multivariate probit model mvprobit: predict, xb vs predict, p

[Karl Yesler]

Hello Statalist,

I am using a mvprobit model and would like to obtain predicted probabilities post-estimation (I would use predict, p after probit). However, that option is unavailable after mvprobit. Only predict, xb is available. How would I obtain the predicted probabilities by hand? Thanks!

I illustrate below with some sample code:

use http://www.stata-press.com/data/r7/school.dta, clear

mvprobit (private = years logptax loginc) (vote = years logptax loginc)

mvppred ,xb

[Ariel Karlinsky]

mvprobit is a user added package (ado) - you shold mention it in the post.
also, from what I see was last updated in 2006... in your example, I see that the offical biprobit produces very similar, yet different results...

. mvprobit (private = years logptax loginc) (vote = years logptax loginc)

Iteration 0:   log likelihood = -89.946246  
Iteration 1:   log likelihood = -89.568527  
Iteration 2:   log likelihood = -89.567809  
Iteration 3:   log likelihood = -89.567809  

Multivariate probit (SML, # draws = 5)            Number of obs   =         95
                                                  Wald chi2(6)    =       9.01
Log likelihood = -89.567809                       Prob > chi2     =     0.1731

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
private      |
       years |  -.0089447   .0241705    -0.37   0.711     -.056318    .0384285
     logptax |  -.1018381    .667898    -0.15   0.879    -1.410894    1.207218
      loginc |   .3787381   .5363334     0.71   0.480    -.6724561    1.429932
       _cons |  -4.267809   4.852966    -0.88   0.379    -13.77945    5.243828
-------------+----------------------------------------------------------------
vote         |
       years |  -.0160871   .0146924    -1.09   0.274    -.0448837    .0127095
     logptax |  -1.260877   .5696835    -2.21   0.027    -2.377437   -.1443183
      loginc |   .9744685   .4343956     2.24   0.025     .1230688    1.825868
       _cons |  -.4944369   4.053135    -0.12   0.903    -8.438436    7.449562
-------------+----------------------------------------------------------------
    /atrho21 |  -.1729528   .2009747    -0.86   0.389     -.566856    .2209503
-------------+----------------------------------------------------------------
       rho21 |  -.1712487   .1950809    -0.88   0.380    -.5130465    .2174236
------------------------------------------------------------------------------
Likelihood ratio test of  rho21 = 0:  
             chi2(1) =  .756875   Prob > chi2 = 0.3843

. biprobit private vote years logptax loginc

Fitting comparison equation 1:

Iteration 0:   log likelihood = -31.967097  
Iteration 1:   log likelihood = -31.452424  
Iteration 2:   log likelihood = -31.448958  
Iteration 3:   log likelihood = -31.448958  

Fitting comparison equation 2:

Iteration 0:   log likelihood = -63.036914  
Iteration 1:   log likelihood = -58.534843  
Iteration 2:   log likelihood = -58.497292  
Iteration 3:   log likelihood = -58.497288  

Comparison:    log likelihood = -89.946246

Fitting full model:

Iteration 0:   log likelihood = -89.946246  
Iteration 1:   log likelihood = -89.258897  
Iteration 2:   log likelihood = -89.254028  
Iteration 3:   log likelihood = -89.254028  

Bivariate probit regression                     Number of obs     =         95
                                                Wald chi2(6)      =       9.59
Log likelihood = -89.254028                     Prob > chi2       =     0.1431

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
private      |
       years |  -.0118884   .0256778    -0.46   0.643    -.0622159    .0384391
     logptax |  -.1066962   .6669782    -0.16   0.873    -1.413949    1.200557
      loginc |   .3762037   .5306484     0.71   0.478     -.663848    1.416255
       _cons |  -4.184694   4.837817    -0.86   0.387    -13.66664    5.297253
-------------+----------------------------------------------------------------
vote         |
       years |  -.0168561   .0147834    -1.14   0.254    -.0458309    .0121188
     logptax |  -1.288707   .5752266    -2.24   0.025    -2.416131   -.1612839
      loginc |    .998286   .4403565     2.27   0.023     .1352031    1.861369
       _cons |  -.5360573   4.068509    -0.13   0.895    -8.510188    7.438073
-------------+----------------------------------------------------------------
     /athrho |  -.2764525   .2412099    -1.15   0.252    -.7492153    .1963102
-------------+----------------------------------------------------------------
         rho |  -.2696186   .2236753                     -.6346806    .1938267
------------------------------------------------------------------------------
LR test of rho=0: chi2(1) = 1.38444                       Prob > chi2 = 0.2393

[Karl Yesler]

Thanks for the points Ariel, I think the results may be different since mvprobit uses maximum simulated likelihood while biprobit uses simulated likelihood. Regardless, how might I use the post-estimation
mvppred ,xb to calculate the predicted probability of success for each regression?

