Nearly one out of every four families with children in 13 Greater Boston communities pay more than half their income for housing, while nearly 1 in 10 live in overcrowded conditions with more than two people per bedroom, according to a new study released today by the Metropolitan Area Planning Council.

Conditions are even more dire for low-income households and residents of color, the study found. The research area included Boston, Brookline, Cambridge, Chelsea, Everett, Malden, Medford, Milton, Newton, Quincy, Revere, Somerville and Winthrop.

“Our collective failure to act on the Commonwealth’s dire housing shortage has a direct impact on children. We make them pay for our mistakes. A low or moderate-income family who pays more than half their income for housing can’t possibly meet other expenses, such as transportation, food, and health care,” MAPC Executive Director Marc Draisen said in a statement.

MAPC is the regional planning agency serving Greater Boston.

At the same time, the study shows that the supply of “family-sized” units isn’t matched to demand, with only 39 percent of units with more than 3 bedrooms occupied by families with a child under the age of 18. The culprit among rental properties appears to be roommates: Three or more adults without children renting together occupy 34 percent of these “family-sized” units, while renters with children occupy 43 percent of the supply. Conversely, in ownership units, two-adult households without children occupy 30 percent of the study area’s “family-sized” houses and condominiums, while families with children occupy 36 percent.

“Even as large families in Greater Boston are increasingly overcrowded and overburdened by housing costs, most family-sized units in the area don’t actually house families,” Sarah Philbrick, a socioeconomic analyst at MAPC and one author of the report, said in a statement.

On average, these roommate households can pay $450 or more in monthly rent than a family. However, the report shows most of these roommates would not be able to live on their own. Fewer than 1 in 10 roommates in a large unit could afford the median-priced one-bedroom unit in the area where they lived, and the lack of affordable smaller options has pushed more younger householders into roommate households since 2000, increasing competition for the limited supply of large units, MAPC found.

Similarly, senior households who might want to downsize and free up home for families with children, can’t find affordable options in or near the community where they currently live.

“Just one of the many unfortunate realities of the current housing crisis is that individuals and couples who would normally live in smaller units can’t afford to, and instead need to live with roommates to make ends meet. Not only do we need more and larger units for families, but we have to make sure smaller units are affordable so that groups of roommates, with multiple incomes, aren’t competing with one- or two-income families for the same housing,” Somerville Mayor Joe Curtatone, who leads the Metro Mayors Coalition, said in a statement. “This is just one of the reasons that the Metro Mayors Housing Task Force committed to addressing our housing challenges on a regional level. We all have to work together to produce the right types of housing for our residents.”

The report recommends building more family-sized units and more senior-friendly housing to deal with the problem. The senior-oriented units, the report argues, could help attract more Baby Boomers to downsize faster, freeing up more family-sized units. Alternatively, the authors write, producing more affordable one-bedroom apartments could draw younger residents away from roommate situations and reduce competition for family-sized units.

“There is no one cause, and no one solution, to the lack of family housing in Greater Boston,” MAPC Data Services Director Tim Reardon said in a statement. “We can’t solve the problem for families unless we are also meeting the needs of seniors and young adults. That means more housing of all types across all of our communities, so people have more choices. With additional supply, we’ll see more family units come back on the market and reduced competition for the ones that are available.”

The study used data from the U.S. Census Bureau’s 2012-2016 American Community Survey.