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Moderation in Management Research: What, Why, When, and How

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Abstract

Many theories in management, psychology, and other disciplines rely on moderating variables: those which affect the strength or nature of the relationship between two other variables. Despite the near-ubiquitous nature of such effects, the methods for testing and interpreting them are not always well understood. This article introduces the concept of moderation and describes how moderator effects are tested and interpreted for a series of model types, beginning with straightforward two-way interactions with Normal outcomes, moving to three-way and curvilinear interactions, and then to models with non-Normal outcomes including binary logistic regression and Poisson regression. In particular, methods of interpreting and probing these latter model types, such as simple slope analysis and slope difference tests, are described. It then gives answers to twelve frequently asked questions about testing and interpreting moderator effects.

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Notes

  1. This test of moderation involves the same assumptions as does any “ordinary least squares” (OLS) regression analysis—i.e., residuals are independent and Normally distributed, and their variance is not related to predictors—and for most of this article I will assume this to be the case without further comment; I will deal separately with non-Normal outcomes later.

  2. Technically, the test is to compare the ratio of the coefficient to its standard error with a t-distribution with 196 degrees of freedom: 196 because it is 200 (the sample size) minus the number of parameters being estimated (four: three coefficients for three independent variables, and one intercept).

  3. Note that the variance of a coefficient can be taken from the diagonal of the coefficient covariance matrix, i.e., the variance of a coefficient with itself; alternatively, it can be calculated by squaring the standard error of that coefficient.

  4. Template for plotting such effects, along with the simple slope and slope difference tests described later are available at www.jeremydawson.com/slopes.htm.

  5. This is the method used by the relevant template at www.jeremydawson.com/slopes.htm, where there are also appropriate templates for three-way interactions, and two- and three-way interactions with Poisson regression.

  6. There is a specific template for binary moderators at www.jeremydawson.com/slopes.htm, as well as a generic template which allows any combination of binary and continuous independent and moderating variables.

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Acknowledgments

I am grateful to Ron Landis, Scott Tonidandel, and Steven Rogelberg for their comments on earlier drafts of this article.

Author information

Authors and Affiliations

  1. Institute of Work Psychology, Management School, University of Sheffield, Sheffield, S10 1FL, UK

    Jeremy F. Dawson

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  1. Jeremy F. Dawson
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Correspondence to Jeremy F. Dawson.

Appendix: SPSS Syntax for the Models Described in the Article

Appendix: SPSS Syntax for the Models Described in the Article

In this Appendix, variable names are shown in upper case (capitals) and SPSS commands in lower case. In reality the case does not matter for either.

Variable names:

  • Dependent variable (DV) 1—PERFORM (Job performance—continuous)

  • Dependent variable (DV) 2—ABSENCE (Absenteeism—binary)

  • Dependent variable (DV) 3—TIMESABS (Number of occasions absent—discrete)

  • Independent variable (IV) 1—TRAIN (Training provision—continuous; mean 3.42)

  • Independent variable (IV) 2—WKPRES (Work pressure—continuous; mean 2.95)

  • Moderator 1—AUTON (Autonomy—continuous; mean 3.20)

  • Moderator 2—EXPER (Experience—continuous; mean 6.5)

  • Moderator 3—AGE (Age—continuous; mean 43.7)

  • Moderator 4—ROLE (Job role—three levels, scored 1, 2, 3)

*Descriptions of what the commands are doing are shown with asterisks in front of them. SPSS will ignore any commands that begin with an asterisk. Note that the execute commands are not necessary to run any analysis, but commands that do not produce output will not be performed until either a command that does produce output, or an execute command, is run afterwards.

*(1) Syntax to create centered versions of continuous IVs and moderators:

  • compute TRAINC = TRAIN − 3.42.

  • compute WKPRESC = WKPRES − 2.95.

  • compute AUTONC = AUTON − 3.20.

  • compute EXPERC = EXPER − 6.5.

  • compute AGEC = AGE − 43.7.

  • execute.

*(2) Syntax to created standardized versions of continuous IVs and moderators. N.B. the variables created will have the same names as the originals but preceded by a Z.

descriptives TRAIN WKPRES AUTON EXPER AGE /save.

*(3) Syntax to create and test 2-way interaction with continuous moderator. Note that the inclusion of “bcov” ensures that coefficient variances and covariances are included in the output—helpful for testing of simple slopes.

  • compute TRAXAUT = TRAINC*AUTONC.

  • regression /statistics = r coeff cha anova bcov

  •  /dependent = PERFORM

  •  /method = enter TRAINC AUTONC

  •  /method = enter TRAXAUT.

*(4) Syntax for alternative method of testing simple slope: for value of AUTON = 4.10. Test of simple slope is given by significance of TRAINC term in final model.

  • compute AUTONT = AUTON − 4.10.

  • compute TRAXAUTT = TRAINC*AUTONT.

  • regression /statistics = r coeff cha anova bcov

  •  /dependent = PERFORM

  •  /method = enter TRAINC AUTONT

  •  /method = enter TRAXAUTT.

