Statistical model validation
In statistics, model validation is the task of confirming that the outputs of a statistical model are acceptable with respect to the real data-generating process. In other words, model validation is the task of confirming that the outputs of a statistical model have enough fidelity to the outputs of the data-generating process that the objectives of the investigation can be achieved.
Model validation can be based on two types of data: data that was used in the construction of the model and data that was not used in the construction. Validation based on the first type usually involves analyzing the goodness of fit of the model or analyzing whether the residuals seem to be random (i.e. residual diagnostics). Validation based on the second type usually involves analyzing whether the model's predictive performance deteriorates non-negligibly when applied to pertinent new data.
Validation based on only the first type (data that was used in the construction of the model) is often inadequate.Validation is usually not based on only considering data that was used in the construction of the model; rather, validation usually also employs data that was not used in the construction. In other words, validation usually includes testing some of the model's predictions.
A model can be validated only relative to some application area. A model that is valid for one application might be invalid for some other applications.
Methods for validating
When doing a validation, there are three notable causes of potential difficulty, according to the Encyclopedia of Statistical Sciences. The three causes are these: lack of data; lack of control of the input variables; uncertainty about the underlying probability distributions and correlations. The usual methods for dealing with difficulties in validation include the following: checking the assumptions made in constructing the model; examining the available data and related model outputs; applying expert judgment. Note that expert judgment commonly requires expertise in the application area.
Expert judgment can sometimes be used to assess the validity of a prediction without obtaining real data. Additionally, expert judgment can be used in Turing-type tests, where experts are presented with both real data and related model outputs and then asked to distinguish between the two.
For some classes of statistical models, specialized methods of performing validation are available. As an example, if the statistical model was obtained via a regression, then specialized analyses for regression model validation exist and are generally employed.
