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st: constant option in fixed and random logistic regression with time indicators


From   Nahla Betelmal <[email protected]>
To   "[email protected]" <[email protected]>
Subject   st: constant option in fixed and random logistic regression with time indicators
Date   Mon, 23 Sep 2013 15:41:38 +0100

Dear Statalist,

I am using logit fixed and random logistic regressions on my data ,
Stata version 12 . However, I have found some difficulties in
understanding their commands in Stata.

I do not understand why fixed effect command ( xtlogit, fe) or
(clogit, i(group) produces a regression without a constant term. this
is a source of concern to me because I am controlling for year effect
in my regression using i.year  ( I have years 1993 to 2010) as one of
the independent variables.

the fixed effect logistic regression will  produce the result without
a constant and omit one of the years as well. As you can see from the
the output below , there is no constant and no year for 1993.


I am worried that there is a bias in the fixed effect model because it
omits both the constant and the base year altogether . Is there a way
to include a constant  or the base year dummy in the fixed effect
model? I understand that we can not include both together due to the
dummy-trap, only one should be included. the fixed logistic model
seems to drop both!




. xtlogit To IV1 IV2 IV3 i.year, or fe
note: multiple positive outcomes within groups encountered.
note: 879 groups (3751 obs) dropped because of all positive or
      all negative outcomes.

Conditional fixed-effects logistic regression   Number of obs      =     10342
Group variable: gvkey                           Number of groups   =      1254

                                                Obs per group: min =         2
                                                               avg =       8.2
                                                               max =        18

                                                LR chi2(29)        =   1212.25
Log likelihood  = -3837.8092                    Prob > chi2        =    0.0000

------------------------------------------------------------------------------------------
                      To |         OR   Std. Err.      z    P>|z|
[95% Conf. Interval]
-------------------------+----------------------------------------------------------------
               IV1 |   1.412172   .1186089     4.11   0.000
1.197829     1.66487
               IV2 |   .8076188   .0256471    -6.73   0.000
.7588838    .8594835
                IV3 |   1.308746   .3431965     1.03   0.305
.7827841    2.188107
                        |
                   year |
                   1994  |   1.880812   .5677725     2.09   0.036
1.040849    3.398623
                   1995  |   2.680557   .7873787     3.36   0.001
1.507286    4.767102
                   1996  |   2.283253     .68579     2.75   0.006
1.267331    4.113562
                   1997  |   3.572044   1.043096     4.36   0.000
2.015357    6.331138
                   1998  |   25.63506   7.222488    11.51   0.000
14.75756    44.53014
                   1999  |   34.39778   9.736953    12.50   0.000
19.75066    59.90725
                   2000  |   34.67391   9.890064    12.43   0.000
19.82503    60.64453
                   2001  |   27.87145   8.018454    11.57   0.000
15.85893    48.98299
                   2002  |   25.53222   7.345258    11.26   0.000
14.52814    44.87115
                   2003  |   25.24796   7.294939    11.17   0.000
14.33135    44.48008
                   2004  |   31.73301   9.207977    11.91   0.000
17.96875    56.04084
                   2005  |   37.77634   11.09489    12.37   0.000
21.24332    67.17649
                   2006  |   32.32968   9.584978    11.72   0.000
18.08175    57.80459
                   2007  |   32.13949   9.550568    11.68   0.000
17.9513     57.5416
                   2008  |    27.4974   8.208442    11.10   0.000
15.3177    49.36166
                   2009  |   18.87728   5.671577     9.78   0.000
10.47612    34.01562
                   2010  |   27.66689    8.30931    11.06   0.000
15.35732    49.84311
------------------------------------------------------------------------------------------



I also tried to enter the year dummies manually , but still no
constant and one year got omitted.

I want to test the same equation under random effect, however, random
effect allows for option to show or suppress a constant (why fixed
effect does not have it?) . So, if I suppress the constant term in the
random effect model I get similar results to the fixed effect one, but
if I allow the constant term, IV3 becomes significant.


Random effect with NO constant

 xtlogit To  IV1 IV2 IV3  i.year, or nocon


Random-effects logistic regression              Number of obs      =     14093
Group variable: gvkey                           Number of groups   =      2133

Random effects u_i ~ Gaussian                   Obs per group: min =         1
                                                               avg =       6.6
                                                               max =        18

                                                Wald chi2(29)      =   1392.73
Log likelihood  =  -7350.075                    Prob > chi2        =    0.0000

