Interaction model significant in multiple linear regression

Question

This question is not about interaction effect, but about interaction model in Hierarchical Linear Regression. I have 1 DV and 5 IVs. I want to see which of the IVs is significant predictor of DV. Although I am not controlling for any moderator variable here, but to do multiple regression I had to use hierarchical style where I put IVs in Block 1, and interaction terms (10 in number) in Block 2 of SPSS. I used non-centered DV but had centered all the IVs before forming their interaction terms.

Now lets say I have IV1, IV2, IV3, IV4, and IV5 as the independent variables. In Model 1, IV1, IV2, IV3 are coming significant and Model 1 is significant too. In Model 2, IV3 and IV4 are coming significant while interaction terms are not significant, and Model itself is again significant.

My question is that what do I have to do now? Which IVs should be considered significant predictors (I think Model 2 predictors)? Why did interaction terms altered the whole picture?

By the way, this is first part of the whole statistical procedure. In second part, I have a moderator variable, M1. And I put it in the Block 1, IVs in Block 2, and interaction terms (this time 15 in number, IVs with M1 too) in Block 3. Here everything is fine. In Model 1, M1 is significant. In Model 2 with IVs and control predictor, only IV2 is significant, and in the Model 3, no interaction term was significant but IV4 was significant, IV2 became insignificant and Model itself was not significant. Therefore, since model is insignificant, so significance of IV4 does not matter.

Similarly, does it mean that in first step of regression, without M1, second model should be accepted as it is significant?

Is it ok if model with interaction terms comes significant but interaction terms are insignificant? From what I have been able to understand so far, interaction terms need to be insignificant but the model in which they are entered can be significant. Am I correct here?

Answer 1

Don't do hierarchical linear regression unless some of your predictors are theoretically grouped. This is a common error. Run a single multiple regression with all predictors included at once.

Include any and all interaction terms that you have theoretical reasons to include. Then look and see which ones are significant. Some people then re-run a different model excluding all the non-significant interaction terms. But this last step is somewhat debated as far as I can tell.

Answer 2

I wonder if SPSS use t test to evaluation the significance of each inputs including your interaction terms, but I guess so. by adding interaction terms, you add a great deal of correlation between inputs, which can trigger unstable estimate of parameters (multicolinearity). Use Anova, you might be able to see significance of each interaction terms, but it depends on the order you enter them in.

The significance of model with interaction tell you that the interactions give you signals, but the more saturated model need to be used more carefully, LASSO can help you reduce the model variance, and LASSO models generally have better performance in prediction.