# st: random effects logistic model

 From "Eleonora Bartoloni06" To Subject st: random effects logistic model Date Sun, 08 Mar 2009 17:43:26 +0000

```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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```