How to check linearity in binary logistic regression with many covariates having 0 as a value I'm trying to check linearity in my binary logistic regression. According to my handbook (Discovering Statistics Using SPSS, by Andy Fields: ch.19.8.1) this should be done by adding var*log(var) to the model and check for significance. 
Many of my covariates however are binary variables which can be 0 or 1. Doing log(0) doesn't give an outcome which results in a lot of missing values when recoding the data. Now only 8% of my variables is used in the regression and I don't get the desired results. How do I do this check on my data where lots of values are 0?
 A: This problem is no problem. You are quite correct that this method can't be applied given zeros as data points, but there is a deeper issue. 
Setting aside logistic regression, imagine that you are plotting any response on the $y$ axis against a covariate with just two distinct values on the $x$ axis. 
In your case the values are 0 and 1, but that doesn't affect the explanation I am going to give. Any transformation that I can apply that changes those two distinct values to two distinct values (whether the same or different) will not affect the linearity of the relation on the graph. At most, I might flip the values around (exchange smaller and larger) and then my relation will change sign (positive to negative, or vice versa). But there's no scope to play with a non-linear version of the covariate as an alternative. Using a logit link doesn't affect this: any transformation of a binary covariate just changes coefficients given different measurements, but it can't affect goodness of fit. 
So, not being able to apply this device to binary covariates scored $(0, 1)$ is not a problem. It doesn't apply even in principle. 
In general, it certainly can't work with variables that are ever negative or zero. In general also, you need at least three distinct values of a covariate for working on a transformed scale ever to be different. 
I don't have access to the book by Field [N.B.] to check his rationale and whether he mentions any qualifications. 
N.B.: What I call "distinct" values are sometimes called "unique" values. I don't follow that usage. Although language is always shifting, the term "unique" is best reserved in my view for values that occur precisely once. 
