GLZ Introductory Overview - Types of Analyses

The design for an analysis can include effects for continuous as well as categorical predictor variables. Designs may include polynomials for continuous predictors (e.g., squared or cubic terms) as well as interaction effects (i.e., product terms) for continuous predictors. For categorical predictor variables, one can fit ANOVA-like designs, including full factorial, nested, and fractional factorial designs, etc. Designs can be incomplete (i.e., involve missing cells), and effects for categorical predictor variables can be represented using either the sigma-restricted parameterization or the overparameterized (i.e., indicator variable) representation of effects.

The topics below give complete descriptions (in the context of the General Linear Model (GLM) module) of the types of designs that can be analyzed using the generalized linear model, as well as types of designs that can be analyzed using the general linear model.

Signal detection theory. The list of designs shown below is by no means comprehensive, i.e., it does not describe all possible research problems to which the generalized linear model can be applied. For example, an important application of the generalized linear model is the estimation of parameters for signal detection theory (SDT) models. SDT is an application of statistical decision theory used to detect a signal embedded in noise. SDT is used in psychophysical studies of detection, recognition, and discrimination, and in other areas such as medical research, weather forecasting, survey research, and marketing research. For example, DeCarlo (1998) shows how signal detection models based on different underlying distributions can easily be considered by using the generalized linear model with different link functions.

For discussion of the generalized linear model and the link functions it uses, see the Introductory Overview for the Generalized Linear Model module.

Between-subject designs