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A factorial logistic regression is used when there two or more categorical independent variables but a dichotomous dependent variable
It is used to predict a nominal dependent variable given one or more independent variables.
When running a multiple regression, one needs to separate variables into covariates and factors. SPSS will automatically classify continuous independent variables as covariates and nominal independent variables as factors. Therefore, when dealing with ordinal independent variables you must choose if you will consider them as covariates or factors.
The output window generates a Goodness- of- Fit table, the first row presents the Pearson chi-square statistic. If the P value is less than 0.05 (p<.05) indicate the model does not fit the data well.
Another way to check the measure your model is to consider the Model Fitting Information table. Check the Final row p-value “sig” value or the pseudo R2 measures.