On the uncanny relationship between nonnormality and moderated multiple regression.

IF 7.8 1区心理学 Q1 PSYCHOLOGY, MULTIDISCIPLINARY

Psychological methods Pub Date : 2025-09-08 DOI:10.1037/met0000797

Oscar L Olvera Astivia,Xijuan Zhang,Edward Kroc,Bruno D Zumbo

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引用次数: 0

Abstract

Moderated multiple regression is one of the most established, popular methods to model nonlinear associations in social sciences. A mostly unacknowledged fact is that a particular type of nonnormality can make the coefficient capturing this association nonzero. To further understand this connection, a theoretical investigation was conducted. A generalization of Isserlis' theorem from multivariate normal densities to all elliptical densities is presented. Through this generalization, it was found that the family of elliptical densities (which includes the multivariate normal) cannot generate a product-interaction term. Moreover, asymmetry in lower and/or higher dimensions can induce a product-interaction term. Special case studies are presented where the variables are unidimensional symmetric, but jointly nonsymmetric, resulting in a moderated multiple regression model. A call is made for researchers to think carefully and decide when they have a true interaction term, theorized a priori, and when nonnormality is mimicking an interaction effect. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

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论异常与适度多元回归之间的神秘关系。

适度多元回归是社会科学中最成熟、最流行的非线性关联建模方法之一。一个大多数未被承认的事实是，一种特殊类型的非正态性可以使捕获这种关联的系数非零。为了进一步了解这种联系，进行了理论研究。将Isserlis定理从多元正态密度推广到所有椭圆密度。通过这种推广，发现椭圆密度族（包括多元正态）不能产生积相互作用项。此外，低维和/或高维的不对称可以诱导产物相互作用项。提出了特殊的案例研究，其中变量是一维对称的，但联合不对称，导致一个有调节的多元回归模型。研究人员需要仔细思考，并决定什么时候他们有一个真正的相互作用条件，理论化的先验，什么时候非正常是模仿相互作用的效果。（PsycInfo Database Record (c) 2025 APA，版权所有）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Psychological methods PSYCHOLOGY, MULTIDISCIPLINARY-

CiteScore

13.10

自引率

7.10%

发文量

159

期刊介绍： Psychological Methods is devoted to the development and dissemination of methods for collecting, analyzing, understanding, and interpreting psychological data. Its purpose is the dissemination of innovations in research design, measurement, methodology, and quantitative and qualitative analysis to the psychological community; its further purpose is to promote effective communication about related substantive and methodological issues. The audience is expected to be diverse and to include those who develop new procedures, those who are responsible for undergraduate and graduate training in design, measurement, and statistics, as well as those who employ those procedures in research.