View in EDS

Principal Component Analysis on the Covariance Matrix for Data Reduction in Large-Scale Assessments

Saved in:
Bibliographic Details
Title: Principal Component Analysis on the Covariance Matrix for Data Reduction in Large-Scale Assessments
Language: English
Authors: Paul A. Jewsbury (ORCID 0000-0001-5571-4623), Matthew S. Johnson
Source: Large-scale Assessments in Education. 2025 13.
Availability: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
Peer Reviewed: Y
Page Count: 40
Publication Date: 2025
Sponsoring Agency: National Center for Education Statistics (NCES) (ED/IES)
Contract Number: 91990019C0045
Document Type: Journal Articles
Reports - Research
Descriptors: Factor Analysis, Matrices, Regression (Statistics), Educational Assessment, Evaluation Methods, Statistical Distributions, Data Analysis, Correlation, Sample Size, Statistical Bias, Error Patterns, Statistical Inference, National Competency Tests
Assessment and Survey Identifiers: National Assessment of Educational Progress
DOI: 10.1186/s40536-025-00264-9
ISSN: 2196-0739
Abstract: 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 as a data reduction method for the contextual variables. This adjustment, compared to the conventional use of a correlation matrix, weights variables with respect to sample size. In a simulation study involving low test reliability for a subset of the sample, we found that PCA-covariance substantially reduces estimation bias and mean squared error. We demonstrate how a large-scale assessment can transition to using PCA-covariance without impacting primary trend inferences using data from the 2022 National Assessment of Educational Progress (NAEP). Our findings demonstrate that PCA-covariance accommodates a broader reporting scope with improved estimation.
Abstractor: As Provided
IES Funded: Yes
Entry Date: 2025
Accession Number: EJ1483248
Database: ERIC
FullText Text:
  Availability: 0
Header DbId: eric
DbLabel: ERIC
An: EJ1483248
AccessLevel: 3
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Principal Component Analysis on the Covariance Matrix for Data Reduction in Large-Scale Assessments
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Paul+A%2E+Jewsbury%22">Paul A. Jewsbury</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0001-5571-4623">0000-0001-5571-4623</externalLink>)<br /><searchLink fieldCode="AR" term="%22Matthew+S%2E+Johnson%22">Matthew S. Johnson</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22Large-scale+Assessments+in+Education%22"><i>Large-scale Assessments in Education</i></searchLink>. 2025 13.
– Name: Avail
  Label: Availability
  Group: Avail
  Data: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 40
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2025
– Name: SourceSuprt
  Label: Sponsoring Agency
  Group: SrcSuprt
  Data: National Center for Education Statistics (NCES) (ED/IES)
– Name: NumberContract
  Label: Contract Number
  Group: NumCntrct
  Data: 91990019C0045
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Factor+Analysis%22">Factor Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices%22">Matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Regression+%28Statistics%29%22">Regression (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Educational+Assessment%22">Educational Assessment</searchLink><br /><searchLink fieldCode="DE" term="%22Evaluation+Methods%22">Evaluation Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+Distributions%22">Statistical Distributions</searchLink><br /><searchLink fieldCode="DE" term="%22Data+Analysis%22">Data Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Correlation%22">Correlation</searchLink><br /><searchLink fieldCode="DE" term="%22Sample+Size%22">Sample Size</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+Bias%22">Statistical Bias</searchLink><br /><searchLink fieldCode="DE" term="%22Error+Patterns%22">Error Patterns</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+Inference%22">Statistical Inference</searchLink><br /><searchLink fieldCode="DE" term="%22National+Competency+Tests%22">National Competency Tests</searchLink>
– Name: SubjectThesaurus
  Label: Assessment and Survey Identifiers
  Group: Su
  Data: <searchLink fieldCode="SU" term="%22National+Assessment+of+Educational+Progress%22">National Assessment of Educational Progress</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1186/s40536-025-00264-9
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 2196-0739
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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 as a data reduction method for the contextual variables. This adjustment, compared to the conventional use of a correlation matrix, weights variables with respect to sample size. In a simulation study involving low test reliability for a subset of the sample, we found that PCA-covariance substantially reduces estimation bias and mean squared error. We demonstrate how a large-scale assessment can transition to using PCA-covariance without impacting primary trend inferences using data from the 2022 National Assessment of Educational Progress (NAEP). Our findings demonstrate that PCA-covariance accommodates a broader reporting scope with improved estimation.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: CodeSource
  Label: IES Funded
  Group: SrcInfo
  Data: Yes
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2025
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1483248
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1483248
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1186/s40536-025-00264-9
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 40
    Subjects:
      – SubjectFull: Factor Analysis
        Type: general
      – SubjectFull: Matrices
        Type: general
      – SubjectFull: Regression (Statistics)
        Type: general
      – SubjectFull: Educational Assessment
        Type: general
      – SubjectFull: Evaluation Methods
        Type: general
      – SubjectFull: Statistical Distributions
        Type: general
      – SubjectFull: Data Analysis
        Type: general
      – SubjectFull: Correlation
        Type: general
      – SubjectFull: Sample Size
        Type: general
      – SubjectFull: Statistical Bias
        Type: general
      – SubjectFull: Error Patterns
        Type: general
      – SubjectFull: Statistical Inference
        Type: general
      – SubjectFull: National Competency Tests
        Type: general
      – SubjectFull: National Assessment of Educational Progress
        Type: general
    Titles:
      – TitleFull: Principal Component Analysis on the Covariance Matrix for Data Reduction in Large-Scale Assessments
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Paul A. Jewsbury
      – PersonEntity:
          Name:
            NameFull: Matthew S. Johnson
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 12
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-electronic
              Value: 2196-0739
          Numbering:
            – Type: volume
              Value: 13
          Titles:
            – TitleFull: Large-scale Assessments in Education
              Type: main
ResultId 1