The Proportional Odds Model

• In SPSS and Stata, ``Ordinal Logistic Regression'' means the proportional odds model:
  
  $$log(\frac{\sum_{k=1}^{j}\pi_k}{1-\sum_{k=1}^{j}\pi_k}) = \alpha + \beta x$$
  
  

• This model is attractive for dependent variables whose ordinality can be seen as being based on an underlying continuous dimension, probably unobserved (Agresti, Ch 8.2)
• Thus it would be better suited to a Likert-style dependent variable, than, say, highest educational qualification

• The model estimates a set of $n-1$ ``cut-points'', dividing the sample into the $n$ ordinal categories; these can be considered as representing the ordinality of the categories on the underlying linear dimension (effectively in terms of the proportions above and below each binary comparison point)
• It then estimates a single $\beta$ for each independent variable, suggesting that the effect of independent variables is the same across the range: