Abstract:
Approximately one-third of international business (IB) articles include conditional hypotheses, yet the vast majority risk errors in testing or interpreting the results. Scholars typically restrict their empirical analysis to the coefficient of the interaction term in the regression, exposing themselves to the hazard of overstating or understating results. To mitigate the risk of misstating, we advocate that IB scholars also evaluate the statistical significance of the marginal effect of the primary independent variable over the range of values of the moderating variable. We demonstrate that overstating results can occur when the interaction term coefficient is statistically significant but the marginal effect is not significantly different from zero for some value(s) of the moderating variable. Understating can occur when the interaction term coefficient is not statistically significant, but the marginal effect is statistically different from zero for some value(s) of the moderating variable. In this article, we describe, using simulated data, these two possibilities associated with testing conditional hypotheses, and offer practical guidance for IB scholars.
Summary:
In “Understating and Overstating Interaction Results in International Business Research,” we identify two important questions for scholars with conditional hypotheses. Question 1 asks whether there is a statistically discernible difference between the marginal effect of a primary explanatory variable across different values of the moderating variable. Question 2 asks if the marginal effects of the primary explanatory variable statistically different from zero, for one, both, or neither level of the moderating variable. We advocate that scholars assess both questions. (Rarely, there may be theoretical reason to only answer Question 1 or Question 2.)
Understating may occur if researchers discard a conditional hypothesis based on obtaining a non-significant coefficient on the interaction term (Question 1), because they may miss seeing a statistically significant non-zero marginal effect of the primary explanatory variable for some value(s) of the moderating variable (Question 2). Overstating may occur if researchers go no further than to report a statistically significant interaction coefficient when, simultaneously, the marginal effect of the primary explanatory variable for one or more values of the moderating variable is not different from zero.
Recommendations:
In the JWB article, we propose the following recommendations for scholars.
1. State the conditional hypothesis so as to clearly articulate whether marginal effects (i.e., relationships between the primary explanatory variable and the dependent variable) differ from one another for any two values of the moderating variable (Question 1) and/or whether a marginal effect differs from zero for any specific value of the moderating variable (Question 2).
2. Properly specify the regression model by including the primary explanatory variable X and moderating variable Z, the interaction term XZ, and all relevant control variables (e.g., Equation 1).
Y = β0 + β1X + β2Z + β3XZ + controls
3. Answer Question 1 by evaluating the statistical significance of 
to ascertain whether the marginal effects are different from each other.
a. Recognize that a statistically significant provides evidence that marginal effects are discernibly different from one another.
b. Recognize that a statistically non-significant provides evidence that marginal effects are not discernibly different from one another.
4. Answer Question 2 by evaluating whether the marginal effects ( 
= β1 + β3Z ) are statistically different from zero.
a. For a dichotomous moderating variable Z, create a table of marginal effects similar to Table 3. See Files 1 and 2 below.
b. For a continuous moderating variable Z, create a figure similar to Figure 1 or 2, in which a confidence interval is constructed around the marginal effect line over the entire range of the moderating variable. See Files 1 and 3 below.
5. Report both the statistical significance of the coefficient estimate for (Question 1) and the range of values of the moderating variable Z and percentage of observations for which marginal effects attain statistical significance (Question 2).
6. Discuss the level of support (e.g. full, partial, none) for the conditional hypothesis given the statistical results of both questions.
Code:
All Stata code to replicate the data, tables, and graphs presented in this paper is available here.
File 1: .do file to replicate the independent variables generated for the simulation analysis.
File 2: .do file to replicate data generating process for dependent variables in the simulation analysis, and results from regressions and marginal effects.
File 3: .do file to replicate figures with embedded histograms for exploring marginal effects over range of values of Innovation. ** These commands are extensions of earlier code made available by Matt Golder.
Interaction Articles Cited in Article:
Aguinis, H., Edwards, J., & Bradley, K. (2016). Improving our understanding of moderation and mediation in strategic management research. Organizational Research Methods, doi:10.1177/1094428115627498. http://journals.sagepub.com/doi/abs/10.1177/1094428115627498
Ai, E. & Norton, E. (2003). Interaction terms in logit and probit models. Economics Letters, 80: 123-129. http://www.sciencedirect.com/science/article/pii/S0165176503000326
Aiken, L. & West, S. (1991). Multiple R\regression: Testing and interpreting interactions. London: Sage Publishing.
Allison, P. (1977). Testing for interaction in multiple regression. American Journal of Sociology, 83(1): 144-153. https://www.jstor.org/stable/2777767?seq=1#page_scan_tab_contents
Andersson, U., Cuervo-Zazurra, A., & Nielson, B. (2014). Explaining interaction effects within and across levels of analysis. Journal of International Business, 45: 1063-1071. http://link.springer.com/article/10.1057/jibs.2014.50
Berry, W., Golder, M., & Milton, D. (2012). Improving tests of theories positing interaction. The Journal of Politics, 0: 1-19. http://mattgolder.com/files/research/jop2.pdf
Blalock, H.M. (1965). Theory building and the statistical concept of interaction. American Sociological Review, 30 (June): 374-80.
Brambor, T., Clark, W.R., & Golder, M. (2006). Understanding interaction models: Improving empirical analyses. Political Analysis, 14: 63-82. http://mattgolder.com/files/research/pa_final.pdf
Dawson, J. (2014). Moderation in management research: What, why, when, and how. Journal of Business and Psychology, 29: 1-19. http://link.springer.com/article/10.1007/s10869-013-9308-7
Esarey, J. & Sumner, J. (2016). Marginal effects in interaction models: Determining and controlling the false positive rate. Manuscript. http://jee3.web.rice.edu/interaction-overconfidence.pdf
Hainmueller, J., Mummolo, J. & Xu, Y. (2016). How much should we trust estimates from multiplicative interaction models? Simple Tools to Improve Empirical Practice. Manuscript. http://q-aps.princeton.edu/sites/default/files/q-aps/files/interaction_to_share.pdf
Schoonhoven, C.B. (1981). Problems with contingency theory: Testing assumptions hidden within the language of contingency “theory”. Administrative Science Quarterly, 26(3): 349-377. https://www.ncbi.nlm.nih.gov/pubmed/10252610
Spiller, S., Fitzsimons, G., Lynch JR., J. & McClelland, G. (2013). Spotlights, floodlights, and the magic number zero: Simple effects tests in moderated regression. Journal of Marketing Research, L (April): 277-288. http://journals.ama.org/doi/abs/10.1509/jmr.12.0420
Zelner, B. (2009). Using simulation to interpret results from logit, probit, and other nonlinear models. Strategic Management Journal, 30: 1335-1348. http://onlinelibrary.wiley.com/doi/10.1002/smj.783/abstract