Rails 4.2.4 - dynamic menus in simple form with associations - ruby-on-rails

Question

I want to populate one selection field based on choice from other selected field. It's about categories / subcategories, when user is trying to submit new product. User picks main category in field 1, after picked main category he gets option to pick from field 2 children subcategories of picked main category from field 1. It's based on associations so it makes it harder for me.
Product model:
class Product < ActiveRecord::Base
belongs_to :user
has_many :categorizations
has_many :categories, through: :categorizations
end
Category model:
class Category < ActiveRecord::Base
belongs_to :parent, class_name: "Category"
has_many :children, class_name: "Category", foreign_key: "parent_id"
has_many :categorizations
has_many :products, through: :categorizations
end
Categorization model:
class Categorization < ActiveRecord::Base
belongs_to :product
belongs_to :category
end
new.html.erb
<%= simple_form_for #product, :html => { multipart: true } do |f| %>
<%= f.association :categories, collection: Category.where(parent_id: nil), prompt: 'Choose category' %>
<%= f.association :categories, collection: Category.where.not(parent_id: nil), prompt: 'Choose subcategory' %>
<%= f.button :submit, "Submit product" %>
<% end %>
UPDATE:
class ProductsController < ApplicationController
def update_categories
#categories = Category.where("parent_id = ?", params[:category_id])
respond_to do |format|
format.js
end
end
end
some routes:
get 'products/update_categories', as: 'update_categories'