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
}
]