Dominance analysis and Multilevel modeling

[Vincent Leroy]

Hello everyone,

I am a PhD student in Economics and for my first paper I want to use the "domin" command on Stata in order to analyse the relative importance of some predictors present in my regression.
My regression model is a multilevel linear mixed effect (mixed dep-var indep-var id || country, mle). My group/id variable is "country". I have 2 level, individual data as level-1, country data as level-2.

But I have several questions :

• Knowing that I am using a multilevel model, should I specify it in the domin command? Here is what I did : domin dep-var indep-var, reg(mixdom, id(country)) fitstat(e(r2_b)). Is it okay to do that way for a multilevel model? I am a bit concerned about the fitstat which is using a "basic" R2.
• Second, I have several control variables in my model and I wanted to know if the domin command could provide me results only for my outcome variables, i.e take into account the control variables in the computaion, but give me Standardized domin stat for my outcome variables only.

Thanks a lot.

[Joseph Luchman]

Hi Vincent,

• Knowing that I am using a multilevel model, should I specify it in the domin command? Here is what I did : domin dep-var indep-var, reg(mixdom, id(country)) fitstat(e(r2_b)). Is it okay to do that way for a multilevel model? I am a bit concerned about the fitstat which is using a "basic" R2.

For a two-level model like you are describing the -mixdom- wrapper you have been working with should apply.

Below is an example of a call to -mixed- as well as that same model applied in a call to -domin-.

. webuse nlswork
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)


. mixed ln_w grade collgrad ttl_exp tenure || id:

Performing EM optimization ...

Performing gradient-based optimization: 
Iteration 0:   log likelihood = -9508.2454  
Iteration 1:   log likelihood = -9508.2454  

Computing standard errors ...

Mixed-effects ML regression                     Number of obs     =     28,099
Group variable: idcode                          Number of groups  =      4,697
                                                Obs per group:
                                                              min =          1
                                                              avg =        6.0
                                                              max =         15
                                                Wald chi2(4)      =    7489.38
Log likelihood = -9508.2454                     Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       grade |   .0655755   .0027717    23.66   0.000      .060143     .071008
    collgrad |   .0730434   .0173449     4.21   0.000      .039048    .1070389
     ttl_exp |   .0242793   .0006444    37.68   0.000     .0230163    .0255422
      tenure |   .0146276   .0008379    17.46   0.000     .0129854    .0162698
       _cons |   .6327172   .0327579    19.31   0.000     .5685129    .6969215
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects parameters  |   Estimate   Std. err.     [95% conf. interval]
-----------------------------+------------------------------------------------
idcode: Identity             |
                  var(_cons) |    .071839   .0019568      .0681042    .0757785
-----------------------------+------------------------------------------------
               var(Residual) |   .0878893   .0008131        .08631    .0894974
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 8552.46       Prob >= chibar2 = 0.0000

. domin ln_w grade collgrad ttl_exp tenure, reg(mixdom, id(id)) fitstat(e(r2_b))

Total of 15 sub-models

General dominance statistics: Mixed-effects ML regression
Number of obs             =                   28099
Overall Fit Statistic     =                  0.4253

            |      Dominance      Standardized      Ranking
 ln_wage    |      Stat.          Domin. Stat.
------------+------------------------------------------------------------------------
 grade      |         0.1721      0.4047            1 
 collgrad   |         0.0896      0.2107            3 
 ttl_exp    |         0.0934      0.2196            2 
 tenure     |         0.0702      0.1650            4 
-------------------------------------------------------------------------------------
Conditional dominance statistics
-------------------------------------------------------------------------------------

           #indepvars:  #indepvars:  #indepvars:  #indepvars:
                    1            2            3            4
   grade       0.3196       0.1875       0.1165       0.0649
collgrad       0.2072       0.1018       0.0474       0.0021
 ttl_exp       0.2085       0.0980       0.0486       0.0185
  tenure       0.1564       0.0715       0.0382       0.0145
-------------------------------------------------------------------------------------
Complete dominance designation
-------------------------------------------------------------------------------------

                      dominated?:  dominated?:  dominated?:  dominated?:
                           grade     collgrad      ttl_exp       tenure
   dominates?:grade            0            1            0            0
dominates?:collgrad           -1            0            0            0
 dominates?:ttl_exp            0            0            0            1
  dominates?:tenure            0            0           -1            0
-------------------------------------------------------------------------------------

Strongest dominance designations

grade completely dominates collgrad
ttl_exp completely dominates tenure
grade conditionally dominates ttl_exp
grade conditionally dominates tenure
ttl_exp generally dominates collgrad
collgrad generally dominates tenure

I don't understand the comment regarding a "basic" R2. Please see the -mixdom- help file for more information on what the R2 values produced by -mixdom- are.

• Second, I have several control variables in my model and I wanted to know if the domin command could provide me results only for my outcome variables, i.e take into account the control variables in the computaion, but give me Standardized domin stat for my outcome variables only.

It is. Any variables put into the -all()- option are treated this way. -domin-'s helpfile and the companion Stata Journal article have examples of how this option is used.

- joe

[Vincent Leroy]

Hi Joseph,

This is great,

Thank you for your quick answers!