misspecificación

Misspecification refers to an error in the formulation of a statistical model. This occurs when the chosen model does not accurately represent the underlying data-generating process. A common example is linear regression when the true relationship between variables is non-linear. Other forms of misspecification include omitting relevant variables, including irrelevant variables, or assuming incorrect error distributions.

The consequences of misspecification can be significant. It can lead to biased parameter estimates, inefficient inference, and incorrect predictions. For instance, if a crucial variable is omitted, the coefficients of the included variables may be biased because they absorb the effect of the missing variable. If the functional form is wrong, the model might fail to capture important patterns in the data, leading to poor out-of-sample performance.

Detecting misspecification is an important part of the modeling process. Various diagnostic tests exist to help identify such errors. These include examining residual plots for systematic patterns, testing for heteroscedasticity (non-constant variance of errors), and performing specification tests that compare alternative model structures. Model selection criteria, like AIC or BIC, can also indirectly help by favoring models that better fit the data without excessive complexity. Addressing misspecification often involves reformulating the model, for example, by transforming variables, adding interaction terms, or using a different class of models.