axmixlogit: get standard deviations of random variable

[Joost Verlaan]

I am estimating a -asmixlogit- model in Stata. I want to obtain the standard deviations of the random variables. A normal
-mixlogit- model returns the standard deviation as default, for example:

Mixed logit model                               Number of obs     =      4,728
                                                LR chi2(2)        =     346.99
Log likelihood = -1143.6588                     Prob > chi2       =     0.0000

------------------------------------------------------------------------------
      choice |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Mean         |
          td |   -.205917    .046748    -4.40   0.000    -.2975415   -.1142926
          at |  -.9214018   .1185973    -7.77   0.000    -1.153848   -.6889554
         fee |  -7.173794   .8711952    -8.23   0.000    -8.881305   -5.466283
-------------+----------------------------------------------------------------
SD           |
          at |   1.104228   .1346034     8.20   0.000       .84041    1.368045
         fee |   1.240044   .9083406     1.37   0.172    -.5402709    3.020359

When I run a -asmixlogit- model, which I need to model my data correctly, the SD is not part of the output. Is there a way to get these?

[Joerg Luedicke (StataCorp)]

Hi Joost,

Stata's asmixlogit reports the scale parameters for coefficients that are specified to be random. In the case of normally distributed random coefficients, these will be the standard deviations:

. asmixlogit choice premium, random(deductible) ///
>                            case(id) alternatives(insurance)

Fitting fixed parameter model:

Fitting full model:

Iteration 0:   log simulated likelihood = -296.14935  (not concave)
Iteration 1:   log simulated likelihood = -295.69689  
Iteration 2:   log simulated likelihood = -295.03152  
Iteration 3:   log simulated likelihood =   -295.029  
Iteration 4:   log simulated likelihood =   -295.029  

Alternative-specific mixed logit               Number of obs      =      1,250
Case variable: id                              Number of cases    =        250

Alternative variable: insurance                Alts per case: min =          5
                                                              avg =        5.0
                                                              max =          5
Integration sequence:      Hammersley
Integration points:                50             Wald chi2(2)    =      99.66
Log simulated likelihood =   -295.029             Prob > chi2     =     0.0000

------------------------------------------------------------------------------
      choice |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
insurance    |
     premium |   -2.67349   .2692025    -9.93   0.000    -3.201118   -2.145863
  deductible |   -1.11102   .3376753    -3.29   0.001    -1.772852    -.449189
-------------+----------------------------------------------------------------
Normal       |
sd(deducti~e)|   .8978139   .3605058                      .4086929    1.972312
-------------+----------------------------------------------------------------
Health       |
       _cons |   .5203306   .2979809     1.75   0.081    -.0637012    1.104363
-------------+----------------------------------------------------------------
HCorp        |  (base alternative)
-------------+----------------------------------------------------------------
SickInc      |
       _cons |  -.8428823   .2910199    -2.90   0.004    -1.413271   -.2724937
-------------+----------------------------------------------------------------
MGroup       |
       _cons |  -2.108393   .4435735    -4.75   0.000    -2.977781   -1.239005
-------------+----------------------------------------------------------------
MoonHealth   |
       _cons |  -3.363821   .6785549    -4.96   0.000    -4.693764   -2.033877
------------------------------------------------------------------------------
LR test vs. fixed parameters: chibar2(01) =     3.02  Prob >= chibar2 = 0.0411

I hope this helps,

Joerg

[Joost Verlaan]

Hi Joerg,

Thank you for your reply and sorry for my late one.
The problem was that I assumed that the random variables are correlated by means of the Cholesky Matrix.
When I removes this feat, I get exactly the same output, but with the desired standard deviations, which is exactly what I needed.
Thank you again!