title: Building an attribution model
body: <p>My problem involves measuring the impact of four activities undertaken by a population of 1,000 individuals that is attempting to lose weight. </p>
  
  <p>The four activities are: (a) Eating healthy food; (b) Walking for an hour daily; (c) Meditation daily for 20-minutes; and (d) In-house physical exercise for 30-minutes.</p>
  
  <p>For the sake of simplicity, let us assume that there are 1,000 participants who signed up on January 1, 2015, and their weights were measured then. Furthermore, let us assume that they will diligently commit to doing the same activity for the entirety of a quarter (i.e., if they commit to eating healthy food in Q1 they don't undertake any other activity; however they may change the activity at the start of Q2 or choose to continue what they did in Q1).</p>
  
  <p>Finally, on December 31, 2015, I catch them before they head to Times Square to celebrate the onset of new year, and weigh them.</p>
  
  <p>So my table looks something like :</p>
  
  <blockquote>
    <p>Individual | Initial Weight | Q1 | Q2 | Q3 | Q4 | Final Weight</p>
    
    <p>A-1 | 183 | A | B | A | C | 176<br>
    A-2 | 265 | D | C | B | B | 223<br>
    A-3 | 331 | A | A | A | D | 322<br>
    .<br>
    .<br>
    A-1000 | 257 | D | B | C | A | 228</p>
  </blockquote>
  
  <p>My goal is to measure the impact of each activity's contribution to the weight loss across the population, keeping in mind that there is a distinct possibility that the order of activities undertaken could have an impact.</p>
  
  <p>( In my real problem one of complexities that I haven't spelt out is that instead of doing the same activity throughout the quarter, individuals would have actually done any of those activity on a daily basis.)</p>
  
  <p>Any thoughts would be appreciated.</p>