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.
http://www.perossi.org/home/bsm-1

`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 3.1-4 Index]