[Carlo Lazzaro]

Mohsin:
I share Steve's post about the satisfying agreement you've reached with your supervisor.
But I mildly disagree with your last statement:

It's OLS regression and CINO is an independent variable there so that analysis is not going to suffer from overfit.

, as overfit can happen with any regression methods.

[Mohsin Khan]

Thank you for raising that issue. In my OLS model, I have 94 observations for 12 predictors, making the ratio of observations to predictors around 8. For the overall model, is that ratio not good? Or is the number of events of CINO still the overriding factor here?

[Carlo Lazzaro]

Moshin:
to allow others to reply helpfully to your query, you should post what you tyoed and what Stata gave you back after -regress-. Thanks.

[Mohsin Khan]

My bad with that - please find below what I typed and the associated results.


Dependent variable is average sales growth:

 regress avsg asg_1 cino avten pcoo avtmt pdc avri avhhi poc0 avlemp avtd avcacq, vce(robust)

Linear regression                                      Number of obs =      94
                                                       F( 12,    81) =    3.15
                                                       Prob > F      =  0.0010
                                                       R-squared     =  0.2397
                                                       Root MSE      =   .1148

------------------------------------------------------------------------------
             |               Robust
        avsg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       asg_1 |   .0878071   .0751663     1.17   0.246    -.0617503    .2373644
        cino |   .0447955   .0317535     1.41   0.162    -.0183839     .107975
       avten |   .0038697   .0027134     1.43   0.158    -.0015291    .0092686
        pcoo |  -.0292565    .042002    -0.70   0.488    -.1128272    .0543143
       avtmt |  -.0021001   .0031878    -0.66   0.512    -.0084429    .0042426
         pdc |  -.0230678   .0305177    -0.76   0.452    -.0837884    .0376529
        avri |   .0189139   .0895013     0.21   0.833    -.1591656    .1969933
       avhhi |   .0000202   .0000249     0.81   0.420    -.0000294    .0000698
        poc0 |  -.0170332   .0307116    -0.55   0.581    -.0781398    .0440733
      avlemp |  -.0222431   .0109718    -2.03   0.046    -.0440736   -.0004127
        avtd |  -.0257174   .0260674    -0.99   0.327    -.0775833    .0261485
      avcacq |  -.0163313   .0300955    -0.54   0.589    -.0762119    .0435493
       _cons |   .0906293   .0431803     2.10   0.039     .0047141    .1765445
------------------------------------------------------------------------------

Dependent variable is Tobin's Q: (in this model, total predictors are 13)

regress avtob avsg atob_1 cino avten pcoo avtmt pdc avri avhhi poc0 avlemp avtd avcacq, vce(robust)

Linear regression                                      Number of obs =      94
                                                       F( 13,    80) =   15.98
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.6128
                                                       Root MSE      =  .71467

------------------------------------------------------------------------------
             |               Robust
       avtob |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        avsg |  -.2090368    .580505    -0.36   0.720    -1.364279     .946205
      atob_1 |   .6045243   .0741142     8.16   0.000     .4570323    .7520163
        cino |   .1195749   .2884703     0.41   0.680    -.4544993    .6936491
       avten |   .0133284   .0127871     1.04   0.300    -.0121187    .0387755
        pcoo |  -.4202749   .3534286    -1.19   0.238     -1.12362    .2830706
       avtmt |   .0486927   .0288923     1.69   0.096    -.0088047    .1061902
         pdc |  -.2247176   .1662624    -1.35   0.180    -.5555904    .1061552
        avri |    .680766   .6940742     0.98   0.330    -.7004857    2.062018
       avhhi |   .0003392   .0002451     1.38   0.170    -.0001486     .000827
        poc0 |   .0521226   .1706209     0.31   0.761    -.2874239    .3916691
      avlemp |  -.0044892   .0525321    -0.09   0.932    -.1090315    .1000531
        avtd |    -.41923   .1935504    -2.17   0.033    -.8044075   -.0340525
      avcacq |  -.2125567    .153599    -1.38   0.170    -.5182285    .0931151
       _cons |  -.2677623    .313738    -0.85   0.396    -.8921207    .3565962
------------------------------------------------------------------------------

I used robust option because for the first model of average sales growth, I get the following results:

estat hettest

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity 
         Ho: Constant variance
         Variables: fitted values of avsg

         chi2(1)      =    17.13
         Prob > chi2  =   0.0000

For the second model, however I am not too sure if I should be using robust option:

estat hettest

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity 
         Ho: Constant variance
         Variables: fitted values of avtob

         chi2(1)      =     4.30
         Prob > chi2  =   0.0381

Best,
Mohsin

[Carlo Lazzaro]

Moshin:
at its face-value, the second model should be preferred (and the heteroskedasticity should be dealth with -vce(robust).
However, as only one predictor seems to boost its R2, I would investigate whether quasi-extreme multicollinearity is an issue via -estat vif- and estat vce, corr-

[Mohsin Khan]

Hi Carlo,

sorry for the late reply. I was out of town due to some family emergency.

