Rachel Bachman in The Oregonian has a nice article on home-field advantage in sports and how it is a bigger factor in MLS than in other major league sports. Andrew Patterson, a Las Vegas oddsmaker, claims that the data show that:
In the NHL, home ice alone is worth about a 3-4 percent advantage. In Major League Baseball, home field is worth 5-6 percent. In the NBA, homecourt is worth 7-8 percent. In the NFL, home field is 8-10 percent.
In MLS, home field generally gives teams a half-goal advantage, Patterson said.
"A half-goal is worth more than 10 percent," he said. "It's huge. It's really big."
Economists have studied home field advantage, perhaps most prominently in soccer, where research from Europe suggests that referees are influenced by home crowds. And there is also a literature that looks at sports betting behavior and whether such betting markets are efficient by adjusting prices to reflect such biases.
But as far as the particular advantage in soccer, I think it is less about the referees (there is no reason to believe that soccer referees are more or less influenced than in other sports I would suggest) but about the nature of the game of soccer with is a continuous flow with few substitutes. There is no stopping and starting and momentum plays a big role so the crowd can help get the team going earlier in games. Players also need to stay energized both mentally and physically for 90 minutes of almost constant running and the crowd can play a big role in keeping the players 'up' especially in the latter parts of the second half.