The researchers set out to answer a fairly simple question: are immigrants more or less prone to violent, criminal, or "antisocial" behaviors than native born Americans? Using the data collected by the National Epidemiologic Survey on Alcohol and Related Conditions interviews they were able to get a sample size large enough to answer their question. Here are their results displayed in graphic format:
As the figure suggests, our researchers found that:
"Across the board, the prevalence of antisocial behavior among native-born Americans was greater than that of immigrants. Particularly large differences were observed in terms of involvement in behaviors that could easily hurt oneself/others, truancy, staying out late without permission from one’s parents, quitting a job without having other options, shoplifting, and taking part in illegal behaviors that could get one arrested." 
While the few media pieces that show cased the study described it as turning "traditional theories on its head" , these results should not come as a surprise to those who have followed this issue closely. Over the last decade a host of studies have shown that Hispanic immigrants are less violent than the American whites and substantially less violent than the American blacks who share their income bracket . But this study does not limit itself to analysis of Hispanic immigrants:
Africans, it seems, are the most pro-social immigrants in America!
The most intriguing aspect of this study, however, barely made the press reports. To quote:
"In these analyses, we wanted to examine whether the age of immigration altered the relationship between immigrant status and nonviolent and violent antisocial behavior. We contrasted these relationships among individuals who had immigrated before the age of 13 and after the age of 13. Controlling for all the same factors presented in our main findings, immigrants who came to the United States at the age of 12 or younger were significantly more likely to report involvement in at least one of the violent (AOR=2.01, 95 % CI=1.87–2.15) or nonviolent (AOR=1.80, 95 % CI=1.71–1.89) antisocial behaviors as compared with immigrants who arrived at the age of 13 or older. However, when compared to native-born Americans, immigrants who arrived as children or arrived at the age of 13 or older are still significantly less likely to take part in violent and nonviolent antisocial behavior than Native-born Americans, though the latter group begins to somewhat resemble the native-born behaviorally. Finally, for all immigrants regardless of age, we estimated what each year in the US translates to with respect to an increased probability of reporting an antisocial act. Results showed that each additional year an immigrant has lived in the United States is associated with a 1.9 % increase in the likelihood of violence and a 0.9 % increase in the likelihood of nonviolent antisociality." In other words, immigrants are not making America a more criminal place. America makes her immigrants become more criminal people!
It is not uncommon for conservatives to bewail the many immigrants America has who have not properly assimilated into broader American culture. These concerns are not without merit. Yet when I think about assimilation my thoughts usually dwell upon on a slightly different problem. I remember well the many immigrant families I worked and lived with when I was a LDS missionary tramping across America's urban ghettos. So many immigrant mothers and fathers would let us in the door because they were worried about their children. They felt like their families were being torn apart, parents and children living in completely different worlds--and reflecting upon it now, it is not difficult to see why they felt this way. Particularly striking were the Haitian families whose parents took pride in their educated French but whose children could only speak the English of the ghetto.
Perhaps we should be less concerned with whether immigrants can assimilate into American culture and more concerned with which American culture immigrants are assimilating into.
EDIT (8 Jan 2013): see also Tyler Cohen's recent post on 'downward assimilation' among African immigrants for more research that echoes these themes.
 Michael G. Vaughn, Christopher P. Salas-Wright, Matt DeLisi, and Brandy R. Maynard. "The immigrant paradox: immigrants are less antisocial than native-born Americans." Social Psychiatry and Psychiatric Epidemiology. Vol. 48, Issue 11. 17 November 2013. p. 3.
 Emily Alpert Reyes, "Immigrants less prone to violence, 'antisocial' behavior, study says," Los Angles Times. 3 December 2013.
 For example: Matthew T. Lee and Ramiro Martinez, "Immigration reduces crime: an emerging scholarly consensus" in William F. Mcdonald (ed.) Immigration, Crime and Justice (Sociology of Crime Law and Deviance, Volume 13), (Bingely: Emerald Group Publishing Limited 2009), pp. 3-16; Casey T. Harris and Ben Feldmeyer, "Latino immigration and White, Black, and Latino violent crime: A comparison of traditional and non-traditional immigrant destinations," Social Science Research, Vol. 42, Issue 1(Jan 2013), pp. 202–216; Ron Unz, "Race and Crime in America," The American Conservative. 20 July 2013.
 Michael G. Vaughn, et. al., "The immigrant paradox," p. 7.