Normalize discrete variables in logistic regression?

I am running the a logistic regression model to test the effects of task variables on choice (left/right). I set up a logistic regression model per subject and test the regression coefficients against zero across subjects later on. One predictor is continuous and I normalize it to account for different possible values across subjects. One regressor is binary and I don't normalize it. One regressor can take on four different values (10,20,30,40) whereas their order and distances are meaningful. However it is still a discrete parameter. Would you normalize the regressor in this case? The results are different whether I do or don't and I wanted to hear your opinion.

I use matlabsglmfitto regress the design matrixxonywith the following optionsbetas = glmfit (x,y,'binomial','link','logit'). When normalize all variables, the respective regression weights for one example subject are (-7.14 4.283 -0.47 -0.49; intercept included). When I only normalize the continuous variablex1 the respective weights are (-5.51 4.283 -0.088 -1.01).

The t values against zero across all participants are [41.52 -3.985 and -0.032] if I normalize all values. If I only normalize the continuous variable they are [20.14 -3.89 -0.48].

• Can you specify exactly what you did to normalize the data? Normally (pun intended) it should not matter for logistic regression, unless you are using regularization or something else you didn't tell us. Please tell us more of the context. – kjetil b halvorsen Aug 5 '19 at 9:04
• Sure! I z-score the data and I do not use any kind of regularization. – Laurie Aug 5 '19 at 9:36
• Then, can you explain in which sense the results differ? They should not ... Edit your post to include some computer output – kjetil b halvorsen Aug 5 '19 at 9:39
• Okay I did that. Thanks – Laurie Aug 5 '19 at 10:31

From your latest edit we can see that the estimated coefficients (which you call weights) have changed. They must, since their role is to be multiplied with the $$x$$'s, which was changed with the normalization (which I would have called standardization). But the models are equivalent, in the sense that the fitted probabilities (logistic regression is a regression for probabilities) will be the same.
• Can you please post complete output? The $t$-values should not differ, but I cannot guess more at what has happened without looking at the output. – kjetil b halvorsen Aug 6 '19 at 7:51