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st: Dynamic RE-Probit, Likelihoodratio test for rho=0, strange results


From   jpasset@rumms.uni-mannheim.de
To   statalist@hsphsun2.harvard.edu
Subject   st: Dynamic RE-Probit, Likelihoodratio test for rho=0, strange results
Date   Fri, 21 May 2010 09:56:53 +0200

Hello,

I want to use a Correlated Dynamic Random Effects Probit (xtprobit) to analyze the probability of social assistance receipt (0/1) conditional on my explanatory variables including the lagged dependent variable. I am using a balanced panel over 3 years. I want to use the Wooldridge Estimator to solve the initial conditions problem.

I started with a simple model and sequentially added additional variables including the individual means for the timevariant variables and the social assistance-status in t1. But now I have problems with the interpretation of the panel-level variance component of my Random Effects Modell. The Likelihood-ratio test of rho sometimes tells me, that the panel estimator is not different from the pooled estimator (output 1 below) and sometimes is (output 2 below). This seems strange to me because model 1 is actually nested in modell 2.
Do interpret the test right (this is what the stata-documentation tells me)?

Now my questions are:
Should I pay attention to the likelihood-ratio test or can I ignore it?
What is the appropriate model, a pooled probit model or the random effects model? (in order to take care about the initial conditions problem I think it should be the RE-Model with the Wooldridge estimator)

I would be thankful for any suggestions and remarks
Jasmin

OUTPUT 1>>>

. xtprobit algII lag1_algII big5_gewissen big5_extra big5_verträgl big5_offen big5_neuro
///
frau age_3544 age_4554 age_5564  migback_g1 migback_g2 ///
casmin_niedrig casmin_mittel casmin_mis status_unregel status_nwreg status_nwsonst /// keinpartner kinder_u18 single_kid2 p_casmin_niedrig p_casmin_mittel p_casmin_mis /// p_status_unregel p_status_nwreg p_status_nwsonst p_status_rente alquote_gl ostdtl /// year2006 year2007 if year==2006 | year==2007 | year==2008

Fitting comparison model:

Iteration 0:   log likelihood = -5603.8881
Iteration 1:   log likelihood = -1842.2454
Iteration 2:   log likelihood = -1657.6332
Iteration 3:   log likelihood = -1644.0719
Iteration 4:   log likelihood = -1644.0041
Iteration 5:   log likelihood = -1644.0041

Fitting full model:

rho =  0.0     log likelihood = -1644.0041
rho =  0.1     log likelihood = -1659.8083

Iteration 0:   log likelihood = -1659.8083
Iteration 1:   log likelihood = -1648.5451
Iteration 2:   log likelihood = -1645.7644
Iteration 3:   log likelihood = -1644.4844
Iteration 4:   log likelihood = -1644.1148
Iteration 5:   log likelihood = -1644.0309
Iteration 6:   log likelihood = -1644.0093
Iteration 7:   log likelihood =  -1644.005
Iteration 8:   log likelihood = -1644.0043
Iteration 9:   log likelihood = -1644.0043
Iteration 10:  log likelihood = -1644.0042
Iteration 11:  log likelihood = -1644.0042

Random-effects probit regression                Number of obs      =     25116
Group variable: id                              Number of groups   =      8372

Random effects u_i ~ Gaussian                   Obs per group: min =         3
                                                               avg =       3.0
                                                               max =         3

                                                Wald chi2(32)      =   3326.90
Log likelihood  = -1644.0042                    Prob > chi2        =    0.0000

