And you get your statistics from where?
"But we do know that home invasions do rise in countries that have outlawed guns."
In actual fact, there are more recorded home invasions in the US per Capita than in Denmark, Sweden, Canada, and Germany combined, according to the statistics published for 2007 (most up to date I could find) for each of those countries. I might note that guns are outlawed or restricted in all of those countries.