In most cases, "的“ can or should be omitted between two nouns in casual conversation, when the relationship between these 2 nouns are very obvious.
e.g. In this case, 我家 obviously means "my home", because this is the only sensible meaning. :) (I am trying to think of other possible meaning , but can't)
On the other hand, if you want to sounds formal and very serious, you should try to use "的" more often, because it makes the relationship between words clear. There is only a very subtle difference.