View in EDS

Orthogonal Regression, the Cleary Criterion, and Lord's Paradox: Asking the Right Questions. Research Report. ETS RR-20-14

Saved in:
Bibliographic Details
Title: Orthogonal Regression, the Cleary Criterion, and Lord's Paradox: Asking the Right Questions. Research Report. ETS RR-20-14
Language: English
Authors: Kane, Michael T., Mroch, Andrew A.
Source: ETS Research Report Series. Dec 2020.
Availability: Educational Testing Service. Rosedale Road, MS19-R Princeton, NJ 08541. Tel: 609-921-9000; Fax: 609-734-5410; e-mail: RDweb@ets.org; Web site: https://www.ets.org/research/policy_research_reports/ets
Peer Reviewed: Y
Page Count: 24
Publication Date: 2020
Document Type: Journal Articles
Reports - Evaluative
Descriptors: Regression (Statistics), Least Squares Statistics, Test Bias, Error of Measurement, Statistical Analysis, Prediction, Factor Analysis, Models
ISSN: 2330-8516
Abstract: Ordinary least squares (OLS) regression and orthogonal regression (OR) address different questions and make different assumptions about errors. The OLS regression of Y on X yields predictions of a dependent variable (Y) contingent on an independent variable (X) and minimizes the sum of squared errors of prediction. It assumes that the independent variable (X) is an observed score that is known without error, and all of the error is assigned to the dependent variable (Y). OLS is not designed to estimate underlying functional relationships, and if both variables contain error, OLS regression tends to yield biased estimates of such functional (or true-score) relationships. OR models, including the errors-in-variables (EIV) and geometric-mean (GM) models, assume that both variables contain error and seek to identify the line that minimizes squared deviations of the data points from the line in both the X and Y directions. OLS and OR address different questions and serve different purposes. If one wants to predict one variable from another variable, OLS regression is an optimal approach and OR is less efficient; in examining the functional relationship between two variables, OR provides a more plausible model. The OR models are hard to apply in many contexts because they depend on strong assumptions about sources of error. As examples of cases where OR can shed light, we examine its use in analyzing test bias as distinct from predictive bias and in making sense of Lord's paradox.
Abstractor: As Provided
Entry Date: 2021
Accession Number: EJ1284925
Database: ERIC
FullText Text:
  Availability: 0
CustomLinks:
  – Url: https://eric.ed.gov/contentdelivery/servlet/ERICServlet?accno=EJ1284925
    Name: ERIC Full Text
    Category: fullText
    Text: Full Text from ERIC
Header DbId: eric
DbLabel: ERIC
An: EJ1284925
AccessLevel: 3
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Orthogonal Regression, the Cleary Criterion, and Lord's Paradox: Asking the Right Questions. Research Report. ETS RR-20-14
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Kane%2C+Michael+T%2E%22">Kane, Michael T.</searchLink><br /><searchLink fieldCode="AR" term="%22Mroch%2C+Andrew+A%2E%22">Mroch, Andrew A.</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22ETS+Research+Report+Series%22"><i>ETS Research Report Series</i></searchLink>. Dec 2020.
– Name: Avail
  Label: Availability
  Group: Avail
  Data: Educational Testing Service. Rosedale Road, MS19-R Princeton, NJ 08541. Tel: 609-921-9000; Fax: 609-734-5410; e-mail: RDweb@ets.org; Web site: https://www.ets.org/research/policy_research_reports/ets
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 24
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2020
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Evaluative
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Regression+%28Statistics%29%22">Regression (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Least+Squares+Statistics%22">Least Squares Statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Test+Bias%22">Test Bias</searchLink><br /><searchLink fieldCode="DE" term="%22Error+of+Measurement%22">Error of Measurement</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+Analysis%22">Statistical Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Prediction%22">Prediction</searchLink><br /><searchLink fieldCode="DE" term="%22Factor+Analysis%22">Factor Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Models%22">Models</searchLink>
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 2330-8516
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Ordinary least squares (OLS) regression and orthogonal regression (OR) address different questions and make different assumptions about errors. The OLS regression of Y on X yields predictions of a dependent variable (Y) contingent on an independent variable (X) and minimizes the sum of squared errors of prediction. It assumes that the independent variable (X) is an observed score that is known without error, and all of the error is assigned to the dependent variable (Y). OLS is not designed to estimate underlying functional relationships, and if both variables contain error, OLS regression tends to yield biased estimates of such functional (or true-score) relationships. OR models, including the errors-in-variables (EIV) and geometric-mean (GM) models, assume that both variables contain error and seek to identify the line that minimizes squared deviations of the data points from the line in both the X and Y directions. OLS and OR address different questions and serve different purposes. If one wants to predict one variable from another variable, OLS regression is an optimal approach and OR is less efficient; in examining the functional relationship between two variables, OR provides a more plausible model. The OR models are hard to apply in many contexts because they depend on strong assumptions about sources of error. As examples of cases where OR can shed light, we examine its use in analyzing test bias as distinct from predictive bias and in making sense of Lord's paradox.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2021
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1284925
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1284925
RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 24
    Subjects:
      – SubjectFull: Regression (Statistics)
        Type: general
      – SubjectFull: Least Squares Statistics
        Type: general
      – SubjectFull: Test Bias
        Type: general
      – SubjectFull: Error of Measurement
        Type: general
      – SubjectFull: Statistical Analysis
        Type: general
      – SubjectFull: Prediction
        Type: general
      – SubjectFull: Factor Analysis
        Type: general
      – SubjectFull: Models
        Type: general
    Titles:
      – TitleFull: Orthogonal Regression, the Cleary Criterion, and Lord's Paradox: Asking the Right Questions. Research Report. ETS RR-20-14
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Kane, Michael T.
      – PersonEntity:
          Name:
            NameFull: Mroch, Andrew A.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 12
              Type: published
              Y: 2020
          Identifiers:
            – Type: issn-electronic
              Value: 2330-8516
          Titles:
            – TitleFull: ETS Research Report Series
              Type: main
ResultId 1