# Logit Loglinear Analysis

The Logit Loglinear Analysis procedure analyzes the relationship between dependent (or response) variables and independent (or explanatory) variables. The dependent variables are always categorical, while the independent variables can be categorical (factors). Other independent variables (cell covariates) can be continuous, but they are not applied on a case-by-case basis. The weighted covariate mean for a cell is applied to that cell. The logarithm of the odds of the dependent variables is expressed as a linear combination of parameters. A multinomial distribution is automatically assumed; these models are sometimes called multinomial logit models. This procedure estimates parameters of logit loglinear models using the Newton-Raphson algorithm.

You can select from 1 to 10 dependent and factor variables combined. 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). The values of the contrast variable are the coefficients for the linear combination of the logs of the expected cell counts.

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.** A study in Florida included 219 alligators. How
does the alligators' food type vary with their size and the four lakes
in which they live? The study found that the odds of a smaller alligator
preferring reptiles to fish is 0.70 times lower than for larger alligators;
also, the odds of selecting primarily reptiles instead of fish were
highest in lake 3.

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

Logit Loglinear Analysis Data Considerations

**Data.** The dependent variables are categorical. Factors
are categorical. Cell covariates can be continuous, but 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 (GLOR). 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 aggregate data. Instead, use Weight Cases on the Data menu.

**Assumptions.** The counts within each combination of categories
of explanatory variables are assumed to have a multinomial distribution.
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 display
the contingency tables. Use the General Loglinear Analysis procedure
when you want to analyze the relationship between an observed count
and a set of explanatory variables.

Obtaining a Logit Loglinear Analysis

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

- From the menus choose:
- In the Logit Loglinear Analysis dialog box, select one or more dependent variables.
- Select one or more factor variables.

The total number of dependent and factor variables must be less than or equal to 10.

Optionally, you can:

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

This procedure pastes GENLOG command syntax.