[Stephen Jenkins]

The results differ for Ariel mostly because he used only 5 draws (a deliberately low default for code checking). Predictions can be derived using -mvppred-, as described in the help file and SJ article.

[Karl Yesler]

Thanks Stephen, for the clarification. But apologies, I did read the help file and article. I only saw the -mvppred-, options of xb stdp pmarg pall; not -mvppred-, p. As you allude, is there a way to derive the predicted probability of success for each regression?

[Stephen Jenkins]

There is confusion on my side or yours about what you really want.

You refer to "the predicted probability of success for each regression". The "pmarg" and "pall" options produce predicted marginal and joint probabilities, respectively. As described in the help file, the joint probabilities refer to the probability that each binary outcome = 1, or that each binary outcome = 0. If you want different predicted joint probabilies (not all ones, or all zeros), then you'll need to adapt the code in the SJ 2006, 6(2), article.

[Ariel Karlinsky]

The results differ for Ariel mostly because he used only 5 draws (a deliberately low default for code checking). Predictions can be derived using -mvppred-, as described in the help file and SJ article.

How can I control the number of draws?

[Stephen Jenkins]

The help file for mvprobit refers to the draws() option. Note also the aa option for antithetic acceleration. (Read about what this is in the associated literature.) Compare the following with your biprobit specification:

. mvprobit (private = years logptax loginc) (vote = years logptax loginc), draws(250) aa

Iteration 0:   log likelihood = -89.946246 
Iteration 1:   log likelihood = -89.250827 
Iteration 2:   log likelihood = -89.246771 
Iteration 3:   log likelihood = -89.246771 

Multivariate probit (MSL, # draws = 500)          Number of obs   =         95
                                                  Wald chi2(6)    =       9.60
Log likelihood = -89.246771                       Prob > chi2     =     0.1426

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
private      |
       years |  -.0118361   .0256661    -0.46   0.645    -.0621407    .0384685
     logptax |  -.1074413   .6668905    -0.16   0.872    -1.414523     1.19964
      loginc |   .3751873   .5305772     0.71   0.479    -.6647249    1.415099
       _cons |  -4.169592   4.838483    -0.86   0.389    -13.65284     5.31366
-------------+----------------------------------------------------------------
vote         |
       years |   -.016935   .0148044    -1.14   0.253     -.045951    .0120809
     logptax |  -1.289671   .5756035    -2.24   0.025    -2.417833   -.1615089
      loginc |   1.000896   .4408392     2.27   0.023      .136867    1.864925
       _cons |  -.5549375   4.069844    -0.14   0.892    -8.531686    7.421811
-------------+----------------------------------------------------------------
    /atrho21 |  -.2779082   .2412053    -1.15   0.249    -.7506618    .1948454
-------------+----------------------------------------------------------------
       rho21 |   -.270968   .2234951    -1.21   0.225    -.6355436    .1924165
------------------------------------------------------------------------------
Likelihood ratio test of  rho21 = 0: 
             chi2(1) =  1.39895   Prob > chi2 = 0.2369

[Ariel Karlinsky]

I thought the draws option was for biprobit, that's why I didn't find it. I didn't know about mvprobit until this thread

[Stephen Jenkins]

biprobit is a built-in command, and allows for 2 binary outcomes. Estimation uses the bivariate normal distribution for which there is a formula that Stata uses. mvprobit allows for more than 2 binary outcomes, but to do this m-variate normal distributions are evaluated by simulation methods. This, and relevant references, are in the help files and the 2 SJ articles by Cappellari-Jenkins 2003, and 2006 (both freely downloadable).

[Tau Zingwena]

I want to run an mvprobit model but the mvtest normality results reject the null hypothesis. Can i continue irregardless of non normality of the dependent variables