Counting the number of homeless people is a challenging proposition, much less quantifying their military backgrounds. The number appears to come from a November 2007 study from the National Alliance to End Homelessness. The nonprofit used data from the U.S. Department of Veterans Affairs that estimated the number of homeless veterans in a given VA facility's service area. The alliance than combined that data with their own population estimates for the homeless nationwide.
The study cited data from 2005 that showed out of 744,313 homeless people in a given year, 194,254 were veterans. That means that 26 percent of the homeless are veterans, even though veterans only make up 11 percent of the U.S. population over 18 years old, according to U.S. Census data. The study counted people who were homeless at any time, even briefly, during the year, not just the chronically homeless.
It's also worth noting that the number of homeless veterans fluctuates over time because of natural demographic changes and because of the numbers of people who served in the military at any given time in history. Homeless advocates expect the percentage of homeless veterans is a number that changes as the years go by.
The 2007 study is an estimate, but it's based on data compiled, at least in part, by a federal agency, and it appears to be the latest data available. Other studies have found lower estimates of the national homeless population, but using a more conservative number for the overall homeless would have the effect of increasing the percentage of homeless veterans.
Although Edwards is relying on the best available data, it's still extremely difficult to count homeless people because not all of them come in contact with service providers or other agencies. Some have health issues like addiction and mental illness that make them reluctant to be counted. Even reputable studies sometimes find different estimates for the homeless.
Though the percentage of homeless veterans is an estimate, the number Edwards cites appears to be based on the latest available and was partially compiled by the federal agency that serves veterans. So he is on solid ground. But we have to take off a little bit for his emphatic statement of what's actually a complex estimate. For that reason, we find his statement to be Mostly True.