*(5) Syntax for ANCOVA version of 2-way interaction with categorical moderator (NB can involve any combination of continuous and categorical IVs/moderators; categorical variables follow “by” command and continuous variables follow “with” command.

  • glm PERFORM by ROLE with TRAINC

  •  /print = parameter

  •  /design = TRAINC ROLE TRAINC*ROLE.

*(6) Syntax to create and test 3-way interaction with continuous moderators.

  • compute TRAXAUT = TRAINC*AUTONC.

  • compute TRAXEXP = TRAINC*EXPERC.

  • compute AUTXEXP = AUTONC*EXPERC.

  • compute TRXAUXEX = TRAINC*AUTONC*EXPERC.

  • regression /statistics = r coeff cha anova bcov

  •  /dependent = PERFORM

  •  /method = enter TRAINC AUTONC EXPERC TRAXAUT TRAXEXP AUTXEXP

  •  /method = enter TRXAUXEX.

*(7) Syntax to test curvilinear interaction.

  • compute TRAINSQ = TRAINC*TRAINC.

  • compute TRASXAUT = TRAINSQ*AUTONC.

  • regression /statistics = r coeff cha anova bcov

  •  /dependent = PERFORM

  •  /method = enter TRAINC TRAINSQ AUTONC

  •  /method = enter TRAXAUT TRASXAUT.

*(8) Syntax to test for (linear or curvilinear) relationship between IV and DV at particular value of moderator (“simple curve”) at AUTON = 4.10. The simple curve or slope is significant if the second step adds significant variance to the model.

  • compute TRAINSQ = TRAINC*TRAINC.

  • compute AUTONT = AUTON − 4.10.

  • compute TRAXAUTT = TRAINC*AUTONT.

  • compute TRASXAUTT = TRAINSQ*AUTONT.

  • regression /statistics = r coeff cha anova bcov

  •  /dependent = PERFORM

  •  /method = enter AUTONT TRAXAUTT TRASXAUTT

  •  /method = enter TRAINC TRAINSQ.

*(9) Syntax to test for difference between simple curves in a curvilinear three-way interaction. In this example the test is for difference between the curvilinear effect of training provision on job performance at high autonomy/high experience and high autonomy/low experience. High autonomy is defined by AUTON = 4.10. The simple curves are significantly different if the second step adds significant variance to the model.

  • compute TRAINSQ = TRAINC*TRAINC.

  • compute AUTONT = AUTON − 4.10.

  • compute TRAXAUTT = TRAINC*AUTONT.

  • compute TRASXAUTT = TRAINSQ*AUTONT.

  • compute TRAXEXP = TRAINC*EXPERC.

  • compute AUTTXEXP = AUTONT*EXPERC.

  • compute TRXAUTXEX = TRAINC*AUTONT*EXPERC.

  • compute TRSQXAUTXEX = TRAINSQ*AUTONT*EXPERC.

  • regression /statistics = r coeff cha anova bcov

  •  /dependent = PERFORM

  •  /method = enter TRAINC TRAINSQ AUTONT EXPERC TRAXEXP AUTTXEXP TRXAUTXEX TRSQXAUTXEX

  •  /method = enter TRAXAUTT TRASXAUTT.

*(10) Syntax to test 2-way interaction with continuous moderator and binary dependent variable. Note that it is not necessary to create the interaction term separately, but it is still advisable to use centered versions of the IV and moderator.

  • logistic regression variables ABSENCE

  •  /method = enter WKPRESC AGEC WKPRESC*AGEC.

*(11) Syntax to test simple slope of an independent variable (WKPRESC) on binary dependent value (ABSENCE) when the moderator, AGE, is equal to 30. Test of simple slope is given by significance of WKPRESC term.

  • compute AGET = AGE − 30.

  • logistic regression variables ABSENCE

  •  /method = enter WKPRESC AGET WKPRESC*AGET.

*(12) Syntax to test 2-way interaction with continuous moderator and count dependent variable using Poisson regression. For negative binomial alternative use “distribution = negbin” instead.

  • genlin TIMESABS with WKPRESC AGEC WKPRESC*AGEC

  •  /model WKPRESC AGEC WKPRESC*AGEC

  •  distribution = poisson link = log.

*(13) Syntax to create dummy variables for a categorical moderator ROLE.

  • recode ROLE (1 = 1)(2 3 = 0) into ROLE1.

  • recode ROLE (2 = 1)(1 3 = 0) into ROLE2.

  • recode ROLE (3 = 1)(1 2 = 0) into ROLE3.

  • execute.

*(14) Syntax to create and test 2-way interaction with categorical moderator (with three levels: for more levels, add in dummy variables and interaction terms accordingly).

  • compute TRAXRO1 = TRAINC*ROLE1.

  • compute TRAXRO2 = TRAINC*ROLE2.

  • regression /statistics = r coeff cha anova bcov

  •  /dependent = PERFORM

  •  /method = enter TRAINC ROLE1 ROLE2

  •  /method = enter TRAXRO1 TRAXRO2.

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Dawson, J.F. Moderation in Management Research: What, Why, When, and How. J Bus Psychol 29, 1–19 (2014). https://doi.org/10.1007/s10869-013-9308-7

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