"Assimilation is a process that takes place over time and over generations. They're not measuring that," he said.

In addition, Passel said that the snapshot of immigrant assimilation is weighed heavily toward new immigrants who are clearly going to be less integrated into the larger society. He added that the study fails to take into account that 30 percent of current immigrants are in the United States illegally, which is vastly different from a century ago.

The study also found:

• Immigrants from developed countries are not necessarily more assimilated. Immigrants born in Korea, which the World Bank classifies as a high-income country, have a lower level of assimilation than immigrants from Cuba or the Philippines, which are classified as low-income countries.

• San Diego has the highest assimilation rate among the 10 cities with the largest immigrant populations. New York City is second.