Now that you are equipped with powerful programming tools we can finally return to modelling. You'll use your new tools of data wrangling and programming, to fit many models and understand how they work. The focus of this book is on exploration, not confirmation or formal inference. But you'll learn a few basic tools that help you understand the variation within your models.
The goal of a model is to provide a simple low-dimensional summary of a dataset. Ideally, the model will capture true "signals" (i.e. patterns generated by the phenomenon of interest), and ignore "noise" (i.e. random variation that you're not interested in). Here we only cover "predictive" models, which, as the name suggests, generate predictions. There is another type of model that we're not going to discuss: "data discovery" models. These models don't make predictions, but instead help you discover interesting relationships within your data. (These two categories of models are sometimes called supervised and unsuperivsed, but I don't think that terminology is particularly illuminating.)
This book is not going to give you a deep understanding of the mathematical theory that underlies models. It will, however, build your intution about how statisitcal models work, and give you a family of useful tools that allow you to use models to better understand your data:
In this book, we are going to use models as a tool for exploration, completing the trifacta of EDA tools introduced in Part 1. This is not how models are usually taught, but they make for a particularly useful tool in this context. Every exploratory analysis will involve some transformation, modelling, and visualisation.
Models are more common taught as tools for doing inference, or for confirming that an hypothesis is true. Doing this correctly is not complicated, but it is hard. There is a pair of ideas that you must understand in order to do inference correctly:
1. You can use an observation as many times as you like for exploration,
but you can only use it once for confirmation. As soon as you use an
observation twice, you've switched from confirmation to exploration.
This is necessary because to confirm a hypothesis you must use data this is independent of the data that you used to generate the hypothesis. Otherwise you will be over optimistic. There is absolutely nothing wrong with exploration, but you should never sell an exploratory analysis as a confirmatory analysis because it is fundamentally misleading. If you are serious about doing an confirmatory analysis, before you begin the analysis you should split your data up into three piecese:
1. 20% is held back for a __test__ set. You can only use this data ONCE, to
test your final model.
This partitioning allows you to explore the training data, occassionally generating candidate hypotheses that you check with the query set. When you are confident you have the right model, you can check it once with the test data.
The modelling chapters are even more opinionated than the rest of the book. I approach modelling from a somewhat different perspective to most others, and there is relatively little space devoted to it. Modelling really deserves a book on its own, so I'd highly recommend that you read at least one of these three books:
