Compute MNP Probabilities

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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

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mnpProb(beta, Sigma, X, r)

Arguments

beta

MNP coefficients

Sigma

Covariance matrix of latents

X

X array for one observation – use createX to make

r

number of draws used in GHK (def: 100)

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.

Value

p x 1 vector of choice probabilites

Author(s)

Peter Rossi, Anderson School, UCLA, perossichi@gmail.com.

References

For further discussion, see Bayesian Statistics and Marketing by Rossi,Allenby and McCulloch, Chapters 2 and 4.
http://www.perossi.org/home/bsm-1

See Also

rmnpGibbs, createX

Examples

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##
## 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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