I am very curious about the results. can you send me the data file by an email at [email protected]? I will check the results.

You should also look for changes in the magnitude of the other independent variables, since those can change when you enter the interaction effects. This can be particularly problematic when the two variables in your interaction effects are both linear (rather than categorical).

IF you start adding multiple interaction terms, without rescaling the original variables, you will run into an issue with colinearity. The colinearity will manifest itself as an increased Std Err for a term. From your description, this is most likely what is happening. 

To rescale your data, I would subtract the mean/median of each variable. For instance, if you have "age" as a variable, and it has a range of 30yrs to 70yrs, subtract 50 from all the values. The range of these new variables will still be 40. But, the range will be -20 to 20. If you have dichotomous variable, say male and female, instead of using 0 and 1, use -1 and 1.

The new coding scheme will eliminate most of the colinearity within your interaction terms.  

I know that this sounds like a weird thing to do. When I use "Design of Experiment" software to analyze a data set, it scales everything to be within the range of -1 to 1.

Dear Aryeh,

As Andrew writes: centering is neccesary when you add interaction terms. I would even advice to standardize all the interval scale variables (dependent variable included).

After standardizing you calculate the interaction terms. Mind: the regresssion coeficients will not be standardized regression coefficients (often called betas) because the interaction terms are not standardized.

And then: it seems that your rule is: an effect is present when it is significant.

Well, eh, significance does not mean 'presence'. It just is significant.

And when it is not significant that does does not mean that it is absent...

go well!

Pierre

I am much more inclined to center the variables (subtract the mean or median from each continuous variable), as per the response by Andrew Ekstrom, and  maintain those variables in their original units. I would not standardize (convert variables into z-scores) as per Pierre Souren although I understand his motivation for wanting to do that. The b-weights for the independent variables in their original metrics are more stable than the betas. 

I also think that Aryeh should cautiously test one two-way interaction at a time.

I don't know how many three-way interactions were entered at the same time but if more than one were entered, the prediction equation will be long because the equation would have to contain every two-way interaction and all the marginal effects. With all the effects being tested, one or two Type I errors may occur.

It is a myth that one must center the variables when including product terms in a regression model.  See point number 2 in Paul Allison's note linked below.  In addition to what he says there, you could try estimating such a model with and without centering the variables, and save the fitted values both times.  They will be identical to each other.  And as Allison notes, so will the model R2 values.

@Aryeh:  The first problem you describe (at Step 2) is not really a problem, as the F-test on the change in R2 is an omnibus test for all three two-way interactions (vs a model with first order effects only), whereas the other tests examine each one separately, and they test vs models that include first order effects and the other two-way interactions.  So you're really looking at apples and oranges there, and there is no reason to expect the same results for all tests.

The second problem is more puzzling.  As someone else noted, it would be helpful if you could post the output.

http://statisticalhorizons.com/multicollinearity

I agree with Bruce Weaver -- centering the variables will not affect colinearity because adding or subtract a constant makes no difference in regressions -- although centering may make those effects easier to interpret.

Have you tested the three interaction effects one-at-a-time yet?

I recommend centering unless a variable has a meaningful zero point, although that is not often the case with variables in social science research. Centering continuously measured predictors (and using as a reference category for dichotomous variables the category with the most individuals) does two things. First, centering reduces collinearity between an interaction term and the marginal terms. In Paul Allison's response to writer Dennis (March 6, 2013), who wrote about a serious problem with an interaction term, Paul recommended using centering as a solution. Second, centering makes the equation meaningful for estimating Y in the average individual, i.e., the individual who is at the mean (or median or mode--for dichotomous variables), for all predictors. It is, however, not necessary to center Y. Cohen, Cohen, West, & Aiken (2003) recommended centering all predictors that will be used to study higher order interactions.