 Nonlinear Estimation Introductory Overview - Estimating Linear and Nonlinear Models

Technically speaking, Nonlinear Estimation is a general fitting procedure that will estimate any kind of relationship between a dependent (or response variable), and a list of independent variables. In general, all regression models can be stated as:

y = F(x1, x2, ... , xn)

In most general terms, we are interested in whether and how a dependent variable is related to a list of independent variables; the term F(x...) in the expression above means that y, the dependent or response variable, is a function of the x's, that is, the independent variables.

An example of this type of model would be the linear multiple regression model as described in Multiple Regression. For this model, we assume the dependent variable to be a linear function of the independent variables, that is:

y = a + b1*x1+ b2*x2+ ... + bn*xn

If you are not familiar with multiple linear regression, you may want to read the Multiple Regression Overviews at this point (however, it is not necessary to understand all of the nuances of multiple linear regression techniques in order to understand the methods discussed here).

Use Nonlinear Estimation to specify essentially any type of continuous or discontinuous regression model. Some of the most common nonlinear models (such as probit, logit, exponential growth, and breakpoint regression) are pre-defined in Nonlinear Estimation and can simply be requested as dialog options; however, note that the Generalized Linear/Nonlinear Models (GLZ) module includes more efficient algorithms for fitting general probit and logit regression models, and STATISTICA only includes these models here for compatibility purposes. You can also type in any type of regression equation, which STATISTICA will then fit to your data (see User-Specified Regression, Least Squares and User-Specified Regression, Custom Loss). Moreover, you can specify either standard least squares estimation, maximum likelihood estimation (where appropriate), or, again, define your own "loss function" (see below) by typing in the respective equation.

In general, whenever the simple linear regression model does not appear to adequately represent the relationships between variables, then the nonlinear regression model approach is appropriate. See the following topics for overviews of the common nonlinear regression models, nonlinear estimation procedures, and evaluation of the fit of the data to the nonlinear model:

Common Nonlinear Regression Models