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A Novel Numerical Method for Solving Unknown Statistical Quantities in Multivariate Regression Models

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Title: A Novel Numerical Method for Solving Unknown Statistical Quantities in Multivariate Regression Models
Language: English
Authors: William R. Dardick, Jeffrey R. Harring
Source: Journal of Educational and Behavioral Statistics. 2025 50(1):102-127.
Availability: SAGE Publications. 2455 Teller Road, Thousand Oaks, CA 91320. Tel: 800-818-7243; Tel: 805-499-9774; Fax: 800-583-2665; e-mail: journals@sagepub.com; Web site: https://sagepub.com
Peer Reviewed: Y
Page Count: 26
Publication Date: 2025
Document Type: Journal Articles
Reports - Evaluative
Descriptors: Statistics, Statistics Education, Problem Solving, Multivariate Analysis, Regression (Statistics), Models, Monte Carlo Methods, Algebra, Mathematical Applications, Mathematical Formulas
DOI: 10.3102/10769986241240083
ISSN: 1076-9986
1935-1054
Abstract: Simulation studies are the basic tools of quantitative methodologists used to obtain empirical solutions to statistical problems that may be impossible to derive through direct mathematical computations. The successful execution of many simulation studies relies on the accurate generation of correlated multivariate data that adhere to a particular model with known parameter values. In this article, we use a kernel inspired by path tracing rules to algebraically solve unknown causal effects in the context of a multivariate general linear model. The algebraic solution is the basis of the mathematical extension, which integrates a model solver. Examples are used to illustrate a range of applications, where information regarding parameter values and predictor correlations can be partially specified. Code for examples is provided.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1457148
Database: ERIC
FullText Text:
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  Data: A Novel Numerical Method for Solving Unknown Statistical Quantities in Multivariate Regression Models
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  Data: Simulation studies are the basic tools of quantitative methodologists used to obtain empirical solutions to statistical problems that may be impossible to derive through direct mathematical computations. The successful execution of many simulation studies relies on the accurate generation of correlated multivariate data that adhere to a particular model with known parameter values. In this article, we use a kernel inspired by path tracing rules to algebraically solve unknown causal effects in the context of a multivariate general linear model. The algebraic solution is the basis of the mathematical extension, which integrates a model solver. Examples are used to illustrate a range of applications, where information regarding parameter values and predictor correlations can be partially specified. Code for examples is provided.
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        Value: 10.3102/10769986241240083
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        StartPage: 102
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      – SubjectFull: Statistics Education
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      – SubjectFull: Problem Solving
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      – SubjectFull: Multivariate Analysis
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      – SubjectFull: Regression (Statistics)
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      – SubjectFull: Models
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      – SubjectFull: Monte Carlo Methods
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      – SubjectFull: Algebra
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      – SubjectFull: Mathematical Applications
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      – SubjectFull: Mathematical Formulas
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      – TitleFull: A Novel Numerical Method for Solving Unknown Statistical Quantities in Multivariate Regression Models
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