Power analysis for moderator effect in regression with two continuous predictors Related to an earlier question on power analysis for multiple regression, a social science researcher asked me about power analysis for moderator regression (i.e., an interaction effect).
The researcher asked me:

I seem to recall that power of tests
  for moderation with two continuous
  predictor variables is low - do you know the
  minimum sample size requirement in
  this context?

From the context, it can  further be assumed that this is an observational study (not an experimental study) and that the dependent variable is continuous.
Question


*

*What advice would you give regarding calculating the minimum sample size required?

*Are there any caveats that you would present?

 A: If I had to do this, I would use a simulation approach. This would involve making assumptions about the regression coefficients, predictor distributions, correlation between predictors, and error variance (with help from the researcher), generating data sets using the assumed model, and seeing what proportion of these give a significant p-value for the interaction. Then use trial and error to find the minimum sample size giving the required power.
A: Assuming that the IV (X) and the Moderator (M) are continuous variables, and your research question is: Is the relationship between X and Y moderated by M?
Your regression model would have 3 predictors X, M, and their (centered) interaction (X*M).
If you run the analysis using GPower (http://gpower.hhu.de/) you would set it up using the following parameters.
F tests - Linear multiple regression: Fixed model, R² deviation from zero
Analysis:   A priori: Compute required sample size 
Input:  Effect size f²  =   0.15
    α err prob  =   0.05
    Power (1-β err prob)    =   0.80
    Number of predictors    =   3
Output: Noncentrality parameter λ   =   11.5500000
    Critical F  =   2.7300187
    Numerator df    =   3
    Denominator df  =   73
    Total sample size   =   77
    Actual power    =   0.8017655
You could vary the effect size, f2 to small .02, medium .15, or large .35.
In my above example f2 was set to .15.
Alpha should be set to .05, and power (1-B err prob) should be set to .80
