# Statistics - Advanced Linear/Nonlinear Models - General Linear Models

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

Classic menus. On the - Advanced Linear/Nonlinear Models submenu, select General Linear Models to display the General Linear Models (GLM) Startup Panel.

The General Linear Models (GLM) module provides a generalization of the linear regression model, such that effects can be tested (1) for categorical predictor variables, as well as for effects for continuous predictor variables and (2) in designs with multiple dependent variables as well as in designs with a single dependent variable.

GLM is a complete implementation of general linear models. You can choose simple or highly customized one-way, main-effect, factorial, or nested ANOVA or MANOVA designs, repeated measures designs, simple, multiple and polynomial regression designs, response surface designs (with or without blocking), mixture surface designs, simple or complex analysis of covariance designs (e.g., with separate slopes), or general multivariate MANCOVA designs. Factors can be fixed or random (in which case synthesized error terms will be computed). GLM offers both the overparameterized and Sigma-restricted parameterization for categorical factor effects. STATISTICA will compute the customary Type I through IV sums of squares for unbalanced and incomplete designs; GLM also offers two additional methods for analyzing missing cell designs: Hockings (1985) "effective hypothesis decomposition," and a method that will automatically drop effects that cannot be fully estimated (e.g., when the least squares means do not exist for all levels of the respective main effect or interaction effect). The latter method is the one commonly applied to the analysis of highly fractionalized designs in industrial experimentation (see also Experimental Design). Results statistics computed by GLM include ANOVA tables with univariate and multivariate tests, descriptive statistics, a comprehensive selection of different types of plots of means (observed, least squares, weighted) for higher-order interactions, with error bars (standard errors) for effects involving between-group factors as well as repeated measures factors; extensive residual analyses and plots (for the "training" or computation sample, for a cross-validation or "verification" sample, or for a prediction sample), desirability profiling, specifications of custom error terms and effects; comprehensive post-hoc comparison methods for between-group effects as well as repeated measures effects, and the interactions between repeated measures and between effects including: Fisher LSD, Bonferroni, Scheffé, Tukey HSD, Unequal N HSD, Newman Keuls, Duncan, and Dunnett's test (with flexible options for estimating the appropriate error terms for those tests), tests of assumptions (e.g., Levene's test, plots of means vs. standard deviations, etc.).

The General Regression Models (GRM) module offers methods for stepwise and best-subset selection of effects in a general linear model; see also the Generalized Linear/Nonlinear Model (GLZ) module for non-linear alternatives to GLM.

Generalized Linear/Nonlinear Models. Select Generalized Linear/Nonlinear Models from the Statistics - Advanced Linear/Nonlinear Models menu 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.