What is variable relativity in logistic regression? Can anyone explain what is relativity? It seems to me it could be calculated from the coefficient estimates? Thanks!
 A: This use of "relativity" seems to have its origin in actuarial science:

Relativity Factors: Factors used to develop the experience of a class of exposures relative to the base risk class; for example, a relativity factor of 5.0 for a given class of risk would indicate that class expected losses to be 5 times the expected losses of the base risk class, 1.0.

That usage would be related to the relative risk, as suggested in a comment.
The SAS documentation explains its relativity plots for generalized linear models as follows:

Relativity Plots — displays a relativity plot for each class main effect included in the final model. This plot shows the relativity for each level with regard to the reference level—that is, the exponential of the parameter estimate. The bands on the plots indicate the lower and upper confidence limits, which are based on the specified Confidence level.

The SAS use of "relativity" thus seems broader than the actuarial use of the term, as it is the exponential of a coefficient from a generalized linear model evidently independent of the specific nature of the model. Note that the log is the default link function for generalized linear models in SAS, so this exponentiation undoes that default link.
Say that you did a typical logistic regression with a multi-level categorical factor as one of the predictors. The coefficients for the non-reference levels of that factor then represent their differences from the reference level in the log-odds of having the outcome event. Exponentiating the coefficients (and their corresponding confidence intervals, CI) transforms the log-odds coefficients (and CI) into odds ratios relative to the reference. That's different from the actuarial relativity or the relative risk, which is related to a ratio of probabilities.
So to reproduce SAS "Relativities" it seems that you start with a set of logistic regression coefficients and their CI, and exponentiate them.
