent variables on numerous contextual variables to estimate proficiency distributions. To reduce the number of contextual variables used in the regression and improve estimation, we propose and evaluate principal component analysis on the covariance matrix…
Descriptors: Factor Analysis, Matrices, Regression (Statistics), Educational Assessment
A Content Analysis of the DMI Mathematics Systems Instructional Objectives Inventory according to the 1985-86 National Assessment of Educational Progress Content by Process Matrix for Mathematics.
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Solomon, Alan – 1988
A study was undertaken to assess the relationship between the DMI Mathematics Systems Objective Inventory (DMIMS) and the National Assessment of Educational Progress (NAEP) content by process matrix prepared for the Fourth Assessment of Mathematics. The DMIMS is a criterion-referenced standardized test comprised of seven levels, and it can be used…
Descriptors: Comparative Analysis, Content Analysis, Elementary Secondary Education, Mathematics Tests
Generating Multiple Imputations for Matrix Sampling Data Analyzed with Item Response Models.
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Thomas, Neal; Gan, Nianci – Journal of Educational and Behavioral Statistics, 1997
Describes and assesses missing data methods currently used to analyze data from matrix sampling designs implemented by the National Assessment of Educational Progress. Several improved methods are developed, and these models are evaluated using an EM algorithm to obtain maximum likelihood estimates followed by multiple imputation of complete data…
Descriptors: Data Analysis, Item Response Theory, Matrices, Maximum Likelihood Statistics
The Role of Secondary Covariates When Estimating Latent Trait Population Distributions.
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Thomas, Neal – Psychometrika, 2002
Studied the improvement in precision of population estimates from the inclusion of extensive covariates in the multivariate procedure that imputes values for the missing proficiencies. Analysis of data from the National Assessment of Educational Progress (samples of 10,291 eighth graders and 8,416 fourth graders) shows that improvement in…
Descriptors: Elementary Education, Elementary School Students, Estimation (Mathematics), Junior High School Students
Estimating Population Characteristics from Sparse Matrix Samples of Item Responses.
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Mislevy, Robert J.; And Others – Journal of Educational Measurement, 1992
Concepts behind plausible values in estimating population characteristics from sparse matrix samples of item responses are discussed. The use of marginal analyses is described in the context of the National Assessment of Educational Progress, and the approach is illustrated with Scholastic Aptitude Test data for 9,075 high school seniors. (SLD)
Descriptors: College Entrance Examinations, Educational Assessment, Equations (Mathematics), Estimation (Mathematics)
Exploring National Assessment Data Using Singular Value Decomposition.
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Sauls, Judith M.; Larson, Robert C. – 1975
National data was obtained from 9-year-old, 13-year-old, 17-year-old, and 26 through 35-year-old populations in order to determine academic achievement in nine subject areas. For each age population, group data was calculated and reported by region, sex, color, parents' educational level, and size and type of community. The application of singular…
Descriptors: Academic Achievement, Age Differences, Community Characteristics, Demography