------------------------------------------------------------------------------------------
                      To |         OR   Std. Err.      z    P>|z|
[95% Conf. Interval]
-------------------------+----------------------------------------------------------------
             IV1 |   1.455917   .0966588     5.66   0.000     1.278277
   1.658243
              IV2 |   .8167012   .0232345    -7.12   0.000
.7724088    .8635334
               IV3 |   1.261685   .2880741     1.02   0.309
.8064927    1.973792

                  year |
                   1994  |   .7614881    .183525    -1.13   0.258
.4748063    1.221265
                   1995  |   1.243601   .2789643     0.97   0.331
.8011978    1.930289
                   1996  |   1.042708   .2424268     0.18   0.857
.6610905    1.644617
                   1997  |   1.575768   .3467249     2.07   0.039
1.023759     2.42542
                   1998  |   11.90875   2.420022    12.19   0.000
7.99632    17.73544
                   1999  |   15.51208    3.16732    13.43   0.000
10.39605    23.14578
                   2000  |   15.44036   3.155944    13.39   0.000
10.34369    23.04832
                   2001  |   12.55376   2.579917    12.31   0.000
8.391581    18.78035
                   2002  |   11.54242   2.361687    11.95   0.000
7.729178    17.23697
                   2003  |   11.13248   2.286437    11.73   0.000
7.44335    16.65004
                   2004  |    14.2687   2.941321    12.89   0.000
9.526197    21.37221
                   2005  |   16.80113   3.503443    13.53   0.000
11.16458    25.28335
                   2006  |   14.19136   2.989611    12.59   0.000
9.390885    21.44578
                   2007  |   13.45456   2.782081    12.57   0.000
8.97142    20.17797
                   2008  |   11.99456   2.453953    12.14   0.000
8.03226    17.91144
                   2009  |    8.05653   1.669634    10.07   0.000
5.367168    12.09347
                   2010  |   12.19368   2.523583    12.08   0.000
8.127773    18.29355
-------------------------+----------------------------------------------------------------
                /lnsig2u |    .750443   .0644942
.6240366    .8768493
-------------------------+----------------------------------------------------------------
                 sigma_u |   1.455314   .0469297
1.36618    1.550263
                     rho |   .3916446   .0153663
.361973    .4221391
------------------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) =  1634.51 Prob >= chibar2 = 0.000



Random effect with constant

 xtlogit To  IV1 IV2 IV3  i.year, or

Random-effects logistic regression              Number of obs      =     14093
Group variable: gvkey                           Number of groups   =      2133

Random effects u_i ~ Gaussian                   Obs per group: min =         1
                                                               avg =       6.6
                                                               max =        18

                                                Wald chi2(29)      =   1065.65
Log likelihood  = -7317.0318                    Prob > chi2        =    0.0000

------------------------------------------------------------------------------------------
                      To |         OR   Std. Err.      z    P>|z|
[95% Conf. Interval]
-------------------------+----------------------------------------------------------------
                IV1 |   1.469466   .0976402     5.79   0.000
1.290032    1.673858
              IV2 |   .8574825   .0247906    -5.32   0.000
.8102449    .9074741
                 IV3 |   1.675989   .3884926     2.23   0.026
1.064054    2.639847

                         |
                   year |
                   1994  |   1.695202    .501163     1.79   0.074
.9496759    3.025989
                   1995  |   2.733662   .7707933     3.57   0.000
1.57303    4.750646
                   1996  |   2.243345   .6456284     2.81   0.005
1.276212    3.943388
                   1997  |   3.388523   .9417797     4.39   0.000
1.965324    5.842339
                   1998  |   25.61627   6.784178    12.25   0.000
15.24351     43.0474
                   1999  |   33.15704   8.797594    13.20   0.000
19.71177    55.77326
                   2000  |   32.94627   8.742157    13.17   0.000
19.5859    55.42033
                   2001  |    26.4393    7.02571    12.32   0.000
15.70581    44.50815
                   2002  |   24.12863   6.388762    12.02   0.000
14.35992    40.54275
                   2003  |   22.92283   6.070519    11.83   0.000
13.6411    38.52006
                   2004  |   28.98688    7.67883    12.71   0.000
17.24694    48.71815
                   2005  |   33.66509   8.962688    13.21   0.000
19.97854     56.7278
                   2006  |   28.23259   7.557373    12.48   0.000
16.70701    47.70925
                   2007  |   28.13377   7.491295    12.53   0.000
16.69456    47.41119
                   2008  |   25.14971   6.657005    12.18   0.000
14.97008    42.25147
                   2009  |   16.61363   4.423448    10.55   0.000
9.858904    27.99629
                   2010  |    24.9653   6.632961    12.11   0.000
14.83145     42.0233
                         |
                   _cons |   .0208179   .0101883    -7.91   0.000
.0079774    .0543269
-------------------------+----------------------------------------------------------------
                /lnsig2u |   .7355081    .064817
.6084692    .8625471
-------------------------+----------------------------------------------------------------
                 sigma_u |   1.444487   .0468136
1.355587    1.539217
                     rho |    .388092   .0153925
.3583855    .4186542
------------------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) =  1595.59 Prob >= chibar2 = 0.000



Thank you , I highly appreciate your kind help

Nahla Betelmal
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