# General Loglinear Analysis

The General Loglinear Analysis procedure analyzes the frequency counts of observations falling into each cross-classification category in a crosstabulation or a contingency table. Each cross-classification in the table constitutes a cell, and each categorical variable is called a factor. The dependent variable is the number of cases (frequency) in a cell of the crosstabulation, and the explanatory variables are factors and covariates. This procedure estimates maximum likelihood parameters of hierarchical and nonhierarchical loglinear models using the Newton-Raphson method. Either a Poisson or a multinomial distribution can be analyzed.

You can select up to 10 factors to define the cells of a table. A cell structure variable allows you to define structural zeros for incomplete tables, include an offset term in the model, fit a log-rate model, or implement the method of adjustment of marginal tables. Contrast variables allow computation of generalized log-odds ratios (GLOR).

Model information and goodness-of-fit statistics are automatically displayed. You can also display a variety of statistics and plots or save residuals and predicted values in the active dataset.

**Example.** Data from a report of automobile accidents in
Florida are used to determine the relationship between wearing a seat
belt and whether an injury was fatal or nonfatal. The odds ratio indicates
significant evidence of a relationship.

**Statistics.** Observed and expected frequencies; raw, adjusted,
and deviance residuals; design matrix; parameter estimates; odds ratio;
log-odds ratio; GLOR; Wald statistic; and confidence intervals. Plots:
adjusted residuals, deviance residuals, and normal probability.

General Loglinear Analysis Data Considerations

**Data.** Factors are categorical, and cell covariates are
continuous. When a covariate is in the model, the mean covariate value
for cases in a cell is applied to that cell. Contrast variables are
continuous. They are used to compute generalized log-odds ratios.
The values of the contrast variable are the coefficients for the linear
combination of the logs of the expected cell counts.

A cell structure variable assigns weights. For example, if some of the cells are structural zeros, the cell structure variable has a value of either 0 or 1. Do not use a cell structure variable to weight aggregated data. Instead, choose Weight Cases from the Data menu.

**Assumptions.** Two distributions are available in General
Loglinear Analysis: Poisson and multinomial.

Under the Poisson distribution assumption:

- The total sample size is not fixed before the study, or the analysis is not conditional on the total sample size.
- The event of an observation being in a cell is statistically independent of the cell counts of other cells.

Under the multinomial distribution assumption:

- The total sample size is fixed, or the analysis is conditional on the total sample size.
- The cell counts are not statistically independent.

**Related procedures.** Use the Crosstabs procedure to examine
the crosstabulations. Use the Logit Loglinear procedure when it is
natural to regard one or more categorical variables as the response
variables and the others as the explanatory variables.

Obtaining a General Loglinear Analysis

This feature requires SPSS® Statistics Standard Edition or the Advanced Statistics Option.

- From the menus choose:
- In the General Loglinear Analysis dialog box, select up to 10 factor variables.

Optionally, you can:

- Select cell covariates.
- Select a cell structure variable to define structural zeros or include an offset term.
- Select a contrast variable.

This procedure pastes GENLOG command syntax.