mnpProb {bayesm}

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, [e-mail].

References

For further discussion, see Chapters 2 and 4, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.

See Also

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)