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  • Seemingly unrelated bivariate probit model - Interpretation of Likelihood-ratio test of rho=0

    Hello everyone,

    I'm using Stata 13 and trying to interpret the results below the text. I'm using a system of seemingly unrelated bivariate probit models to figure out if the correlation between the error terms of the two equations differs from zero to control for selection bias. I assume if rho is insignificantly different from zero then there would be no selection bias.
    Now I'm having a hard time to interpret the results at the bottom:

    Code:
    rho | .1780497 .0912844 -.0048039 .3493819
    ------------------------------------------------------------------------------
    Likelihood-ratio test of rho=0: chi2(1) = 3.73049 Prob > chi2 = 0.0534
    Does this mean that rho is significantly (10% level) different from zero? And as a reason that there is selection bias?


    Here is the whole output:

    Code:
    biprobit (valmethod = risk size boldness recom growth profit dax_past time_1 time_2    time_3 time_4 time_5 time_6 time_7    time_8    time_9    time_10 time_11    broker_1    broker_2    broker_3    broker_4    industry_1    indust
    > ry_2 industry_3 industry_4 industry_5 industry_6 industry_7 industry_8) (met_end =    valmethod risk size boldness recom    growth    profit    dax_future)
    
    Fitting comparison equation 1:
    
    Iteration 0:   log likelihood = -1274.8859  
    Iteration 1:   log likelihood = -968.87038  
    Iteration 2:   log likelihood = -959.25266  
    Iteration 3:   log likelihood = -957.87107  
    Iteration 4:   log likelihood =  -957.7174  
    Iteration 5:   log likelihood = -957.69015  
    Iteration 6:   log likelihood = -957.68504  
    Iteration 7:   log likelihood = -957.68402  
    Iteration 8:   log likelihood =  -957.6838  
    Iteration 9:   log likelihood = -957.68375  
    Iteration 10:  log likelihood = -957.68375  
    
    Fitting comparison equation 2:
    
    Iteration 0:   log likelihood = -1262.3575  
    Iteration 1:   log likelihood = -1113.7912  
    Iteration 2:   log likelihood = -1110.6841  
    Iteration 3:   log likelihood = -1110.6833  
    Iteration 4:   log likelihood = -1110.6833  
    
    Comparison:    log likelihood = -2068.3671
    
    Fitting full model:
    
    Iteration 0:   log likelihood = -2068.3671  
    Iteration 1:   log likelihood = -2066.5212  
    Iteration 2:   log likelihood = -2066.5018  
    Iteration 3:   log likelihood = -2066.5018  
    
    Seemingly unrelated bivariate probit              Number of obs   =       1930
    Wald chi2(38)   =     617.11
    Log likelihood = -2066.5018                       Prob > chi2     =     0.0000
    
    
    Coef.   Std. Err.      z    P>z     [95% Conf. Interval]
    
    valmethod    
    risk   -.3115484   .0820794    -3.80   0.000    -.4724211   -.1506756
    size   -.1547326   .0450794    -3.43   0.001    -.2430866   -.0663786
    boldness   -.0038907   .0031274    -1.24   0.213    -.0100202    .0022389
    recom    .0665691   .0813913     0.82   0.413    -.0929549    .2260931
    growth    .0093777   .0039054     2.40   0.016     .0017234    .0170321
    profit    .4187254   .1786379     2.34   0.019     .0686015    .7688493
    dax_past   -.0001211   .0029369    -0.04   0.967    -.0058773    .0056351
    time_1   -.8219447   .1892348    -4.34   0.000    -1.192838   -.4510512
    time_2   -.6236781   .2084041    -2.99   0.003    -1.032143   -.2152137
    time_3   -.3244276   .1969392    -1.65   0.099    -.7104213    .0615661
    time_4    -.623266   .1832377    -3.40   0.001    -.9824052   -.2641268
    time_5    -.291307   .2049938    -1.42   0.155    -.6930875    .1104736
    time_6   -.5059805   .2807058    -1.80   0.071    -1.056154    .0441927
    time_7   -.4818854   .1752289    -2.75   0.006    -.8253276   -.1384431
    time_8   -.4695556   .1623892    -2.89   0.004    -.7878326   -.1512787
    time_9    -.221224   .1807373    -1.22   0.221    -.5754625    .1330146
    time_10   -.2304714   .1762917    -1.31   0.191    -.5759967     .115054
    time_11   -.1911421   .1783841    -1.07   0.284    -.5407685    .1584842
    broker_1   -1.121648   .1262826    -8.88   0.000    -1.369157   -.8741384
    broker_2   -.5694673   .0908427    -6.27   0.000    -.7475158   -.3914189
    broker_3    -.955237   .0935743   -10.21   0.000    -1.138639   -.7718347
    broker_4   -.1774212   .1414599    -1.25   0.210    -.4546774     .099835
    industry_1    1.275041   .1992633     6.40   0.000      .884492     1.66559
    industry_2    .5504341   .1857927     2.96   0.003     .1862871     .914581
    industry_3   -.2467123   .2391105    -1.03   0.302    -.7153603    .2219357
    industry_4   -.1052097   .1917304    -0.55   0.583    -.4809945     .270575
    industry_5    .0450062   .2149748     0.21   0.834    -.3763366     .466349
    industry_6    -.139522   .2012488    -0.69   0.488    -.5339624    .2549183
    industry_7    .4166587   .1980507     2.10   0.035     .0284865    .8048309
    industry_8    7.671736   1384.863     0.01   0.996    -2706.609    2721.953
    _cons     1.84124   .5802919     3.17   0.002     .7038887    2.978591
    
    met_end      
    valmethod   -.2850019   .1310774    -2.17   0.030    -.5419088    -.028095
    risk    .0454646   .0530483     0.86   0.391    -.0585082    .1494374
    size   -.0357795   .0373738    -0.96   0.338    -.1090309    .0374718
    boldness   -.0304921   .0032121    -9.49   0.000    -.0367877   -.0241964
    recom    .2089467   .0733589     2.85   0.004     .0651658    .3527275
    growth    .0095815   .0034149     2.81   0.005     .0028884    .0162746
    profit   -.0439051   .1278892    -0.34   0.731    -.2945634    .2067531
    dax_future    .0245759    .001917    12.82   0.000     .0208186    .0283333
    _cons    .0425873   .4349468     0.10   0.922    -.8098927    .8950673
    
    /athrho    .1799678    .094273     1.91   0.056     -.004804    .3647395
    
    rho    .1780497   .0912844                     -.0048039    .3493819
    
    Likelihood-ratio test of rho=0:     chi2(1) =  3.73049    Prob > chi2 = 0.0534
    Best regards and thanks in advance,
    Tobias
    Last edited by Tobias Korn; 17 Nov 2017, 11:32.

  • #2
    Take a look at my answer here.

    Comment


    • #3
      Thank you for your reply! I'm going to have a look into the paper you mentioned.

      Comment

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