Also, I don't think it's a proven fact that Janice is based off Janis Joplin (that's how her name is spelled.)
Sure they share the same name, but Joplin was never really a "Valley" kind of girl like Janice (Muppets) more or less is, I think that has been discussed before.
Interesting fact is that when the Muppet character oh Janice was first thought of and drawn, she was going to be a male character based more on Mick Jagger. Her name could of been thought of because of Janis Joplin, however even if that is the case, she dosen't seem anything like the female rocker Janis Joplin, or for that matter, Mick Jagger.