Goodness-of-fit test for mixed effects model?

[Heather Rosen]

Hello,

I am estimating a mixed effects linear regression model and I am wondering what is the appropriate goodness-of-fit test? I work in public health and am not very experienced in this regression method.

Thank you very much!
-Heather

[Carlo Lazzaro]

Heather:
welcome to this forum.
I'd take a look at -mixed postestimation-.
In addition, please note that -mixed- and -xtreg, re mle- are two sides of the same coin:

. use "https://www.stata-press.com/data/r17/pig.dta"
(Longitudinal analysis of pig weights)

. mixed weigh i.week || id:

Performing EM optimization ...

Performing gradient-based optimization: 
Iteration 0:   log likelihood = -1007.0675  
Iteration 1:   log likelihood = -1007.0675  

Computing standard errors ...

Mixed-effects ML regression                     Number of obs     =        432
Group variable: id                              Number of groups  =         48
                                                Obs per group:
                                                              min =          9
                                                              avg =        9.0
                                                              max =          9
                                                Wald chi2(8)      =   26412.22
Log likelihood = -1007.0675                     Prob > chi2       =     0.0000

------------------------------------------------------------------------------
      weight | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
        week |
          2  |   6.760417   .4187014    16.15   0.000     5.939777    7.581056
          3  |   13.84375   .4187014    33.06   0.000     13.02311    14.66439
          4  |     19.375   .4187014    46.27   0.000     18.55436    20.19564
          5  |   25.13542   .4187014    60.03   0.000     24.31478    25.95606
          6  |   31.42708   .4187014    75.06   0.000     30.60644    32.24772
          7  |    37.4375   .4187014    89.41   0.000     36.61686    38.25814
          8  |   44.28125   .4187014   105.76   0.000     43.46061    45.10189
          9  |   50.19792   .4187014   119.89   0.000     49.37728    51.01856
             |
       _cons |   25.02083   .6298893    39.72   0.000     23.78627    26.25539
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects parameters  |   Estimate   Std. err.     [95% conf. interval]
-----------------------------+------------------------------------------------
id: Identity                 |
                  var(_cons) |   14.83704    3.12421      9.819998     22.4173
-----------------------------+------------------------------------------------
               var(Residual) |   4.207462   .3036474      3.652498    4.846747
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 484.84        Prob >= chibar2 = 0.0000

. xtset id week

Panel variable: id (strongly balanced)
 Time variable: week, 1 to 9
         Delta: 1 unit

. xtreg weight i.week, mle

Fitting constant-only model:
Iteration 0:   log likelihood = -1827.2124
Iteration 1:   log likelihood = -1827.2118

Fitting full model:
Iteration 0:   log likelihood = -1008.0493
Iteration 1:   log likelihood = -1007.0894
Iteration 2:   log likelihood = -1007.0675
Iteration 3:   log likelihood = -1007.0675

Random-effects ML regression                        Number of obs    =     432
Group variable: id                                  Number of groups =      48

Random effects u_i ~ Gaussian                       Obs per group:
                                                                 min =       9
                                                                 avg =     9.0
                                                                 max =       9

                                                    LR chi2(8)       = 1640.29
Log likelihood = -1007.0675                         Prob > chi2      =  0.0000

------------------------------------------------------------------------------
      weight | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
        week |
          2  |   6.760417   .4187015    16.15   0.000     5.939777    7.581056
          3  |   13.84375   .4187015    33.06   0.000     13.02311    14.66439
          4  |     19.375   .4187015    46.27   0.000     18.55436    20.19564
          5  |   25.13542   .4187015    60.03   0.000     24.31478    25.95606
          6  |   31.42708   .4187015    75.06   0.000     30.60644    32.24772
          7  |    37.4375   .4187015    89.41   0.000     36.61686    38.25814
          8  |   44.28125   .4187015   105.76   0.000     43.46061    45.10189
          9  |   50.19792   .4187015   119.89   0.000     49.37728    51.01856
             |
       _cons |   25.02083    .629889    39.72   0.000     23.78627    26.25539
-------------+----------------------------------------------------------------
    /sigma_u |   3.851886   .4055422                      3.133686    4.734688
    /sigma_e |    2.05121   .0740167                      1.911151    2.201533
         rho |   .7790719    .038439                      .6968047    .8468207
------------------------------------------------------------------------------
LR test of sigma_u=0: chibar2(01) = 484.84             Prob >= chibar2 = 0.000

.

Hence, some postestimation methods that work for this panel data estimator are suitable for -mixed-, too