About the data: My dependent variable is discrete (hypothetical example: number of years/months between graduating high school and applying to university) and my independent variables are mostly nominal ( characteristics of the students, like place of birth, name of high school etc). The distribution of the data looks like there are two populations. Those that apply very early (1 to 3 months) and those that apply later (4 to 12 months). Also, the dependent variable is not normally distributed but positively skewed.
I would like to know if there is a certain profile of students (based on the independent variables ) that applies earlier or later.
Knowing the behaviour of a certain profile of my past data, I would like to apply this "knowledge" to future high school students and use regression/classification to predict what will be the time between high school and university application in number of months .
Question 1: What statistical methods would you recommend to determine the factors/characteristics that influence early or late applicants (there could be several reasons why there are two populations, what is the "profile" of students that make up the two populations) ? I thought of Kruskal-Wallis test or clustering?
Question 2: What kind of regression would you recommend to predict the time for future university applicants? I thought of multinomial logistic regression but knowing that there are two populations, I have concerns.
Note: the example is hypothetical