st: random effects logistic model

["Eleonora Bartoloni06" <Eleonora.Bartoloni06@phd.wbs.ac.uk>]

Hallo,

I’m running a random effects logistic regression. My dependent variable
is adummy (new_inn) indicating if a firm has or has not introduced an
innovation in the reference year. Among the regressors ros is a
profitability ratio. Other regressors are time invariant (inizio,
north_ea north_we centre). 

When the model is estimated with contemporaneous regressors, rho is
important and quite “big”, thus signalling that the contribution of the
random effect to the total variance is significant (results shown
below).

xtlogit new_inn inizio add dredbv innset  north_ea north_we centre ros 
q_immmat offat imat leverage, re  
> nolog

Random-effects logistic regression              Number of obs      =    
20728
Group variable: codice_i                        Number of groups   =    
 2591

Random effects u_i ~ Gaussian                   Obs per group: min =    
    8
                                                               avg =    
  8.0
                                                               max =    
    8

                                                Wald chi2(12)      =  
1711.52
Log likelihood  = -7360.2547                    Prob > chi2        =   
0.0000

------------------------------------------------------------------------------
     new_inn |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------------
      inizio |  -.0284325   .0044661    -6.37   0.000    -.0371859  
-.0196792
         add |   .0002841   .0000894     3.18   0.001      .000109   
.0004592
      dredbv |   .3748549   .0764724     4.90   0.000     .2249716   
.5247381
      innset |   .2618379   .0071342    36.70   0.000     .2478551   
.2758208
    north_ea |    3.97223   .3135382    12.67   0.000     3.357706   
4.586753
    north_we |   3.357463   .3099188    10.83   0.000     2.750033   
3.964892
      centre |   2.508734   .3235104     7.75   0.000     1.874665   
3.142803
         ros |   .0249554    .005251     4.75   0.000     .0146636   
.0352472
    q_immmat |  -.0004576   .0016871    -0.27   0.786    -.0037642    
.002849
       offat |   .2740084   .0215686    12.70   0.000     .2317347   
.3162821
        imat |   4.71e-06   1.61e-06     2.93   0.003     1.56e-06   
7.86e-06
    leverage |   -.001068   .0004716    -2.26   0.024    -.0019923  
-.0001437
       _cons |  -15.90129   .7207558   -22.06   0.000    -17.31394  
-14.48863
-------------+----------------------------------------------------------------
    /lnsig2u |   1.721848   .0741979                      1.576422   
1.867273
-------------+----------------------------------------------------------------
     sigma_u |   2.365345   .0877518                      2.199459   
2.543742
         rho |   .6297163    .017301                       .595217   
.6629404
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) =   931.71 Prob >= chibar2 =
0.000


when I introduce lagged regressors (for example past profitability
l1.ros) , rho becomes small and the Likelihood-ratio test of rho=0 is
significant (results shown below)

xtlogit new_inn inizio add dredbv innset  north_ea north_we centre
l1.ros  q_immmat offat imat leverage
> , re  nolog

Random-effects logistic regression              Number of obs      =    
18137
Group variable: codice_i                        Number of groups   =    
 2591

Random effects u_i ~ Gaussian                   Obs per group: min =    
    7
                                                               avg =    
  7.0
                                                               max =    
    7

                                                Wald chi2(12)      =  
2372.31
Log likelihood  = -6130.5857                    Prob > chi2        =   
0.0000

------------------------------------------------------------------------------
     new_inn |      Coef.   Std. Err.      z-------------+----------------------------------------------------------------
      inizio |  -.0102302   .0016877    -6.06   0.000     -.013538  
-.0069225
         add |   .0001232   .0000313     3.94   0.000     .0000619   
.0001845
      dredbv |    .300137   .0474086     6.33   0.000     .2072178   
.3930561
      innset |   .0957805   .0021794    43.95   0.000      .091509    
.100052
    north_ea |   1.830958   .1539548    11.89   0.000     1.529212   
2.132703
    north_we |   1.691782   .1539812    10.99   0.000     1.389984   
1.993579
      centre |   1.248131   .1606678     7.77   0.000     .9332275   
1.563034
         ros |
         L1. |   .0282246   .0032985     8.56   0.000     .0217597   
.0346895
    q_immmat |   .0010361   .0010641     0.97   0.330    -.0010496   
.0031217
       offat |   .1227618   .0140188     8.76   0.000     .0952855   
.1502382
        imat |   2.68e-06   8.63e-07     3.10   0.002     9.84e-07   
4.37e-06
    leverage |  -.0008187   .0003264    -2.51   0.012    -.0014585   
-.000179
       _cons |  -7.596277   .2974736   -25.54   0.000    -8.179314  
-7.013239
-------------+----------------------------------------------------------------
    /lnsig2u |  -9.570329    6.08817                     -21.50292   
2.362265
-------------+----------------------------------------------------------------
     sigma_u |   .0083528   .0254265                      .0000214   
3.258061
         rho |   .0000212   .0001291                      1.39e-10   
.7634011
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) =  2.2e-03 Prob >= chibar2 =
0.481


Is there someone who can help me to interpret these results?
thank you 
Eleonora Bartoloni


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