title: How to simulate the data I need for use in a multinomial logit model?
body: <p>I want to simulate data for use in a multinomial logit model. My model is based on customer choice and their preference and willingness to pay for certain delivery timeslots.</p>
  <p>I have done extensive research and have information on the following:</p>
  <ul>
  <li><p>The individual willingness to pay for a timeslot. These are:</p>
  <ul>
  <li>Full day: 66.1%</li>
  <li>Morning:  10.0%</li>
  <li>Afternoon: 20.5%</li>
  <li>Evening: 3.4%</li>
  </ul>
  </li>
  <li><p>The individual preference for a timeslot: These are:</p>
  <ul>
  <li>Full day: 42.9%</li>
  <li>Morning:  36.4%</li>
  <li>Afternoon: 14.3%</li>
  <li>Evening: 6.4%</li>
  </ul>
  </li>
  </ul>
  <p>Now what I would like run a simulation and create a dataset where: given a certain price, what was the customers choice of timeslot.</p>
  <p>Do I have enough data here to be able to run that simulation? How would I do this (I am proficient in Python and R, so if possible please using these tools)?</p>
  <p>I would finally like to run it in a multinomial logit model as shown below:</p>
  <p><a href="https://i.stack.imgur.com/Pu6h9.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Pu6h9.png" alt="enter image description here" /></a></p>
  <p>Where:</p>
  <ul>
  <li>\beta_0 = base utility across all options</li>
  <li>\beta_s = utility attributed to the slot itself (so the preference)</li>
  <li>\beta_d = sensitivity to the utility to the delivery costs</li>
  <li>d_s = the delivery costs</li>
  </ul>
  <p>Thanks in advance for all help.</p>