Unable to obtain AIC and BIC after random effect

[John Fasano]

Hi,
After running a random effect model (xtreg vars , re), I type estat ic but I get this message: likelihood information not found in last estimation results. How could I get AIC and BIC?
Many many thanks.

[Clyde Schechter]

You can't. The AIC and BIC are both calculated from the log-likelihood of the model. But -xtreg, re- is not estimated by maximum likelihood, so there is no log-likelihood, and hence no AIC or BIC. They are simply not defined for this model.

Added: if having an AIC and BIC are important for your research goals, you can use a different analysis. Instead of using -xtreg, re-, use -mixed-. For a two-level model, -xtreg, re- and -mixed- estimate the same model, but -mixed- estimates it using maximum likelihood. After -mixed-, you can then use -estat ic- to get AIC and BIC. Note: although -xtreg, re- and -mixed- estimate the same model, because they use different estimation procedures the results are not necessarily going to be identical. They should be very close, however.

[John Fasano]

Dear Clyde,
Thank you so much for this.
Best

[Felix Stips]

Clyde Schechter How come you can compute AIC and BIC after regression then?

[Carlo Lazzaro]

Felix:
elaborating on Clyde's helpful advice, you can take a look at the following toy-example:

. use "https://www.stata-press.com/data/r16/nlswork.dta"
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. xtreg ln_wage c.age##c.age, vce(cluster idcode) mle

Fitting constant-only model:
Iteration 0:   log likelihood =  -12878.37
Iteration 1:   log likelihood = -12864.036
Iteration 2:   log likelihood = -12863.892
Iteration 3:   log likelihood = -12863.892

Fitting full model:
Iteration 0:   log likelihood = -11322.802
Iteration 1:   log likelihood = -11264.949
Iteration 2:   log likelihood = -11264.776
Iteration 3:   log likelihood = -11264.776

Random-effects ML regression                    Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          1
                                                              avg =        6.1
                                                              max =         15

                                                Wald chi2(2)      =    1261.77
Log likelihood  = -11264.776                    Prob > chi2       =     0.0000

                             (Std. Err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0592303   .0041053    14.43   0.000     .0511842    .0672765
             |
 c.age#c.age |  -.0006789   .0000688    -9.87   0.000    -.0008137   -.0005441
             |
       _cons |    .545105   .0587335     9.28   0.000     .4299895    .6602205
-------------+----------------------------------------------------------------
    /sigma_u |    .357561   .0048399                      .3481996     .367174
    /sigma_e |   .3031159   .0036457                       .296054    .3103463
         rho |   .5818521   .0092125                      .5637158    .5998159
------------------------------------------------------------------------------

. estat ic

Akaike's information criterion and Bayesian information criterion

-----------------------------------------------------------------------------
       Model |          N   ll(null)  ll(model)      df        AIC        BIC
-------------+---------------------------------------------------------------
           . |     28,510  -12863.89  -11264.78       5   22539.55   22580.84
-----------------------------------------------------------------------------
Note: BIC uses N = number of observations. See [R] BIC note.

.

[Felix Stips]

Thanks Carlo, my point or confusion was that aic and bic are also reported for non mle models

use "https://www.stata-press.com/data/r16/nlswork.dta"
reg ln_wage c.age##c.age, robust
Linear regression                               Number of obs     =     28,510
                                                F(2, 28507)       =    1532.84
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0882
                                                Root MSE          =     .45654

------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0855891   .0036933    23.17   0.000       .07835    .0928282
             |
 c.age#c.age |  -.0010982   .0000629   -17.46   0.000    -.0012215   -.0009749
             |
       _cons |   .1647917   .0520218     3.17   0.002     .0628265    .2667568
------------------------------------------------------------------------------


estat ic


Akaike's information criterion and Bayesian information criterion

-----------------------------------------------------------------------------
       Model |          N   ll(null)  ll(model)      df        AIC        BIC
-------------+---------------------------------------------------------------
           . |     28,510  -19415.15  -18098.45       3   36202.91   36227.68
-----------------------------------------------------------------------------

[Carlo Lazzaro]

Felix:
see https://stats.stackexchange.com/ques...linear-regress.
Probably for -xtreg,re- the formula would be too complicated.