Statistics - Advanced Linear/Nonlinear Models - Nonlinear Estimation

Ribbon bar. Select the Statistics tab. In the Advanced/Multivariate group, click Advanced Models and on the menu, select Nonlinear Estimation to display the Nonlinear Estimation Startup Panel.

Classic menus. On the Statistics - Advanced Linear/Nonlinear Models submenu, select Nonlinear Estimation to display the Nonlinear Estimation Startup Panel.

Nonlinear estimation involves finding the best fitting relationship between the values of a dependent variable and the values of a set of one or more independent variables (it is used as either a hypothesis testing or exploratory method).

In the Nonlinear Estimation module, you can specify any type of model by typing in the respective equation into an equation editor. The equations can include logical operators; thus, discontinuous (piecewise) regression models and models including indicator variables can also be estimated. The equations can also include a wide selection of distribution functions and cumulative distribution functions. The models can be fit using least squares or maximum-likelihood estimation, or any user-specified loss function. When using the least-squares criterion, the very efficient Levenberg-Marquardt and Gauss-Newton algorithms can be used to estimate the parameters for arbitrary linear and nonlinear regression problems. When using arbitrary loss functions, you can choose from among four very different procedures (quasi-Newton, Simplex, Hooke-Jeeves pattern moves, and Rosenbrock pattern search method of rotating coordinates). You have full control over all aspects of the estimation procedure (e.g., starting values, step sizes, convergence criteria, etc.). The most common nonlinear regression models are predefined in the Nonlinear Estimation module, and can be chosen simply as menu commands. Those regression models include stepwise Probit and Logit regression, the exponential regression model, and linear piecewise (break point) regression. Standard results nonlinear include the parameter estimates and their standard errors, the variance/covariance matrix of parameter estimates, the predicted values, residuals, and appropriate measures of goodness of fit (e.g., log-likelihood of estimated/null models and Chi-square test of difference, proportion of variance accounted for, classification of cases and odds-ratios for Logit and Probit models, etc.). Predicted and residual values can be appended to the data file for further analyses.

STATISTICA also includes implementations of powerful algorithms for fitting Generalized Linear/Nonlinear Models (GLZ), including probit and multinomial logit models, and Generalized Additive Models (GAM); see the respective descriptions for additional details.