Arguments/Advantages of Additive Model Construction Analysis in an Experimental Design Assume I perform a psychological experiment with a number of manipulations, each hypothesized to influence the dependent variable. For instance, we perform a mixed-design short-term memory experiment where:


*

*DV = Number of letters recalled

*IV1 = Number of letters

*IV2 = Number of distractions

*IV3 = Delay time between presentation of stimuli and recall

*IV4 = Whether memory is being stored internally (biologically) or externally (i.e., pen and paper)


Assuming the presence of interactions between terms, is there any argument for constructing a number of analytical model (e.x., ~IV1*IV2, ~IV1*IV2*IV4, ~IV1*IV2*IV3*IV4) in order to best understand the phenomena? This is in the context of performing successive mixed-design ANOVA's to come to some multiple conclusions regarding the experiment. I have a basic understanding of regression/multivariate regression and recognize the folly of including unnecessary variables - but if they're all hypothesized to exert some effect, isn't the final model the most sound?
 A: Yes there are several advantages to sequential model building above and beyond obtaining a better understanding of the phenomena under investigation.
First, you can obtain model diagnostics at each step of your model building process as you move from the least complex main effects model to the most complex 4-way interaction model. This may allow you to better detect issues as they arise rather than attempting to target a problem in what will be a very complex final model. 
Second, you can determine whether adding a higher order interaction term significantly improves your model. Additionally, you can easily determine the amount of variance accounted for by adding a higher order interaction term, if you build and test models sequentially.
Third, as you move through your model building, when you detect significant interactions you can probe those interactions more easily right then and there so to speak. Now, there may still be higher order interaction effects that need to be considered, but having an understanding of how less complex interaction effects are operating will help you tell the story of your data. 
Finally, I want to echo the comment above that high dimensional interactions are generally VERY under-powered in practice as they require large samples. Additionally, it can be difficult to offer clear interpretations of the simple effects contained within a 4-way interaction. I would just be certain that your research question/hypothesis truly requires such a complex model (for instance, would adding some variables as covariates be a better option?).   
