Section B.11 Model Building and Variable Selection
How do you construct a good model? This partly depends on your goal, although there are commonalities. You do want to start with theory as a way to select your predictors and when specifying the nature of the relationship to your response variable (e.g., additive, multiplicative). [188] provide a series of general principles. I would like to emphasise at this stage two of them:
-
Include all input variables that, for substantive reasons, might be expected to be important in predicting the outcome.
-
For inputs with large effects, consider including their interactions as well.
It is often the case that for any model, the response variable is only related to a subset of the predictors. There are some scenarios where you may be interested in understanding what is the best subset of predictors. Imagine that you want to develop a risk assessment tool to be used by police officers that respond to a domestic violence incident, so that you could use this tool for forecasting the future risk of violence. There is a cost to adding too many predictors. A police officer’s time should not be wasted gathering information on predictors that are not associated with future risk. So you may want to identify the predictors that will help in this process.
Ideally, we would like to perform variable selection by trying out a lot of different models, each containing a different subset of the predictors. There are various statistics that help in making comparisons across models. Unfortunately, as the number of potentially relevant predictors increases, the number of potential models to compare increases exponentially. So you need methods that help you in this process. There are a number of tools that you can use for variable selection but this goes beyond the aims of this introduction.
