{
  "id": 1283,
  "title": "Reducing the bias in the baseline model",
  "url": "/competitions/WhatDoYouKnow/discussion/1283",
  "author_name": "",
  "post_date": "2012-01-18T14:29:50.790Z",
  "votes": null,
  "comment_count": 1,
  "views": 1709,
  "content": "<p>In my opinion the mixed effects model in the benchmark is an underfit for the item difficulty and the student ability parameters. This is because each student only answers a small subset of the questions in a track(or sub-track). So, the student vs question-answered\r\n matrix is highly sparse and might lead to a high bias estimate. I feel that the estimates could be more accurate, if you find dense sub-regions of the matrix and then apply the parameter estimation techniques within each sub-region. Has anyone tried something\r\n like this? Any thoughts?</p>",
  "messages": [
    {
      "id": "8158",
      "postDate": "01/18/2012 14:29:50",
      "content": "<p>In my opinion the mixed effects model in the benchmark is an underfit for the item difficulty and the student ability parameters. This is because each student only answers a small subset of the questions in a track(or sub-track). So, the student vs question-answered\r\n matrix is highly sparse and might lead to a high bias estimate. I feel that the estimates could be more accurate, if you find dense sub-regions of the matrix and then apply the parameter estimation techniques within each sub-region. Has anyone tried something\r\n like this? Any thoughts?</p>",
      "rawMarkdown": "",
      "votes": null
    },
    {
      "id": "8163",
      "postDate": "01/19/2012 01:04:13",
      "content": "<p>It's true that the average student skill estimate is likely less accurate than the average question difficulty estimate, but I think that's just a fact of the data.</p>\r\n<p>The mixed models such as lme4 do independent estimates of the relative accuracy from each coefficient group, so I don't see how this makes them &quot;high biased&quot;. In fact, the nature of mixed modeling with shrunken coefficients is all about trying to get just\r\n the right level of bias.</p>\r\n<p>Anyway, best of luck!</p>",
      "rawMarkdown": "",
      "votes": null
    }
  ],
  "comments": [
    {
      "id": 8163,
      "author_name": "biasvariance",
      "author_url": "",
      "post_date": "01/19/2012 01:04:13",
      "content": "<p>It's true that the average student skill estimate is likely less accurate than the average question difficulty estimate, but I think that's just a fact of the data.</p>\r\n<p>The mixed models such as lme4 do independent estimates of the relative accuracy from each coefficient group, so I don't see how this makes them &quot;high biased&quot;. In fact, the nature of mixed modeling with shrunken coefficients is all about trying to get just\r\n the right level of bias.</p>\r\n<p>Anyway, best of luck!</p>",
      "votes": null,
      "replies": []
    }
  ],
  "raw_markdown_by_id": {
    "8158": "",
    "8163": ""
  },
  "source": "meta"
}