------------------------------------------------------------------------------
       algII |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  lag1_algII |   2.123838   .0548959    38.69   0.000     2.016244    2.231432
big5_gewis~n |   .0291793    .029853     0.98   0.328    -.0293315      .08769
  big5_extra |  -.0071263   .0225933    -0.32   0.752    -.0514084    .0371557
big5_vertr~l |    .017215   .0263722     0.65   0.514    -.0344736    .0689035
  big5_offen |   .0123025   .0216701     0.57   0.570    -.0301701     .054775
  big5_neuro |   .0166685   .0208929     0.80   0.425    -.0242808    .0576177
        frau |   .0249978   .0552069     0.45   0.651    -.0832057    .1332013
    age_3544 |  -.0830398   .0691929    -1.20   0.230    -.2186554    .0525757
    age_4554 |  -.1160687   .0727131    -1.60   0.110    -.2585838    .0264464
    age_5564 |   -.127606   .0880695    -1.45   0.147    -.3002191     .045007
  migback_g1 |   .1790896   .0692197     2.59   0.010     .0434215    .3147578
  migback_g2 |  -.0511563   .1326324    -0.39   0.700    -.3111111    .2087985
casmin_nie~g |    .276275    .071267     3.88   0.000     .1365943    .4159556
casmin_mit~l |   .1234304   .0684506     1.80   0.071    -.0107303    .2575911
  casmin_mis |   .3073567   .1583099     1.94   0.052     -.002925    .6176385
status_unr~l |   1.311907    .067841    19.34   0.000     1.178941    1.444873
status_nwreg |   1.927292   .0601123    32.06   0.000     1.809474     2.04511
status_nws~t |   .8877028   .0857642    10.35   0.000      .719608    1.055798
 keinpartner |   1.141455   .1053762    10.83   0.000      .934921    1.347988
  kinder_u18 |   .1537921   .0735284     2.09   0.036      .009679    .2979052
 single_kid2 |   .3045685   .1069978     2.85   0.004     .0948567    .5142802
p_casmin_n~g |   .3510707   .0976399     3.60   0.000        .1597    .5424414
p_casmin_m~l |   .3407302   .0953828     3.57   0.000     .1537835     .527677
p_casmin_m~s |   .3458119   .2292545     1.51   0.131    -.1035187    .7951425
p_status_u~l |   .8632316   .1001453     8.62   0.000     .6669504    1.059513
p_status_n~g |   .8370829    .084246     9.94   0.000     .6719638    1.002202
p_status_n~t |   .5358837   .1239302     4.32   0.000      .292985    .7787824
p_status_r~e |   .1154514   .1268318     0.91   0.363    -.1331345    .3640372
  alquote_gl |   .0442618    .010573     4.19   0.000     .0235391    .0649844
      ostdtl |   .1556372    .093774     1.66   0.097    -.0281564    .3394309
    year2006 |  -.0803976   .0682343    -1.18   0.239    -.2141344    .0533392
    year2007 |  -.1024604   .0622426    -1.65   0.100    -.2244536    .0195328
       _cons |  -4.526917    .267775   -16.91   0.000    -5.051746   -4.002088
-------------+----------------------------------------------------------------
    /lnsig2u |  -13.04064   14.60695                     -41.66973    15.58846
-------------+----------------------------------------------------------------
     sigma_u |   .0014732   .0107595                      8.94e-10    2426.557
         rho |   2.17e-06   .0000317                      8.00e-19    .9999998
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) =  2.8e-04 Prob >= chibar2 = 0.493


 >>>OUTPUT 2 (Wooldridge Model>>>

. xtprobit algII lag1_algII big5_gewissen big5_extra big5_verträgl big5_offen big5_neuro
///
frau age_3544 age_4554 age_5564  migback_g1 migback_g2 ///
casmin_niedrig casmin_mittel casmin_mis status_unregel status_nwreg status_nwsonst /// keinpartner kinder_u18 single_kid2 p_casmin_niedrig p_casmin_mittel p_casmin_mis /// p_status_unregel p_status_nwreg p_status_nwsonst p_status_rente alquote_gl ostdtl /// m_status_unregel m_status_nwreg m_status_nwsonst m_casmin_niedrig m_casmin_mittel m_cas
min_mis ///
m_kinder_u18 m_partner m_single_kid2 m_p_casmin_niedrig m_p_casmin_mittel ///
m_p_status_unregel m_p_status_nwreg m_p_status_nwsonst m_p_status_rente m_alquote_gl //
/
t1_algII year2006 year2007 if year==2006 | year==2007 | year==2008, re

Fitting comparison model:

Iteration 0:   log likelihood = -5603.8881
Iteration 1:   log likelihood = -1775.7389
Iteration 2:   log likelihood = -1577.8584
Iteration 3:   log likelihood = -1559.9784
Iteration 4:   log likelihood = -1559.7847
Iteration 5:   log likelihood = -1559.7846

Fitting full model:

rho =  0.0     log likelihood = -1559.7846
rho =  0.1     log likelihood = -1557.7495
rho =  0.2     log likelihood = -1577.7734

Iteration 0:   log likelihood = -1557.7495
Iteration 1:   log likelihood = -1537.8051
Iteration 2:   log likelihood = -1529.7425
Iteration 3:   log likelihood =  -1528.838
Iteration 4:   log likelihood = -1528.8044
Iteration 5:   log likelihood = -1528.8044

Random-effects probit regression                Number of obs      =     25116
Group variable: id                              Number of groups   =      8372

Random effects u_i ~ Gaussian                   Obs per group: min =         3
                                                               avg =       3.0
                                                               max =         3

                                                Wald chi2(49)      =    903.42
Log likelihood  = -1528.8044                    Prob > chi2        =    0.0000

