How do I perform a regression with a categorical outcome?
The usual analysis of variance and linear regressions are not appropriate with a categorical dependent variable. One way to see the results of associations between categories and predictors is using binary logistic regression (2 outcome categories) or multinomial or nominal logistic regression (3 or more categories).
These may both be fitted in SPSS in the analyze>regression submenu. Instead of a 'F' or 't' statistic the model is assessed using a (likelihood ratio) chi-square statistic.
This statistic represents the fit between the observed outcome categories and probabilities of belonging to these categories based upon a model containing the predictor variables.
For further details with examples see Chapter 10 of Tabachnick and Fidell (2007) (available in the CBSU library).
Multigroup logistic regressions and proportional odds models are extensions of the binary logistic regression to three or more groups. Worked examples are given [http://users.iit.demokritos.gr/~paliourg/papers/CBR.pdf here] and in Hosmer and Lemeshow (2001).
References
Hosmer, DW and Lemeshow, S (2001) Applied logistic regression. 2nd Edition. Wiley:New York. Note: A third edition is due for publication in 2013.
Tabachnick, BG and Fidell, LS (2007) Using multivariate statistics fifthe edition. Pearson Education:Boston, USA.