# [R] Multi-variate Probit model using Bayesm in R

Date: Thu, 21 Jun 2007 10:37:46 -0400

Hello,

I have built a multi-variate probit model using the package "bayesm", which requires that the X data is constructed using the function "CreateX". I've gone through the documentation and run my model, but wanted to be sure about my interpretation of the results for the coefficients - beta.

Steps:
1) I have 5 choices for the dependent variable Y, so p=5 2) I have 8 covariates, so the x data I read in has n rows (n=no. of respondents) and 8 columns. As follows:

[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] -3.202 0.583 0.026 0.398 -0.117 2.250 1.521 0

3) when I use CreateX (setting INT=TRUE and DIFF=FALSE) I get a matrix of n*5 rows and 36 columns.

```          [,1] [,2] [,3] [,4]   [,5]     [,6]      [,7]   [,8]       [,9]
[,10]    [,11]   [,12]  [,13]     [,14]   [,15]     [,16]  [,17]   [,18]
```

[1,] 1 0 0 0 -3.202 0.000 0.000 0.000 0.583 0.000 0.000
0.000 0.026 0.000 0.000 0.000 0.398 0.000

[2,] 0 1 0 0 0.000 -3.202 0.000 0.000 0.000 0.583 0.000
0.000 0.000 0.026 0.000 0.000 0.000 0.398

[3,] 0 0 1 0 0.000 0.000 -3.202 0.000 0.000 0.000 0.583
0.000 0.000 0.000 0.026 0.000 0.000 0.000

[4,] 0 0 0 1 0.000 0.000 0.000 -3.202 0.000 0.000
0.000 0.583 0.000 0.000 0.000 0.026 0.000 0.000

[5,] 0 0 0 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000

```           [,19]  [,20]    [,21]    [,22]    [,23]  [,24]     [,25]
[,26]     [,27]   [,28]    [,29]   [,30]    [,31]  [,32] [,33] [,34] [,35]

[1,]  0.000  0.000 -0.117  0.000  0.000  0.000  2.250  0.000  0.000

0.000  1.521  0.000  0.000  0.000     0     0     0

[2,]  0.000  0.000  0.000 -0.117  0.000  0.000  0.000  2.250  0.000

0.000  0.000  1.521   0.000  0.000     0     0     0

[3,]  0.398  0.000  0.000  0.000 -0.117  0.000  0.000  0.000  2.250

0.000  0.000  0.000  1.521  0.000     0     0     0

[4,]  0.000  0.398  0.000  0.000  0.000 -0.117  0.000  0.000  0.000

2.250  0.000  0.000  0.000  1.521     0     0     0

[5,]  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000

0.000  0.000  0.000  0.000  0.000     0     0     0
[,36]

[1,]     0

[2,]     0
[3,]     0
[4,]     0
[5,]     0

```

4) My understanding is that the first four columns are the intercepts for the first four choices of y, and the value of each covariate is replicated in four columns (diagonal values) to correspond to the first four choices of y. Every 5th row is 0. This pattern is repeated for all n respondents. Does this mean for the FIFTH customer choice - there is NO calculation done??

5) Once I run rmvpgibbs with this data structure, my "betadraw" output summary is of 36 variables (showing the first 11):

mean std dev num se rel eff s size 1 -2.999 3.32 0.216 77 234 2 -20.62 5.3 0.514 170 106 3 -17.973 2.87 0.276 166 108 4 -14.595 5.1 0.505 177 102 5 2.551 2.13 0.165 109 165 6 -0.235 1.11 0.071 74 240 7 -0.772 0.78 0.061 110 162 8 0.917 0.89 0.061 86 209 9 -1.329 1.58 0.1 72 247 10 1.002 1.05 0.074 89 200 11 0.108 0.66 0.052 111 161 QUESTIONS:

1. To interpret these results, my understanding is that "1"-"4" correspond to the intercepts for the first four customer choices. Similarly "5"-"9" correspond to the beta coefficient of the first covariate for the first four customer choices and so on. Hence, I have NOTHING for the 5th customer choice. Now I have set DIFF=FALSE in CreateX, but even then it looks like the interpretation is w.r.t. to the beta coefficients of the fifth customer choice as Zero. Is this correct??
2. In the summary of out\$betadraw, can somebody please tell me - what is "num se" "rel eff" and "s size"??
3. The beta output is not identified. For identification, I should divide all the outputs for channel 1 with sigma(1,1) and so on....Is this correct??

Really appreciate whatever help I can get for the MVP model.

Thanks a lot,
Regards,
Mahima

```--
PhD Student, Marketing
Penn State University

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