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 and Sigma parameters. Uses the GHK method to compute choice probabilities. To simulate a distribution of probabilities, loop over the beta and 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 Chapters 2 and 4, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.

rmnpGibbs, createX

### Examples

## example of computing MNP probabilites
## here Xa has 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, 0.5, 0.5, 1), ncol=2)

mnpProb(beta, Sigma, X)


[Package bayesm version 3.1-6 Index]