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

Author

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  • William R. Dardick

    (The George Washington University)

  • Jeffrey R. Harring

    (University of Maryland)

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.

Suggested Citation

  • William R. Dardick & Jeffrey R. Harring, 2025. "A Novel Numerical Method for Solving Unknown Statistical Quantities in Multivariate Regression Models," Journal of Educational and Behavioral Statistics, , vol. 50(1), pages 102-127, February.
    • Handle: RePEc:sae:jedbes:v:50:y:2025:i:1:p:102-127
    DOI: 10.3102/10769986241240083
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