mnpProb: Compute MNP Probabilities

Description

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.

Usage

mnpProb(beta, Sigma, X, r)

Arguments

beta

MNP coefficients

Sigma

Covariance matrix of latents

X array for one observation -- use createX to make

number of draws used in GHK (def: 100)

Value

p x 1 vector of choice probabilites

concept

MNP
Multinomial Probit Model
GHK
market share simulator

Details

see 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 rmnpGibbs output.

References

For further discussion, see Bayesian Statistics and Marketing by Rossi,Allenby and McCulloch, Chapters 2 and 4. http://faculty.chicagogsb.edu/peter.rossi/research/bsm.html

Examples

Run this code

##
## 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)

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