How do I test for an interaction involving a continuous variable (moderation analysis)?

Occasionally you might want to test an interaction involving at least one continuous variable in a regression e.g. for looking at moderation effects. This involves obtaining the product of the continuous variable with any other terms in the interaction. This term may then be fitted in a regression also including lower order combinations of the variables involved in the interactions.

It is suggested (Aiken and West, 1991) that any continuous variables involved in an interaction are centred. This is done by subtracting the variable's sample mean. This ensures that the value 'zero' is meaningful for the covariate. When the covariate is zero the response is simply the covariate adjusted difference between the groups so a zero value of the covariate has special importance in ANCOVA.

Perhaps, the easiest way to do this in SPSS is to use the anova procedures available using the menu procedures under analyze>general linear model.

Although interactions involving continuous variables (called covariates in SPSS) are not fitted by default in SPSS, you can create these product terms by clicking on the model button in the GLM univariate or repeated measures options.

Examples involving continuous variable interactions are available:

• [attachment:int.pdf Two way interaction between one categorical and one continuous variable (any number of categories).]
• [:FAQ/intslopes:Two way interaction between one categorical and one continuous variable (2 categories)]

• [http://www.psychwiki.com/wiki/Interaction_between_two_continuous_variables Interaction between two continuous variables.] The Aiken and West (1991) reference in this wikipedia article is available from the CBSU library. They suggest following Cohen and Cohen (1983, p.323) centering the moderator variable (Z) and comparing three regression lines of X on Y at Z values equal to -1, 0 and +1 which correspond to one sd below (the moderator variable) mean, the mean and one sd above the mean. This approach is also illustrated by O'Connor (1998).

There is also an on-line calculator which uses the method "Simple Intercepts, Simple Slopes, and Regions of Significance in MLR 2-Way Interactions" suggested by Aiken and West (1991) are described in pdf format [attachment:modregion.pdf here] and work by Preacher, Curran and Bauer (2006) [http://www.people.ku.edu/~preacher/interact/index.html here.] A copy of their paper is also [attachment:modelration.pdf here]. This latter website utilises R code via a web interface to produce results using the regression estimates, their variances and covariances which may be obtained from any standard linear regression output e.g. in SPSS. A region of significance looks at how the group difference varies with values of the covariate. Alternatively SPSS (and SAS) macros to compute regions of significance are given by Hayes and Matthes (2009).

The covariance involving intercepts, however, is not outputted directly in SPSS (see [:FAQ/constregSPSS: here]).

References

Hayes, A. and Matthews, J. (2009). Computational procedures for probing interactions in OLS and logistic regression: SPSS and SAS implementations. Behavior Research Methods 41 924-936.

O'Connor, B. P. (1998). All-in-one programs for exploring interactions in moderated multiple regression. Educational and Psychological Measurement 58 833-837.

Preacher, K. J., Curran, P. J., & Bauer, D. J. (2006). Computational tools for probing interaction effects in multiple linear regression, multilevel modeling, and latent curve analysis. Journal of Educational and Behavioral Statistics, 31, 437-448.