This is potentially a more difficult question than you may realize. There are several different possibilities. You could perhaps construct a set of binary variables Yk, for k=0,1,2,3,4..... as follows. Yk=0 for women with k children; Yk=1 for women with more than k children; Yk="." for women with fewer than k children. You would then be describing the probability of going from parity k to parity k+1. This would be better for number of children ever born than for number of living children. Logit regression is not well suited for an outcome that is a count. Another possibility would be to use poisson regression or negative binomial regression. There is not a general agreement on a single way to analyze this outcome.

I hope another user of the forum can help you with this question, or you can directly contact the author, Sanjukta Chaudhuri, whose contact information must be provided in the article.