User Guide

71
Chapter
7
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.
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.