models

A statistical model embodies a set of assumptions concerning the generation of the observed data, and similar data from a larger population. A model represents, often in considerably idealized form, the data-generating process. The model assumptions describe a set of probability distributions, some of which are assumed to adequately approximate the distribution from which a particular data set is sampled. A model is usually specified by mathematical equations that relate one or more random variables and possibly other non-random variables. As such, “a model is a formal representation of a theory” (Herman Ad’r quoting Kenneth Bollen). All statistical hypothesis tests and all statistical estimators are derived from statistical models. More generally, statistical models are part of the foundation of statistical inference.