I haven't tried to put all the pieces together yet to see if it's usable, but when I was trying to download submission data to include with Starfish, I inadvertently found quiz submission data. I didn't want it, it really slows things down, but there doesn't appear to be a way to not get it with the call I'm using.
If you fetch the submissions for an assignment and include[]=submission_history, then there is a property called submission_data that is included for quizzes.
It is an array with one element for each question. Here's what it looks like for one of my recent quizzes with 4 questions composed of multiple-drop downs.
"submission_data": [{ "correct": "partial", "points": 1.5, "question_id": 90432031, "text": "", "answer_for_tail": 25196, "answer_id_for_tail": 25196, "answer_for_distribution": 61563, "answer_id_for_distribution": 61563, "answer_for_method": 19986, "answer_id_for_method": 19986, "answer_for_conclusion": 10295, "answer_id_for_conclusion": 10295, "answer_for_claim": 13208, "answer_id_for_claim": 13208, "answer_for_groups": 28251, "answer_id_for_groups": 28251, "answer_for_type": 87115, "answer_id_for_type": 87115, "answer_for_ci": 15394, "answer_id_for_ci": 15394 }, { "correct": "partial", "points": 1.5, "question_id": 90432027, "text": "", "answer_for_evidence": 24718, "answer_id_for_evidence": 24718, "answer_for_groups": 4707, "answer_id_for_groups": 4707, "answer_for_action": 5303, "answer_id_for_action": 5303, "answer_for_method": 86834, "answer_id_for_method": 86834, "answer_for_mu": 44212, "answer_id_for_mu": 44212, "answer_for_distribution": 98118, "answer_id_for_distribution": 98118, "answer_for_result": 68307, "answer_id_for_result": 68307, "answer_for_pvalue": 64708, "answer_id_for_pvalue": 64708, "answer_for_type": 475, "answer_id_for_type": 475, "answer_for_tail": 5003, "answer_id_for_tail": 5003 }, { "correct": "partial", "points": 1.5, "question_id": 90432040, "text": "", "answer_for_groups": 55434, "answer_id_for_groups": 55434, "answer_for_method": 69146, "answer_id_for_method": 69146, "answer_for_mu": 29235, "answer_id_for_mu": 29235, "answer_for_distribution": 67257, "answer_id_for_distribution": 67257, "answer_for_conclusion": 99253, "answer_id_for_conclusion": 99253, "answer_for_pvalue": 55570, "answer_id_for_pvalue": 55570, "answer_for_tail": 36563, "answer_id_for_tail": 36563, "answer_for_type": 61334, "answer_id_for_type": 61334 }, { "correct": "partial", "points": 2.25, "question_id": 90432039, "text": "", "answer_for_method": 34332, "answer_id_for_method": 34332, "answer_for_type": 69963, "answer_id_for_type": 69963, "answer_for_conclusion": 43630, "answer_id_for_conclusion": 43630, "answer_for_alternative": 65351, "answer_id_for_alternative": 65351, "answer_for_tail": 69714, "answer_id_for_tail": 69714, "answer_for_df": 49660, "answer_id_for_df": 49660, "answer_for_groups": 74851, "answer_id_for_groups": 74851, "answer_for_distribution": 62939, "answer_id_for_distribution": 62939 }]