ABSTRACT
This chapter explores statistical models—how to think about them, specify them, fit them, and analyze them. Statistical models are simplified descriptions of data, usually constructed from some mathematically or numerically defined relationships. The chapter presents statistical models in three parts: formula that defines the structural part of the model—that is, what data are being modeled and by what other data, in what form; data to which the modeling should be applied. Finally, the stochastic part of the model—that is, how to regard the discrepancy or residuals between the data and the fit. Models are objects that imitate the properties of other, "real" objects, but in a simpler or more convenient form. We make inferences from the models and apply them to the real objects, for which the same inferences would be impossible or inconvenient. The modeling formula defines the structural form of the model, and is used by the model-fitting functions to carry out the actual fitting.
