Sample Size Calculation and Optimal Design for Multivariate Regression-Based Norming.
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| Title: | Sample Size Calculation and Optimal Design for Multivariate Regression-Based Norming. |
|---|---|
| Authors: | Innocenti, Francesco1 (AUTHOR) francesco.innocenti@maastrichtuniversity.nl, Candel, Math J. J. M.1 (AUTHOR), Tan, Frans E. S.1 (AUTHOR), van Breukelen, Gerard J. P.1 (AUTHOR) |
| Source: | Journal of Educational & Behavioral Statistics. Oct2024, Vol. 49 Issue 5, p817-847. 31p. |
| Subject Terms: | Regression analysis, False positive error, Statistical hypothesis testing, Reference values, Hypothesis |
| Abstract: | Normative studies are needed to obtain norms for comparing individuals with the reference population on relevant clinical or educational measures. Norms can be obtained in an efficient way by regressing the test score on relevant predictors, such as age and sex. When several measures are normed with the same sample, a multivariate regression-based approach must be adopted for at least two reasons: (1) to take into account the correlations between the measures of the same subject, in order to test certain scientific hypotheses and to reduce misclassification of subjects in clinical practice, and (2) to reduce the number of significance tests involved in selecting predictors for the purpose of norming, thus preventing the inflation of the type I error rate. A new multivariate regression-based approach is proposed that combines all measures for an individual through the Mahalanobis distance, thus providing an indicator of the individual's overall performance. Furthermore, optimal designs for the normative study are derived under five multivariate polynomial regression models, assuming multivariate normality and homoscedasticity of the residuals, and efficient robust designs are presented in case of uncertainty about the correct model for the analysis of the normative sample. Sample size calculation formulas are provided for the new Mahalanobis distance-based approach. The results are illustrated with data from the Maastricht Aging Study (MAAS). [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Educational & Behavioral Statistics is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Education Research Complete |
| FullText | Text: Availability: 0 |
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| Header | DbId: ehh DbLabel: Education Research Complete An: 180041366 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Sample Size Calculation and Optimal Design for Multivariate Regression-Based Norming. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Innocenti%2C+Francesco%22">Innocenti, Francesco</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> francesco.innocenti@maastrichtuniversity.nl</i><br /><searchLink fieldCode="AR" term="%22Candel%2C+Math+J%2E+J%2E+M%2E%22">Candel, Math J. J. M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Tan%2C+Frans+E%2E+S%2E%22">Tan, Frans E. S.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22van+Breukelen%2C+Gerard+J%2E+P%2E%22">van Breukelen, Gerard J. P.</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Educational+%26+Behavioral+Statistics%22">Journal of Educational & Behavioral Statistics</searchLink>. Oct2024, Vol. 49 Issue 5, p817-847. 31p. – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Regression+analysis%22">Regression analysis</searchLink><br /><searchLink fieldCode="DE" term="%22False+positive+error%22">False positive error</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+hypothesis+testing%22">Statistical hypothesis testing</searchLink><br /><searchLink fieldCode="DE" term="%22Reference+values%22">Reference values</searchLink><br /><searchLink fieldCode="DE" term="%22Hypothesis%22">Hypothesis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Normative studies are needed to obtain norms for comparing individuals with the reference population on relevant clinical or educational measures. Norms can be obtained in an efficient way by regressing the test score on relevant predictors, such as age and sex. When several measures are normed with the same sample, a multivariate regression-based approach must be adopted for at least two reasons: (1) to take into account the correlations between the measures of the same subject, in order to test certain scientific hypotheses and to reduce misclassification of subjects in clinical practice, and (2) to reduce the number of significance tests involved in selecting predictors for the purpose of norming, thus preventing the inflation of the type I error rate. A new multivariate regression-based approach is proposed that combines all measures for an individual through the Mahalanobis distance, thus providing an indicator of the individual's overall performance. Furthermore, optimal designs for the normative study are derived under five multivariate polynomial regression models, assuming multivariate normality and homoscedasticity of the residuals, and efficient robust designs are presented in case of uncertainty about the correct model for the analysis of the normative sample. Sample size calculation formulas are provided for the new Mahalanobis distance-based approach. The results are illustrated with data from the Maastricht Aging Study (MAAS). [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Educational & Behavioral Statistics is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.3102/10769986231210807 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 31 StartPage: 817 Subjects: – SubjectFull: Regression analysis Type: general – SubjectFull: False positive error Type: general – SubjectFull: Statistical hypothesis testing Type: general – SubjectFull: Reference values Type: general – SubjectFull: Hypothesis Type: general Titles: – TitleFull: Sample Size Calculation and Optimal Design for Multivariate Regression-Based Norming. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Innocenti, Francesco – PersonEntity: Name: NameFull: Candel, Math J. J. M. – PersonEntity: Name: NameFull: Tan, Frans E. S. – PersonEntity: Name: NameFull: van Breukelen, Gerard J. P. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 10769986 Numbering: – Type: volume Value: 49 – Type: issue Value: 5 Titles: – TitleFull: Journal of Educational & Behavioral Statistics Type: main |
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