Nonlinear Models

Mariana Medina

In political science, as in many other disciplines, linear regression is the workhorse tool for statistical analysis. It is easy to interpret, and under many conditions the estimates it provides are unbiased and efficient. Unfortunately, many of the theories in the social sciences imply a nonlinear relationship between variables. In those cases, it is inappropriate to use a classic linear regression model because, at a minimum, one of the assumptions of the model would be violated. This entry discusses two types of linear models: first, those that through a relatively simple process can be transformed in a way that allows running of a classical linear regression model; second, those that are essentially nonlinear, for which a transformation is not possible. In that situation, nonlinear least squares estimation is necessary. The linear regression model specifies a linear relationship between a response —or dependent—variable and an explanatory —or independent—variable. It is assumed ...

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