DALLAS >> A big drop in customer complaints helped U.S. airlines post their best ratings ever even though more flights were late and more bags were mishandled, according to a report released Monday by university researchers.

Virgin America topped the ratings, and three regional airlines scored at the bottom.

Among the four biggest airlines, Delta ranked best followed by Southwest, American and United, according to researchers from Wichita State University and Embry-Riddle Aeronautical University.

The researchers have graded airlines since 1991 on government figures for on-time performance, mishandled bags, bumping passengers, and complaints filed with the U.S. Department of Transportation.

Their key findings:

ON-TIME PERFORMANCE: Airlines operated 78.4 percent of their flights on time in 2013, down from 81.8 percent in 2012. Best: Hawaiian Airlines; worst: American Eagle. Only two airlines improved: American Airlines and United.

BAG HANDLING: The rate of lost, stolen or delayed bags rose 5 percent. Best: Virgin America; worst: American Eagle.

BUMPING: The rate of bumping passengers from flights fell 8 percent. Best: JetBlue Airways; worst: SkyWest.

COMPLAINTS: Consumer complaints to the government dropped 15 percent in 2013 after rising 20 percent the year before. Best: Southwest Airlines; worst: Frontier.

One of the report’s authors, Wichita State business professor Dean Headley, credited the drop in complaints partly to United Airlines. The company suffered several computer-network outages and grounded hundreds of flights in 2012 when it combined the United and Continental computer networks after a merger, but "got their act together" in 2013, he said.

Headley said the drop in complaints might also reflect "a certain amount of resignation" that "it’s never wonderful for airline passengers."

It’s not clear that the researchers captured the mood of travelers. No matter how much people gripe about airlines, very few of the millions of fliers ever bother to file a complaint with the government. The Department of Transportation, or DOT, received just 9,684 complaints last year after getting 11,447 in 2012.

Chris Lopinto, CEO of ExpertFlyer.com and not involved in the academic report, said he believes that most consumers complain directly to the airlines instead.

"The DOT can’t comp you miles or comp you a voucher — only the airlines can do that," Lopinto said. "A passenger might not think to file with DOT."

Most of the worst grades — from late flights and lost bags to bumping passengers off planes — were earned by smaller regional airlines. In the overall standings, American Eagle, the regional affiliate of American Airlines, finished last, just ahead of SkyWest and ExpressJet, which operate regional flights for United and Delta.

Regional airlines fly smaller planes, their flights are the first to be canceled in bad weather, and they operate at smaller airports that might lack the maintenance capability of bigger airports. However, they have become critical to the so-called hub-and-spoke system that United, American and Delta use to connect passengers to flights at big "hub" airports.

"If you have hubs, you need spokes or the wheel doesn’t work," Headley said.