# [Limdep Nlogit List] random effects logistic model

Eleonora Bartoloni bartolon at istat.it
Mon Mar 9 05:01:26 EST 2009

```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).

--> sample;all\$
--> LOGIT; lhs=new_inn; RHS= one,add,inizio, dredbv, INNSET,NORTH_EA,north_we...
PANEL;PDS=8;PERIOD=time; RANDOM EFFECTS\$  ? dredbv, red_add_, red_imim,in...
+--------------------------------------------------+
| Panel Data Binomial Logit Model                  |
| Number of individuals          =    2591         |
| Number of periods              =       8         |
| Random effects model for panel data.             |
+--------------------------------------------------+
Normal exit from iterations. Exit status=0.

+---------------------------------------------+
| Logit Model for Panel Data                  |
| Maximum Likelihood Estimates                |
| Model estimated: Mar 08, 2009 at 06:51:26PM.|
| Dependent variable              NEW_INN     |
| Weighting variable                 None     |
| Number of observations            20728     |
| Iterations completed                 40     |
| Log likelihood function       -7360.178     |
| Hosmer-Lemeshow chi-squared = *********     |
| P-value=  .00000 with deg.fr. =       8     |
| Random Effects Logit Model for Panel Data   |
| Variance decomposition: Rho =     .630189   |
| Var[e] = pi-squared/3       =    3.289868   |
| Var[u] = Var[e]*Rho/(1-Rho) =    5.606223   |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+
|Variable | Coefficient  | Standard Error |b/St.Er.|P[|Z|>z] |
+---------+--------------+----------------+--------+---------+
Characteristics in numerator of Prob[Y = 1]
Constant     -11.3248235      .49514852   -22.872   .0000
ADD            .00021605    .460196D-04     4.695   .0000
INIZIO        -.01952131      .00308193    -6.334   .0000
DREDBV         .25955100      .05556371     4.671   .0000
INNSET         .18523351      .00482228    38.412   .0000
NORTH_EA      2.80927316      .21278967    13.202   .0000
NORTH_WE      2.38145592      .21016688    11.331   .0000
CENTRE        1.76615375      .21813424     8.097   .0000
ROS            .01751809      .00406118     4.314   .0000
IMAT         .325059D-05    .120828D-05     2.690   .0071
OFFAT          .19390741      .01492164    12.995   .0000
LEVERAGE      -.00073968      .00029694    -2.491   .0127
Q_IMMMAT      -.00022810      .00107902     -.211   .8326
Rho            .63018950      .01070766    58.854   .0000

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)

--> sample;all\$
--> reject;time=1996\$
--> LOGIT; lhs=new_inn; RHS= one,add,inizio, dredbv, INNSET,NORTH_EA,north_we...
PANEL;PDS=7;PERIOD=time; RANDOM EFFECTS\$  ? dredbv, red_add_, red_imim,in...
+--------------------------------------------------+
| Panel Data Binomial Logit Model                  |
| Number of individuals          =    2591         |
| Number of periods              =       7         |
| Random effects model for panel data.             |
+--------------------------------------------------+
Line search does not improve fn. Exit iterations. Status=3
Error   806: Line search does not improve fn. Exit iterations. Status=3
Function=  .12571290575D+05, at entry,  .61305847660D+04 at exit

+---------------------------------------------+
| Logit Model for Panel Data                  |
| Maximum Likelihood Estimates                |
| Model estimated: Mar 08, 2009 at 06:44:26PM.|
| Dependent variable              NEW_INN     |
| Weighting variable                 None     |
| Number of observations            18137     |
| Iterations completed                 28     |
| Log likelihood function       -6130.585     |
| Hosmer-Lemeshow chi-squared =  54.46803     |
| P-value=  .00000 with deg.fr. =       8     |
| Random Effects Logit Model for Panel Data   |
| Variance decomposition: Rho =     .000000   |
| Var[e] = pi-squared/3       =    3.289868   |
| Var[u] = Var[e]*Rho/(1-Rho) =     .000000   |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+
|Variable | Coefficient  | Standard Error |b/St.Er.|P[|Z|>z] |
+---------+--------------+----------------+--------+---------+
Characteristics in numerator of Prob[Y = 1]
Constant     -5.37119662      .25054257   -21.438   .0000
ADD          .870916D-04    .162709D-04     5.353   .0000
INIZIO        -.00723346      .00114506    -6.317   .0000
DREDBV         .21222777      .03454865     6.143   .0000
INNSET         .06772354      .00291373    23.243   .0000
NORTH_EA      1.29464549      .11161528    11.599   .0000
NORTH_WE      1.19623940      .11050248    10.825   .0000
CENTRE         .88253976      .11292736     7.815   .0000
ROS[-1]        .01995731      .00250428     7.969   .0000
IMAT         .189168D-05    .631310D-06     2.996   .0027
OFFAT          .08680035      .01040113     8.345   .0000
LEVERAGE      -.00057893      .00016112    -3.593   .0003
Q_IMMMAT       .00073268      .00073521      .997   .3190
Rho          .259782D-15     399458.387      .000  1.0000

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

```