mnpProb computes MNP probabilities for a given X matrix corresponding to one
observation. This function can be used with output from
rmnpGibbs to simulate
the posterior distribution of market shares or fitted probabilties.
Covariance matrix of latents
X array for one observation – use
number of draws used in GHK (def: 100)
rmnpGibbs for definition of the model and the interpretation of
the beta, Sigma parameters. Uses the GHK method to compute choice probabilities.
To simulate a distribution of probabilities, loop over the beta, Sigma draws from
p x 1 vector of choice probabilites
Peter Rossi, Anderson School, UCLA, firstname.lastname@example.org.
For further discussion, see Bayesian Statistics and Marketing
by Rossi,Allenby and McCulloch, Chapters 2 and 4.
1 2 3 4 5 6 7 8
## ## example of computing MNP probabilites ## here I'm thinking of Xa as having the prices of each of the 3 alternatives Xa=matrix(c(1,.5,1.5),nrow=1) X=createX(p=3,na=1,nd=NULL,Xa=Xa,Xd=NULL,DIFF=TRUE) beta=c(1,-1,-2) ## beta contains two intercepts and the price coefficient Sigma=matrix(c(1,.5,.5,1),ncol=2) mnpProb(beta,Sigma,X)