I have slaves that I've been interacting with, and every stat is still zero. It does count the number of days owned and the amount of money and food gathered, but that's it.

Am I doing something wrong?

Are you talking about mental stats or the core stats? Mental stats are increased by going to the character window, selecting "Learn Skill" and increasing mental skills at the cost of learning points. No learning points? Well put them in a library or teach them via interaction.

To increase their core stats, goto their character window and look right of their character portrait. There should be plus buttons. No plus buttons? You either lack skill points or their stats are already at max. No skill points? Level them up! How? Get their EXP to 100/100 and then talk to them. Select the 1st dialogue option to find out what they need to level up. Can be:

Grade them up

Have them learn a Speciality

Give them items (press the 1st button again to proceed)

Give them a vacation (press the 1st button again to proceed)

Have them win in a fight