# Logit Loglinear Analysis

### 谢益辉 / 2006-03-27

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.

SPSS automatically displays model information and goodness-of-fit statistics. You can also display a variety of statistics and plots or save residuals and predicted values in the working data file.

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.