I'm also looking for the information on how to check for linearity in logit in spss. Surprisingly it's not so easy to find a reliable source of information for this topic. However, I can share some links that I've found. Hope that they will be useful.
The following procedure was taken from here
Instructions for performing a Box-Tidwell test for non-linearity
1. Begin by assuming the candidate independent variables are linear in the logit
2. Build your logistic regression model
3. Stop assuming your model is properly specified
4. Add the term x ln(x) to the multiple regression model for each continuous covariate (x)
5. Re-run the regression with these additional terms (keep your original x variables in the model)
7. If any of the terms you’ve added are significant, then you’ve evidence that those covariates are have a non-linear relationship with the dependent variable.
8. Identify a transformation that will facilitate linearity.
Another info is from here
9. What is the Box-Tidwell test? P. 523
It is a way of screening the data to see if one may assume linearity in the logit. You add terms representing the interaction of each IV with its log transform (ex., IV*log(IV)). None of these interaction terms should be significant predictors of the DV or otherwise the assumption of linearity in the logit is violated. To the extent that this assumption is violated, logistic regression will lack power and will underestimate the relationship (Type II error).
The next info was taken from here
Box-Tidwell Transformation (Test): Add to the logistic model interaction terms which are the crossproduct of each independent times its natural logarithm [(X)ln(X)]. If these terms are significant, then there is nonlinearity in the logit. This method is not sensitive to small nonlinearities.
Also in the following books there are some examples of Box-Tidwell tests:
Using Multivariate Statistics, by Barbara G. Tabachnick and Linda S. Fidell
Applied logistic regression analysis, by Scott W. Menard