We're Only Human...: In the Eye of the Storm:
"The survivors themselves told a very different story, however. When the psychologists surveyed actual Katrina survivors, they found that those who stayed behind did not feel powerless or passive. To the contrary, they saw themselves as connected with their neighbors—communitarian rather than self-reliant. Their stories emphasized their faith in God and their
feelings of caring for others. In short, they didn’t see themselves as failing to take action, but rather as taking a different kind of action—adapting to life’s travails and staying strong despite hardship."
This is from a Stanford article by Nicole Stephens. You can read more about it at ScienceDaily.com.
I will also add in the many conversations we have had with survivors who stayed, there was a mix of responses. Some said they had no means of leaving (this was what got most of the press coverage after Katrina), but a not small percentage said things that were more like the above article. For instance: "I had to stay to watch my parent's house" or "The last time we left there were many looters, so I stayed to protect the my, and my neighbors'/friends'/family's property."