Workspace Node: Nonlinear Estimation - Specifications - Regression Specification Tab

The Nonlinear Estimation workspace node can be accessed from the Feature Finder, ribbon bar, or Node Browser. The Regression specification tab of the specifications dialog box is displayed by default when you double-click the node.

Note: Generalized Linear Model (GLZ). You can also use Generalized Linear/Nonlinear Model (GLZ) to analyze continuous, binomial, or multinomial dependent variables. GLZ is an implementation of the generalized linear model and can be used to compute a standard, stepwise, or best subset multiple regression analysis with continuous as well as categorical predictors, and for continuous,  binomial, or multinomial dependent variables (probit regression, binomial and multinomial logit regression, Poisson regression, etc.; see also Link functions). In general, the estimation algorithms implemented in Generalized Linear/Nonlinear Model (GLZ) are more efficient, and STATISTICA only includes the models here for compatibility purposes.

Quick logit regression. When you select this option button, the general logistic model can be stated as:

y = b0 /{1+b1 *exp(b2 *x)}

You can think of this model as an extension of the logit or logistic model for binary responses. However, while the logit model restricts the dependent response variable to only two values, this model allows the response to vary within a particular lower and upper limit. For example, suppose we are interested in the population growth of a species that is introduced to a new habitat, as a function of time. The dependent variable would be the number of individuals of that species in the respective habitat. Obviously, there is a lower limit on the dependent variable, since fewer than 0 individuals cannot exist in the habitat; however, there also is most likely an upper limit that will be reached at some point in time.

Quick probit regression. In the probit regression model, the predicted values for the dependent variable will never be less than (or equal to) 0, or greater than (or equal to) 1, regardless of the values of the independent variables; it is, therefore, commonly used to analyze binary dependent or response variables (see also the binomial distribution). This is accomplished by applying the following regression equation (the term probit was first used by Bliss, 1934):

y = NP(b0 + b1 *x1 ...)

where NP stands for normal probability (space under the normal distribution; or cumulative distribution function of the normal distribution). It is easily recognized that, regardless of the regression coefficients or the magnitude of the x values, this model will always produce predicted values (predicted y's) in the range of 0 to 1.

Exponential growth regression. When you select this option button Statistica will estimate, using least squares, the model:

y = c + exp(b0 + b1 *x1 + b2 *x2 + ... + bm *xm )

where

c, bi are parameters (for the m independent variables)

This model is commonly used to study the growth of populations.

Piecewise linear regression. When you select this option button, Statistica estimates, using least squares, the model:

y = (b01 +b11 *x1 +...+bm1 *xm )*(y ≤ bn ) + (b02 +b12 *x1 +...+bm2 *xm )*(y > bn )

Thus, Statistica estimates two separate linear regression equations; one for the y values that are less than or equal to the breakpoint (b0) and one for the y values that are greater than the breakpoint. (For a general description of these types of models, see Common Nonlinear Regression Models.)

Options / C / W. See Common Options.

OK. Click the OK button to accept all the specifications made in the dialog box and to close it. The analysis results will be placed in the Reporting Documents node after running (updating) the project.

See also, Specifications - Quick tab, Specifications - Advanced tab, Results - Quick tab, Results - Advanced tab, Results - Residuals tab, Results - Review tab, Downstream tab, and Home tab.