A recentering approach for interpreting interaction effects from logit, probit, and other nonlinear models

• Date: 01 November 2020
• Published date: 01 November 2020
• Author: Jordan I. Siegel,Whitney K. Newey,Sophie Yu‐Pu Chen,Yujin Jeong
• DOI: http://doi.org/10.1002/smj.3202

RESEARCH ARTICLE

A recentering approach for interpreting

interaction effects from logit, probit, and other

nonlinear models

Yujin Jeong

1

| Jordan I. Siegel

2

| Sophie Yu-Pu Chen

3

|

Whitney K. Newey

4

1

Department of Management, American

University, Washington, District of

Columbia

2

Strategy Area, University of Michigan,

Ann Arbor, Michigan

3

Department of Biostatistics, University

of Michigan, Ann Arbor, Michigan

4

Department of Economics,

Massachusetts Institute of Technology,

Cambridge, Massachusetts

Correspondence

Yujin Jeong, Kogod School of Business,

American University, 4400 Massachusetts

Avenue, NW, Washington, DC 20016.

Email: yjeong@american.edu

Abstract

Research Summary: Strategic management has seen

numerous studies analyzing interaction terms in

nonlinear models since Hoetker's (StratMgmtJ., 2007,

28(4), 331–343) best-practice recommendations and

Zelner's (StratMgmtJ.,2009, 30 (12), 1335–1348)

simulation-based approach. We suggest an alternative

recentering approach to assess the statistical and eco-

nomic importance of interaction terms in nonlinear

models. Our approach does not rely on making assump-

tions about the values of the control variables; it takes the

existing model and data as is and requires fewer compu-

tational steps. The recentering approach not only provides

a consistent answer about statistical meaningfulness of

the interaction term at a given point of interest, but also

helps to assess the effect size using the template that we

offer in this study. We demonstrate how to implement

our approach and discuss the implications for strategy

researchers.

Managerial Summary: In industry settings, the rela-

tionship between multiple corporate strategy-related

inputs and corporate performance is often nonlinear in

nature. Furthermore, such relationships tend to vary for

different types of firms represented within the broader

population of firms in a given industry. It is thus impera-

tive for managers to know how to take nonlinear rela-

tionships between related business factors into account

Received: 4 December 2018 Revised: 31 January 2020 Accepted: 7 February 2020 Published on: 16 July 2020

DOI: 10.1002/smj.3202

2072 © 2020 John Wiley & Sons, Ltd. Strat Mgmt J. 2020;41:2072–2091.wileyonlinelibrary.com/journal/smj

when they make strategic decisions. We suggest a simple

and easily implementable way of assessing and inter-

preting interactions in a nonlinear setting, which we term

a recentering approach. We demonstrate how to apply

our approach to a strategic management setting.

KEYWORDS

effect size, interaction effects, nonlinear models, odds ratio,

recentering

1|INTRODUCTION

Interaction terms are frequently modeled in strategic management research in order to evaluate

the effect of one explanatory variable on the response variable given the magnitude of another

explanatory variable (e.g., the relationship between corporate strategy-related inputs and man-

agement performance outcomes varies depending on the internal and external business envi-

ronments). Assessing and interpreting interaction terms becomes more complicated when

models are nonlinear. Unlike linear models where the effect of a one-unit change in a covariate

on the outcome variable (i.e., marginal or partial effect) is constant over the whole range of the

covariate given the level of the other covariates in the model, the same effect in nonlinear

models relies on the values of all other covariates in the model (Ai & Norton, 2003; Norton,

Wang, & Ai, 2004). Given the frequency with which strategic management researchers have

encountered interaction terms in nonlinear models (see, e.g., Hoetker, 2007; Shook, Ketchen,

Cycyota, & Crockett, 2003), we will argue and show by way of mathematical proof and empiri-

cal analysis that there is room for another methodological option for achieving simplicity and

consistency of interpretation of those interaction terms.

In strategic management research, Hoetker (2007) recommended a set of best practices for

the use of logit and probit models, including interpreting interaction terms. To further improve

the assessment of statistical meaningfulness and interpretation of logit and probit results,

Zelner (2009, p. 1336) suggested “a simulation-based technique developed by King, Tomz, and

Wittenberg (2000)”

1

and argued for the benefits of this technique over the conventional

calculus-based method known as the delta method (Zelner, 2009, pp. 1341–1,342)

2

proposed by

Dorfman (1938). In particular, Zelner proposed (a) calculating and interpreting a difference in

predicted probabilities associated with discrete changes in key predictor values (known as the

cross-partial derivative or cross-difference, which measures how the marginal effect of one

variable changes when the other variable in the interaction term changes) and (b) testing

whether the difference in predicted probabilities is different from zero by constructing a

confidence interval (CI) around the estimated quantity and finding out if the interval

1

For an introduction to the simulation method, see Krinsky and Robb (1986, 1990, 1991). See Greene (2018,

pp. 647–648, 752) for an instructive discussion on the simulation-based method and the specific method of Krinsky

and Robb.

2

For an analysis comparing the delta method and the simulation method, see Krinsky and Robb (1990). For an

additional description of the delta method, see Rothenberg (1984) and Horowitz (2001). For a separate way to

implement the simulation method, see the NLOGIT software package and its WALD command.

JEONG ET AL.2073