Police say the suspect first developed signs of mental health problems shortly after the death of his mother about a decade ago.
Rivera had a juvenile criminal record that included three convictions including assault with a firearm.
The Rivera family released a statement on Saturday expressing their sympathy for the death of Officer Simmons and the injuries suffered by Officer James Veenstra, who was wounded during the standoff.
The statement says:
"The family is grief-stricken over the recent events that resulted in so much loss and devastation. We would appreciate any help we might receive that could aid us as we try to bury the four lost members of our family.
"We are at a loss on how to manage in the face of such an enormous undertaking."
A memorial fund has been set up for the Rivera family. The Washington Mutual account is in the name of Wilfredo Rivera, the only surviving brother. The account number is 395-4532-913.