# 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

Overview

One-way ANOVA

Main effect ANOVA

Factorial ANOVA

Nested designs

Simple regression

Multiple regression

Factorial regression

Polynomial regression

Response surface regression

Mixture surface regression

Analysis of covariance (ANCOVA)

Separate slopes designs

Homogeneity of slopes