xtmlogit constraints

[Oivind Nilsen]

How to use constraints with xtmlogit?

I try to put constraints on the variance of the random effects in the xtmlogit command. I either get error r(111) or r(133). How should it be actually written?

Best,

Oivind A Nilsen

. use https://www.stata-press.com/data/r17/estatus
. xtset id

. qui xtmlogit estatus i.hhchild age hhincome i.hhsigno i.bwinner
. lincom _b[/:var(u1)]
( 1) [/]var(u1) = 0
------------------------------------------------------------------------------
estatus | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | .8587807 .1090216 7.88 0.000 .6451022 1.072459
------------------------------------------------------------------------------

. lincom _b[/:var(u2)]
( 1) [/]var(u2) = 0
------------------------------------------------------------------------------
estatus | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | .7370366 .1388917 5.31 0.000 .4648138 1.009259
------------------------------------------------------------------------------

. lincom _b[/:var(u1)] - _b[/:var(u2)]
( 1) [/]var(u1) - [/]var(u2) = 0
------------------------------------------------------------------------------
estatus | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
(1) | .1217441 .1693622 0.72 0.472 -.2101996 .4536879
------------------------------------------------------------------------------

. constraint 1 _b[/:var(u1)] = _b[/:var(u2)]
. constraint 2 var(u1) = var(u2)

. xtmlogit estatus i.hhchild age hhincome i.hhsigno i.bwinner, re constraint(1)
(note: constraint number 1 caused error r(111))
:
:

. xtmlogit estatus i.hhchild age hhincome i.hhsigno i.bwinner, re constraint(2)
(note: constraint number 2 caused error r(133))
:
:

[Andrew Musau]

Look at the -covariance()- option:

use https://www.stata-press.com/data/r17/estatus
xtset id
xtmlogit estatus i.hhchild age hhincome i.hhsigno i.bwinner, cov(identity)

Res.:

. xtmlogit estatus i.hhchild age hhincome i.hhsigno i.bwinner, cov(identity)

Fitting comparison model ...

Refining starting values:

Grid node 0:   log likelihood = -4483.1721
Grid node 1:   log likelihood = -4516.6753

Fitting full model:

Iteration 0:   log likelihood = -4483.1721  
Iteration 1:   log likelihood = -4470.6708  
Iteration 2:   log likelihood = -4469.0996  
Iteration 3:   log likelihood = -4469.0937  
Iteration 4:   log likelihood = -4469.0937  

Random-effects multinomial logistic regression  Number of obs     =      4,761
Group variable: id                              Number of groups  =        800

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          5
                                                              avg =        6.0
                                                              max =          7

Integration method: mvaghermite                 Integration pts.  =          7

                                                Wald chi2(10)     =     237.67
Log likelihood  = -4469.0937                    Prob > chi2       =     0.0000

 ( 1)  [/]var(u1) - [/]var(u2) = 0
------------------------------------------------------------------------------------
           estatus | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------------+----------------------------------------------------------------
Out_of_labor_force |
           hhchild |
              Yes  |   .4594018   .0955743     4.81   0.000     .2720795     .646724
               age |  -.0048037   .0065878    -0.73   0.466    -.0177156    .0081081
          hhincome |  -.0046924   .0018168    -2.58   0.010    -.0082532   -.0011315
                   |
           hhsigno |
              Yes  |   .4940244   .0942887     5.24   0.000      .309222    .6788268
                   |
           bwinner |
              Yes  |  -.4725241   .0725275    -6.52   0.000    -.6146754   -.3303729
             _cons |  -.4714592   .2823061    -1.67   0.095    -1.024769    .0818507
-------------------+----------------------------------------------------------------
Unemployed         |
           hhchild |
              Yes  |  -.0396524    .120952    -0.33   0.743     -.276714    .1974092
               age |   .0044433   .0083021     0.54   0.593    -.0118285    .0207151
          hhincome |   -.031131   .0026716   -11.65   0.000    -.0363672   -.0258947
                   |
           hhsigno |
              Yes  |   .0955353    .119958     0.80   0.426    -.1395781    .3306487
                   |
           bwinner |
              Yes  |    -.22569   .0957551    -2.36   0.018    -.4133666   -.0380133
             _cons |  -.1076647    .355049    -0.30   0.762     -.803548    .5882186
-------------------+----------------------------------------------------------------
Employed           |  (base outcome)
-------------------+----------------------------------------------------------------
            var(u1)|   .8180218   .0890205                      .6608967    1.012503
            var(u2)|   .8180218   .0890205                      .6608967    1.012503
------------------------------------------------------------------------------------
LR test vs. multinomial logit: chibar2(01) = 224.80   Prob >= chibar2 = 0.0000

.

[Oivind Nilsen]

Thanks, Andrew. My questions was really more general. Sorry for not being precise. How to specify a constraint that involve either the two var - var(u1) and var(u2), or the cov(u1,u2) if I had first estimated a xtmlogit.., covariance(unstructured), and then want to run a new xtmlogit based with these new constraints? I'm not able to include constraints based on either the var() or cov().

[Joseph Coveney]

I'm not able to include constraints based on either the var() or cov().

