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Quantities of Interest

• The expected values (qi$ev) for the multinomial logistics regression model are the predicted probability of belonging to each category:
  
  
  and
  
  
  given the posterior draws of for all categories from the MCMC iterations.

• The predicted values (qi$pr) are the draws of from a multinomial distribution whose parameters are the expected values(qi$ev) computed based on the posterior draws of $\beta$ from the MCMC iterations.

• The first difference (qi$fd) in category $j$ for the multinomial logistic model is defined as
  
  
  

• The risk ratio (qi$rr) in category $j$ is defined as
  
  
  

• In conditional prediction models, the average expected treatment effect (qi$att.ev) for the treatment group in category $j$ is
  
  
  where is a binary explanatory variable defining the treatment () and control () groups, and is the number of treated observations in category $j$.

• In conditional prediction models, the average predicted treatment effect (qi$att.pr) for the treatment group in category $j$ is
  
  
  where is a binary explanatory variable defining the treatment () and control () groups, and is the number of treated observations in category $j$.