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Signposts on the Path from Nominal to Ordinal Scales: Moving from a Discrete to a Continuous View

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Title: Signposts on the Path from Nominal to Ordinal Scales: Moving from a Discrete to a Continuous View
Language: English
Authors: Roza Nalbandyan, Joshua B. Gilbert, Vithor R. Franco, Benjamin W. Domingue
Source: Grantee Submission. 2026.
Peer Reviewed: Y
Page Count: 42
Publication Date: 2026
Sponsoring Agency: Institute of Education Sciences (ED)
Contract Number: R305D240025
Document Type: Reports - Evaluative
Descriptors: Item Response Theory, Models, Computation, Efficiency, Serial Ordering, Accuracy, Nonparametric Statistics
Abstract: Polytomous item response data are typically classified as either nominal or ordinal, but this binary distinction may oversimplify their true structure. In this paper, we reframe the nominal--ordinal distinction as a continuum and introduce six empirical indices to quantify the degree of category ordering in item response data. Through extensive simulations with various IRT models and applications to 245 empirical datasets, we evaluate the indices' sensitivity, computational efficiency, and interpretability across diverse measurement contexts. Our findings show that two parametric indices--Mean Difference between Slope Parameters (Index 5) and Arctangent of Paired Category Ratios (Index 6)--are particularly robust and informative, even with low-frequency categories. These indices offer a practical tool for assessing whether and how item categories align with ordinal assumptions, supporting more accurate measurement and model selection. We conclude that treating ordering as a continuum, rather than a binary property, provides deeper insights for psychometric practice and strengthens the connection between empirical response patterns and their theoretical representations. [This paper will be published in "Educational and Psychological Measurement."]
Abstractor: As Provided
IES Funded: Yes
Entry Date: 2026
Access URL: https://journals.sagepub.com/home/EPM
Accession Number: ED679456
Database: ERIC
FullText Text:
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PubType: Report
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  Data: Signposts on the Path from Nominal to Ordinal Scales: Moving from a Discrete to a Continuous View
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  Data: <searchLink fieldCode="SO" term="%22Grantee+Submission%22"><i>Grantee Submission</i></searchLink>. 2026.
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  Data: Y
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  Data: 42
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  Label: Publication Date
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  Data: 2026
– Name: SourceSuprt
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  Data: Institute of Education Sciences (ED)
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  Data: R305D240025
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  Data: Reports - Evaluative
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  Data: <searchLink fieldCode="DE" term="%22Item+Response+Theory%22">Item Response Theory</searchLink><br /><searchLink fieldCode="DE" term="%22Models%22">Models</searchLink><br /><searchLink fieldCode="DE" term="%22Computation%22">Computation</searchLink><br /><searchLink fieldCode="DE" term="%22Efficiency%22">Efficiency</searchLink><br /><searchLink fieldCode="DE" term="%22Serial+Ordering%22">Serial Ordering</searchLink><br /><searchLink fieldCode="DE" term="%22Accuracy%22">Accuracy</searchLink><br /><searchLink fieldCode="DE" term="%22Nonparametric+Statistics%22">Nonparametric Statistics</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: Polytomous item response data are typically classified as either nominal or ordinal, but this binary distinction may oversimplify their true structure. In this paper, we reframe the nominal--ordinal distinction as a continuum and introduce six empirical indices to quantify the degree of category ordering in item response data. Through extensive simulations with various IRT models and applications to 245 empirical datasets, we evaluate the indices' sensitivity, computational efficiency, and interpretability across diverse measurement contexts. Our findings show that two parametric indices--Mean Difference between Slope Parameters (Index 5) and Arctangent of Paired Category Ratios (Index 6)--are particularly robust and informative, even with low-frequency categories. These indices offer a practical tool for assessing whether and how item categories align with ordinal assumptions, supporting more accurate measurement and model selection. We conclude that treating ordering as a continuum, rather than a binary property, provides deeper insights for psychometric practice and strengthens the connection between empirical response patterns and their theoretical representations. [This paper will be published in "Educational and Psychological Measurement."]
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    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 42
    Subjects:
      – SubjectFull: Item Response Theory
        Type: general
      – SubjectFull: Models
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      – SubjectFull: Computation
        Type: general
      – SubjectFull: Efficiency
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      – SubjectFull: Serial Ordering
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      – SubjectFull: Accuracy
        Type: general
      – SubjectFull: Nonparametric Statistics
        Type: general
    Titles:
      – TitleFull: Signposts on the Path from Nominal to Ordinal Scales: Moving from a Discrete to a Continuous View
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            NameFull: Roza Nalbandyan
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            NameFull: Vithor R. Franco
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            NameFull: Benjamin W. Domingue
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              Type: published
              Y: 2026
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            – TitleFull: Grantee Submission
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