------------------------------------------------------------------------------
       algII |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  lag1_algII |   .8919706   .1203705     7.41   0.000     .6560487    1.127892
big5_gewis~n |   .0548956   .0483427     1.14   0.256    -.0398543    .1496455
  big5_extra |   -.032175   .0367441    -0.88   0.381    -.1041921    .0398422
big5_vertr~l |  -.0004728   .0427336    -0.01   0.991    -.0842291    .0832835
  big5_offen |   .0313043   .0353433     0.89   0.376    -.0379672    .1005759
  big5_neuro |   .0105572   .0338118     0.31   0.755    -.0557128    .0768271
        frau |   .1024652   .0929796     1.10   0.270    -.0797715     .284702
    age_3544 |  -.1694081   .1068252    -1.59   0.113    -.3787816    .0399655
    age_4554 |  -.3513676   .1176912    -2.99   0.003     -.582038   -.1206971
    age_5564 |  -.3751153   .1439726    -2.61   0.009    -.6572964   -.0929343
  migback_g1 |   .2449559   .1139723     2.15   0.032     .0215742    .4683376
  migback_g2 |  -.0392087   .2080327    -0.19   0.851    -.4469454    .3685279
casmin_nie~g |   1.192158   5.434328     0.22   0.826    -9.458929    11.84324
casmin_mit~l |  -.7985941   1.831785    -0.44   0.663    -4.388826    2.791638
  casmin_mis |  -.1847348   3.615367    -0.05   0.959    -7.270724    6.901254
status_unr~l |   1.384364   .1408501     9.83   0.000     1.108302    1.660425
status_nwreg |   1.883271   .1253821    15.02   0.000     1.637527    2.129016
status_nws~t |   1.130012   .1723101     6.56   0.000     .7922901    1.467733
 keinpartner |   1.578449   .5334616     2.96   0.003      .532884    2.624015
  kinder_u18 |   .6446815   .2631479     2.45   0.014      .128921    1.160442
 single_kid2 |   .3156377   .3864969     0.82   0.414    -.4418824    1.073158
p_casmin_n~g |   .4168073   .6069354     0.69   0.492    -.7727643    1.606379
p_casmin_m~l |   .6972134   .6226993     1.12   0.263    -.5232548    1.917682
p_casmin_m~s |   .6257764   .3614691     1.73   0.083      -.08269    1.334243
p_status_u~l |   .6547824   .2151686     3.04   0.002     .2330596    1.076505
p_status_n~g |   .2659097   .1860339     1.43   0.153      -.09871    .6305294
p_status_n~t |  -.2982912    .275429    -1.08   0.279    -.8381221    .2415397
p_status_r~e |   .0211003   .4233166     0.05   0.960    -.8085849    .8507855
  alquote_gl |  -.0133963    .075066    -0.18   0.858    -.1605229    .1337302
      ostdtl |   .1082546   .1627778     0.67   0.506    -.2107839    .4272932
m_status_u~l |   .8374096   .2203783     3.80   0.000     .4054761    1.269343
m_status_n~g |   1.713071   .2421179     7.08   0.000     1.238529    2.187614
m_status_n~t |   .1241671   .2434695     0.51   0.610    -.3530243    .6013584
m_casmin_n~g |  -.8872669   5.434967    -0.16   0.870    -11.53961    9.765074
m_casmin_m~l |   .9483972   1.835344     0.52   0.605    -2.648811    4.545605
m_casmin_mis |   .4171617   3.626497     0.12   0.908    -6.690642    7.524965
m_kinder_u18 |  -.5387809   .2921233    -1.84   0.065    -1.111332    .0337702
   m_partner |  -.0874154   .5373746    -0.16   0.871     -1.14065    .9658196
m_single_k~2 |   .2904519   .4441113     0.65   0.513    -.5799904    1.160894
m_p_casmin~g |   .0960674   .6080532     0.16   0.874    -1.095695     1.28783
m_p_casmin~l |  -.1999828   .6252895    -0.32   0.749    -1.425528    1.025562
m_p_status~l |   .8648717   .3334481     2.59   0.009     .2113255    1.518418
m_p_status~g |   1.430915   .2658448     5.38   0.000     .9098689    1.951961
m_p_status~t |   1.346991   .3548293     3.80   0.000     .6515388    2.042444
m_p_status~e |   .1038106   .4817877     0.22   0.829    -.8404759    1.048097
m_alquote_gl |   .0750055    .076817     0.98   0.329    -.0755531    .2255641
    t1_algII |   1.607892   .1882352     8.54   0.000     1.238958    1.976826
    year2006 |   -.029871   .2554048    -0.12   0.907    -.5304552    .4707132
    year2007 |  -.0507152   .1525223    -0.33   0.740    -.3496535    .2482231
       _cons |   -6.21627   .7545591    -8.24   0.000    -7.695179   -4.737362
-------------+----------------------------------------------------------------
    /lnsig2u |  -.0862257   .2111008                     -.4999758    .3275243
-------------+----------------------------------------------------------------
     sigma_u |   .9578033   .1010965                      .7788102    1.177934
         rho |   .4784569   .0526772                      .3775464    .5811569
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) =    61.96 Prob >= chibar2 = 0.000






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