It seems to be a bug. I recommend taking it up with StataCorp's Technical Support

In the meantime, you can use gsem.

version 17.0

clear *

quietly use https://www.stata-press.com/data/r17/estatus

quietly gsem ///
    (2.estatus <- i.hhchild c.age c.hhincome i.hhsigno i.bwinner M1[id]) ///
    (3.estatus <- i.hhchild c.age c.hhincome i.hhsigno i.bwinner M2[id]), ///
        mlogit ///
            covariance(M1[id]*M2[id]@0)
estimates store Unconstrained

*
* Begin here
*
constraint define 1 _b[/var(M1[id])] = _b[/var(M2[id])]

gsem ///
    (2.estatus <- i.hhchild c.age c.hhincome i.hhsigno i.bwinner M1[id]) ///
    (3.estatus <- i.hhchild c.age c.hhincome i.hhsigno i.bwinner M2[id]), ///
        mlogit ///
            covariance(M1[id]*M2[id]@0) ///
            constraints(1) ///
                nocnsreport nodvheader nolog
lrtest Unconstrained

exit

[Oivind Nilsen]

Thanks, Joseph. How do I contact the TechSupport?

[Andrew Musau]

Thanks, Andrew. My questions was really more general. Sorry for not being precise. How to specify a constraint that involve either the two var - var(u1) and var(u2), or the cov(u1,u2) if I had first estimated a xtmlogit.., covariance(unstructured), and then want to run a new xtmlogit based with these new constraints? I'm not able to include constraints based on either the var() or cov().

I don't think the command will allow you to do that as the covariance options imply some form of constraint on the variances for the random effects.

vartype Description
------------------------------------------------------------------------------------------------
independent distinct variances for each random effect and all covariances 0;
the default
shared one common random effect
identity equal variances for random effects and all covariances 0
exchangeable equal variances for random effects and one common pairwise
covariance
unstructured all variances and covariances to be distinctly estimated

But let's see what Tech Support have to say. Follow https://www.stata.com/support/tech-support/contact/ in contacting them and have your license information ready. Also post back with any replies.

[Joerg Luedicke (StataCorp)]

Hi all, Oivind has uncovered a bug that we will fix in a future update. In the meantime, constraints on variance components can be specified by adding a period after the u in the variance component handle. For example:

. use https://www.stata-press.com/data/r17/estatus
(Fictional employment status data)

. xtset id

Panel variable: id (unbalanced)

. constraint 1 _b[/:var(u.1)] = _b[/:var(u.2)]

. xtmlogit estatus i.hhchild age hhincome i.hhsigno i.bwinner, re constraint(1)

Fitting comparison model ...

Refining starting values:

Grid node 0:   log likelihood = -4483.1721
Grid node 1:   log likelihood = -4516.6753

Fitting full model:

Iteration 0:   log likelihood = -4483.1721  
Iteration 1:   log likelihood = -4470.6708  
Iteration 2:   log likelihood = -4469.0996  
Iteration 3:   log likelihood = -4469.0937  
Iteration 4:   log likelihood = -4469.0937  

Random-effects multinomial logistic regression       Number of obs    =  4,761
Group variable: id                                   Number of groups =    800

Random effects u_i ~ Gaussian                        Obs per group:
                                                                  min =      5
                                                                  avg =    6.0
                                                                  max =      7

Integration method: mvaghermite                      Integration pts. =      7

                                                     Wald chi2(10)    = 237.67
Log likelihood = -4469.0937                          Prob > chi2      = 0.0000

 ( 1)  [/]var(u1) - [/]var(u2) = 0
------------------------------------------------------------------------------
     estatus | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
Out_of_lab~e |
     hhchild |
        Yes  |   .4594018   .0955743     4.81   0.000     .2720795     .646724
         age |  -.0048037   .0065878    -0.73   0.466    -.0177156    .0081081
    hhincome |  -.0046924   .0018168    -2.58   0.010    -.0082532   -.0011315
             |
     hhsigno |
        Yes  |   .4940244   .0942887     5.24   0.000      .309222    .6788268
             |
     bwinner |
        Yes  |  -.4725241   .0725275    -6.52   0.000    -.6146754   -.3303729
       _cons |  -.4714592   .2823061    -1.67   0.095    -1.024769    .0818507
-------------+----------------------------------------------------------------
Unemployed   |
     hhchild |
        Yes  |  -.0396524    .120952    -0.33   0.743     -.276714    .1974092
         age |   .0044433   .0083021     0.54   0.593    -.0118285    .0207151
    hhincome |   -.031131   .0026716   -11.65   0.000    -.0363672   -.0258947
             |
     hhsigno |
        Yes  |   .0955353    .119958     0.80   0.426    -.1395781    .3306487
             |
     bwinner |
        Yes  |    -.22569   .0957551    -2.36   0.018    -.4133666   -.0380133
       _cons |  -.1076647    .355049    -0.30   0.762     -.803548    .5882186
-------------+----------------------------------------------------------------
Employed     |  (base outcome)
-------------+----------------------------------------------------------------
      var(u1)|   .8180218   .0890205                      .6608967    1.012503
      var(u2)|   .8180218   .0890205                      .6608967    1.012503
------------------------------------------------------------------------------

I hope this helps, we apologize for the inconvenience.

Joerg

[Oivind Nilsen]

Great. Thanks. This might be helpful when one is searching for starting values. Best regards, Øivind