There are other selection effects, as well. If you have a large population of young, single males with poor employment prospects, there's not much to keep them attached to their home country. If all they have to do is walk across a border (which they can probably muster the resources to attempt, as opposed to a transcontinental voyage), then there's a huge pull to immigrate to the US. In a circumstance like this, there would be a selection effect for the least capable young men (since more capable young men with better prospects would stay behind).

In my opinion, this is probably what explains the vast divergence between the professions that immigrants from Latin American end up in vs. the professions that immigrants from Asia end up in.