Stocks closed broadly higher. Retail and industrial shares made the biggest gains, lifted by company earnings, some good news about China’s economy, and hope that Japan’s struggling economy will get another boost. Major indexes were higher all day and nearly matched the big gains on Friday, when the S&P 500 rose 2 percent. US markets were closed Monday. Stocks traded higher even though the price of oil slumped again. Investors were skeptical that OPEC will back a deal to freeze production, so US crude sank after a big rally on Friday. ADT surged after it accepted a buyout offer from Apollo Global worth $42 per share, or $6.94 billion. Its stock rose 47.5 percent; Apollo Global added 5.4 percent. Hormel had its best day in almost seven years on stronger-than-expected profit. It climbed 7.1 percent and is up 60 percent in the last year. Hospital stocks tumbled as Community Health said admissions fell; its shares plunged 22.1 percent. Groupon was up 41.2 percent after Alibaba said it had taken a 5.6 percent stake in the company. Groupon jumped 29 percent Friday after it reported earnings but the stock is still way down over the past year.