Why is Queen Elizabeth a rolemodel to Shakespeare?

Queen Elizabeth was not a role model to Shakespeare. Shakespeare had no desire to base his life on hers. He did not want to wear wigs, paint his face white, wear dresses with incredibly wide hips or do anything that Elizabeth did.

She was the queen, of course, and there were laws about what you could write or perform that might offend her Majesty. But there is no reason to suppose that Shakespeare wrote anything with the queen specifically in mind. She (unlike her successor King James) was not his patron and he did not dedicate any works to her.