8.15: Chapter summary

This chapter explored the most complicated models we’re going to explore. MLR models can incorporate features of SLR and ANOVAs. The MLR’s used in this chapter highlight the flexibility of the linear modeling framework to move from two-sample mean models to multi-predictor models with interactions of categorical and quantitative variables. It is useful to use the pertinent names for the simpler models, but at this point we could have called everything we are doing fitting linear models. The power of the linear model involves being able to add multiple predictor variables to the model and handle categorical predictors using indicator variables. All this power comes with some responsibility in that you need to know what you are trying to fit and how to interpret the results provided. We introduced each scenario working from simple to the most complicated version of the models, trying to motivate when you would encounter them, and the specific details of the interpretations of each type of model. In Chapter 9, case studies are used to review the different methods discussed with reminders of how to identify and interpret the particular methods used.

When you have to make modeling decisions, you should remember the main priorities in modeling. First, you need to find a model that can address research question(s) of interest. Second, find a model that is trustworthy by assessing the assumptions in the model relative to your data set. Third, report the logic and evidence that was used to identify and support the model. All too often, researchers present only a final model with little information on how they arrived at it. You should be reporting the reasons for decisions made and the evidence supporting them, whether that is using p-values or some other model selection criterion. For example, if you were considering an interaction model and the interaction was dropped and an additive model is re-fit and interpreted, the evidence related to the interaction test should still be reported. Similarly, if a larger MLR is considered and some variables are removed, the evidence (reason) for those removals should be provided. Because of multicollinearity in models, you should never remove more than one quantitative predictor at a time or else you could remove two variables that are important but were “hiding” when both were included in the model.