Statistical model

Statistical model is a mathematical representation of a set of data. It is a formalization of relationships between variables in the form of mathematical equations. A statistical model describes how one or more random variables are related to one or more random variables. The model is statistical as the variables are not deterministically but stochastically related.

Definition

In statistics, a statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process.

Types of statistical models

There are several different types of statistical models, including:

• Parametric models
• Non-parametric models
• Semi-parametric models
• Non-parametric regression models
• Generalized linear models
• Graphical models
• Mixed models
• Hierarchical models

Model specification

Model specification involves selecting an appropriate functional form for the model and choosing which variables to include. The choice of model specification can significantly affect the conclusions drawn from the statistical analysis.

Model estimation

Model estimation involves estimating the parameters of the model. This is typically done using maximum likelihood estimation, least squares estimation, or Bayesian estimation.

Model checking

Model checking involves assessing the fit of the model to the data and checking the model's assumptions. This can be done using various diagnostic tests and residual analysis.

Model selection

Model selection involves choosing the best model from a set of candidate models. This is typically done using Akaike's information criterion (AIC), Bayesian information criterion (BIC), or cross-validation.

See also

• Statistical theory
• Statistical inference
• Statistical hypothesis testing
• Regression analysis
• Design of experiments

References

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