title: Testing the Proportional Odds Assumption in R
body: <p>I am working in R with a response variable that is the letter grade the student received in a specific course.  The response is ordinal, and, in my opinion, seems logically proportional.
  My understanding is that I need to test that it is proportional before I can use polr() instead of multinom().</p>
  
  <p>For one of my courses of data, I "tested" the proportionality like this:</p>
  
  <pre><code>M1 &lt;- logLik(polrModel)  #'log Lik.' -1748.180691 (df=8)
  M2 &lt;- logLik(multinomModel)  #'log Lik.' -1734.775727 (df=20)
  G &lt;- -2*(M1$1 - M2$2)) #I used a block bracket here in the real code
  # 26.8099283
  pchisq(G,12,lower.tail = FALSE) #DF is #of predictors
  #0.008228890393     #THIS P-VAL TELLS ME TO REJECT PROPORTIONAL
  </code></pre>
  
  <p>For a second way of testing the proportional odds assumption, I also ran two vglm models, one with <code>family=cumulative(parallel =TRUE)</code> the other with <code>family=cumulative(parallel =FALSE)</code>.  I then ran a <code>pchisq()</code> test with the difference of the models' deviances and the differences of the residual degrees of freedom.  </p>
  
  <p>Is either of these way respectable?   If not, I would love help with the actual coding for determining whether to accept or reject the proportional odds assumption!</p>
  
  <p>In addition to the above two tests, I graphed my cumulative probabilities against each of the predictors, individually.  I read that I want these lines to be parallel.  What I don't understand is, with <code>polr()</code> your output is a single slope for each independent variable (a coefficient) and then a specific intercept depending on which cumulative probability you are working with (ex:  P(Y&lt;=A), P(Y&lt;=B), etc).  So, if your slope coefficients are all the same for each of the equations, how could the lines not be parallel?</p>
  
  <p>I picked up the basics of my knowledge on Chris Bilder's YouTube class; he talks about the parallel graphs <a href="https://youtu.be/qa5k_PwP6Yg?t=41m59s" rel="noreferrer">here at minute 42</a>.</p>
  
  <p>Any help is appreciated!
  Thank you!</p>