mnpProb {bayesm} | R Documentation

## 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` | 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, Graduate School of Business, University of Chicago, Peter.Rossi@ChicagoGsb.edu.

### References

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

### See Also

`rmnpGibbs`, `createX`

### Examples

    ##
    ## 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)

[Package bayesm version 2.0-8 Index]