7.1 What Are the Goals of Formal Modeling?
One key goal of formal modeling is to develop a precise specification of your question and how your data can be used to answer that question. Formal models allow you to identify clearly what you are trying to infer from data and what form the relationships between features of the population take. It can be difficult to achieve this kind of precision using words alone.
Parameters play an important role in many formal statistical models (in statistical language, these are known as parametric statistical models). These are numbers that we use to represent features or associations that exist in the population. Because they represent population features, parameters are generally considered unknown, and our goal is to estimate them from the data we collect.
For example, suppose we want to assess the relationship between the number of ounces of soda consumed by a person per day and that person’s BMI. The slope of a line that you might plot visualizing this relationship is the parameter you want to estimate to answer your question: “How much would BMI be expected to increase per each additional ounce of soda consumed?” More specifically, you are using a linear regression model to formulate this problem.
Another goal of formal modeling is to develop a rigorous framework with which you can challenge and test your primary results. At this point in your data analysis, you’ve stated and refined your question, you’ve explored the data visually and maybe conducted some exploratory modeling. The key thing is that you likely have a pretty good sense of what the answer to your question is, but maybe have some doubts about whether your findings will hold up under intense scrutiny. Assuming you are still interested in moving forward with your results, this is where formal modeling can play an important role.