Hello Sabin,

What is/are your specific research question(s)? That should be the guide as to how to proceed.

If you're happy with individual appraisal of the two possible moderators, then one way to view the problem is simply that of what sample size would be required to investigate whether a full model (say, of IVs 1, 3, and 1*3) predicts scores on 2 significantly better than a partial model (say, of IVs 1 and 3 only). In g*power, that would be: F-tests/Linear multiple regression: Fixed model, R^2 increase, and you'd be adding one variable from the partial model to the full model (the interaction term, such as 1*3). The key is to operationalize the smallest noteworthy effect you'd like your study to be able to detect, should it actually exist (e.g., the effect size).

On the other hand, if you're more interested in a simultaneous test (which likely makes more sense, as one moderator may be somewhat collinear with other variables in the model), then you might consider thinking about a path model framework, and trying some simulations to determine what sort of sample size would permit you to test the full model vs. reduced models (omitting one or both of the interaction terms)...the actual significance test could be the model-data chi-square fit index (if it changes from full to reduced by more than 3.14 times the number of omitted variable paths, then the omitted path/s were "important" to helping the model-data fit).

Have a look at this reference for how to tackle the simulation: Article Power Analysis for Parameter Estimation in Structural Equati...

Good luck with your work.

I think the above suggestions are very clear and comprehensive.

For sample size, to be more simple, you may consider item-sample ratio (at least higher than 1:10, ideally higher than 1:20). For example, if # of variable items are 20 (4 variables, each variable has 5 items), collect the data from more than 200.

For the test, you can test both separate and simultaneous one and provide both results in tables. Of course, your theory should determine.

Hello Sabin,

I would naturally tend to agree with David Morse 's second approach to include both moderators/product terms (although I don't see how a path model would help :) ), there is a problem that using product terms per se induces some sort of colinearity and power loss which makes finding interaction/moderator effects difficult. The reason is that the product term that you create in order to represent the interaction has the original variables "in it" (XZ = X * Z). If you use a second product term, this problem increases. Hence, while adjusting for spurious moderation is a reasonable goal you pay with loss in power.

My personal approach would be to do both:

1) Start with model 1 including XZ1 (the first product)

2) Then do model 2 with XZ2 (the second product)

3) Then include both to see what changes

If #1 or #2 results in one moderator being non-sign. than this won't change in #3 and you have your result. If #1 and #2 results in both moderators being sign. but that changes in #3, you have a tentative result that you can discuss, namely that either colinearity is an issue and destroyed one of the effects OR that correct controlling lead to a correct conclussion. I know that presenting such an result is not what you or readers may want to have but if a study results in stressing uncertainty, than I think this is part of science. Squishing and hacking data to get some sort of spurious certainty has created a lot of damage.

All the best,

Holger