Statistics - Advanced Linear/Nonlinear Models - Generalized Linear/Nonlinear Models

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

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

The Generalized Linear/Nonlinear Models (GLZ) module provides a generalization of the linear regression model such that 1) nonlinear, as well as linear, effects can be tested 2) for categorical predictor variables, as well as for continuous predictor variables, using 3) any dependent variable whose distribution follows several special members of the exponential family of distributions, as well as for any normally distributed dependent variable.

A wide range of distributions (from the exponential family) can be specified for the response variable: Normal, Poisson, Gamma, Binomial, Multinomial, Ordinal Multinomial, and Inverse Gaussian. Available link functions include: Log, Power, Identity, Logit, Probit, Complimentary Log-Log, and Log-Log links. In addition to the standard model fitting techniques, GLZ also provides unique options for exploratory analyses, including model building facilities like forward- or backward-only selection of effects (effects can only be selected for inclusion or removal once during the selection process), standard forward or backward stepwise selection of effects (effects can be entered or removed at each step, using a p to enter or remove criterion), and best-subset regression methods (using the likelihood score statistic, model likelihood, or Akaike information criterion). These methods can be applied to categorical predictors (ANOVA-like designs; effects will be moved in or out of the model as multiple-parameter blocks) as well as continuous predictors. The module will compute all standard results statistics, including likelihood ratio tests, and Wald and score tests for significant effects, parameter estimates and their standard errors and confidence intervals, etc. In addition, for ANOVA-like designs, tables and plots of predicted means (the equivalent of least squares means computed in the general linear model) with their standard errors could be computed to aid in the interpretation of results. GLZ also includes a comprehensive selection of model checking tools such as spreadsheets and graphs for various residuals and outlier detection statistics, including raw residuals, Pearson residuals, deviance residuals, studentized Pearson residuals, studentized deviance residuals, likelihood residuals, differential Chi-square statistics, differential deviance, and generalized Cook distances, etc. Predicted and residual statistics can be requested for observations that were used for fitting the model and those that were not (i.e., for the cross-validation sample).

STATISTICA also includes the Nonlinear Estimation module for fitting arbitrary regression functions using least-squares or user-defined loss functions