Long Islanders are more worried about high housing costs than their counterparts in other New York City suburbs, and as they seek out affordable places to live, they’ve become more likely to support downtown apartments and condominiums, a new survey found.

In a break with their long-held, often fierce opposition to multifamily developments, 54 percent of Long Island respondents supported raising downtown height limits to four stories so developers can build apartments over retail shops — up 10 percentage points from 2010, according to the survey released Wednesday by the Long Island Index, a project of the nonprofit Rauch Foundation in Garden City.

Nearly 30 percent of Island respondents would like to live in an apartment, condominium or town house within five years — double the number who live in such housing types now, the survey found.

“We can just see this crying need for more affordable options and more diverse options,” said Leonie Huddy, a professor at Stony Brook University and author of the survey report.

The telephone survey of 1,561 adults in the tri-state area was done over landlines and cellphones, with a margin of error of 4.3 percentage points. The report focused on Long Islanders’ opinions, but it also included responses from other New York City suburbs for comparison.

To be sure, many Long Islanders voice concerns about multifamily construction. Even supporters of such large-scale development say it needs to be handled with care. Multifamily housing can attract and retain workers, generate jobs and increase tax revenue, said Lawrence Levy, executive dean of Hofstra University’s National Center for Suburban Studies, but “it needs to be green, affordable and not contribute to existing congestion.”

But the survey appeared to show a shift in attitudes. “The concept of suburbia has changed,” said Ann Golob, director of the Long Island Index.

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The poll found that 72 percent of Island respondents said young people leaving is a very or extremely serious problem. By contrast, 44 percent of those in New Jersey and 50 percent of those in Connecticut and northern New York suburbs were equally concerned about young people leaving.

In Smithtown, Christie Ciserano, 26, lives in her parents’ finished basement while she saves up to move into an apartment of her own, preferably near downtown Bay Shore, Babylon or Smithtown. Many of her friends also live with their parents; others pay $1,000 a month for cramped basement apartments or live with multiple roommates.

Long Island “is a great place to live, but there aren’t a lot of options for us to come back to,” said Ciserano, who works as a marketing assistant.

Long Islanders of all ages expressed anxiety about housing costs, with 62 percent saying it was somewhat or very difficult to pay the rent or mortgage — nearly double the 35 percent who said that in 2003.

Centereach resident Richard Flood, 57, said he and his wife, Carla, are considering moving to a less-expensive locale — possibly the Dakotas — and will seek out a condominium or town house so they won’t have to worry about the hassle and expense of home maintenance. “My sister went into a condo and it’s the best thing she ever did,” Flood said. “I said to my wife, if we stayed on Long Island, I’d look for a condo here.”