Actually, in the second model, the dependent variable is changed, that is why the R2 jumps so much. Even though an additional variable is added in the model (apart from the change of dep. var), if the additional variable is removed, the R2 is still in .60+ range. If I understand it correctly, the variables explain a higher portion of variation in the changed depended variable (Tobin Q) that it does for Sales growth. I also ran the following tests:

estat vce, corr

Correlation matrix of coefficients of regress model

        e(V) |     avsg    atob_1      cino     avten      pcoo     avtmt       pdc      avri     avhhi 
-------------+------------------------------------------------------------------------------------------
        avsg |   1.0000                                                                                 
      atob_1 |  -0.1808    1.0000                                                                       
        cino |  -0.3142    0.0082    1.0000                                                             
       avten |  -0.2696   -0.0988    0.2901    1.0000                                                   
        pcoo |   0.5083   -0.0271   -0.3899   -0.4588    1.0000                                         
       avtmt |   0.2675    0.0741   -0.4335   -0.1946    0.4896    1.0000                               
         pdc |   0.3647   -0.1685   -0.2300   -0.3149    0.2487    0.2249    1.0000                     
        avri |   0.0912   -0.2376   -0.0700   -0.2367   -0.0621   -0.1655    0.3104    1.0000           
       avhhi |  -0.1886   -0.0279    0.2398    0.2517   -0.2237   -0.2139   -0.0839   -0.3124    1.0000 
        poc0 |   0.0737    0.2082   -0.1253   -0.0804    0.3241    0.4273   -0.0516   -0.2206   -0.1353 
      avlemp |   0.1416    0.0086    0.2054    0.2475   -0.0646   -0.2772   -0.2839   -0.1130   -0.3009 
        avtd |  -0.0338    0.1698    0.1792    0.0238   -0.0979   -0.3080    0.1145    0.4982    0.1099 
      avcacq |   0.0265   -0.0644    0.1416    0.0894   -0.0685   -0.2735    0.1068    0.3277    0.2464 
       _cons |  -0.3029   -0.1226    0.1331   -0.2321   -0.3871   -0.6991   -0.2900    0.3199   -0.1972 

        e(V) |     poc0    avlemp      avtd    avcacq     _cons 
-------------+--------------------------------------------------
        poc0 |   1.0000                                         
      avlemp |   0.0053    1.0000                               
        avtd |  -0.3333   -0.2235    1.0000                     
      avcacq |  -0.2052   -0.0922    0.4547    1.0000           
       _cons |  -0.3770    0.0559    0.0407   -0.0318    1.0000

Which shows a correlation of greater than .5 for pcoo and avsg. However, the variance inflation factor for pcoo is 1.1, therefore multicollinearity is not be a problem:

estat vif

    Variable |       VIF       1/VIF  
-------------+----------------------
      avlemp |      1.90    0.525198
       avtmt |      1.69    0.591877
         pdc |      1.55    0.646867
       avten |      1.51    0.661710
        avtd |      1.50    0.668493
        avri |      1.44    0.694126
       avhhi |      1.38    0.726808
        avsg |      1.36    0.735523
      atob_1 |      1.28    0.779924
        cino |      1.24    0.807167
      avcacq |      1.19    0.841955
        pcoo |      1.10    0.909646
        poc0 |      1.09    0.917384
-------------+----------------------
    Mean VIF |      1.40

I hope I am correct with my interpretation of the results of correlation and VIF.

Best,
Mohsin

[Carlo Lazzaro]

Moshin:
first of all I do hope that your family emergency was not that severe and it is now solved.
I agree with your take: multicollinearity is not a problem with your model.
Hence, I would go ahead with the second model of your post #34 (did you take the heteroskedasticity into account via -vce(cluster)-?).

[Mohsin Khan]

Carlo, thank you for your concern. Everything's good now

As for heteroskedasticity, I thought vce(robust) accounts for that. Is that not the case?

I tried using vce(cluster) but it gives me error:

regress avtob avsg atob_1 cino avten pcoo avtmt pdc avri avhhi poc0 avlemp avtd avcacq, vce(cluster)
invalid vce(cluster) option
r(198);

[Carlo Lazzaro]

Mohsin:
if you don't have repeated observations on the same unit, vce(robust) is OK for taking heteroskedasticity into account. Sorry for my previous misguidance.

[Mohsin Khan]

Exactly - I had the same feeling, because from my limited understanding, I thought vce(cluster) was for longitudinal data. But I couldn't dare say so because you're the expert here.

P.S: it shows that I am getting a grip on Stata and I should have faith in my understanding

Thank you so much Carlo. Statalist is full of wonderful people!

Best,
Mohsin

[Carlo Lazzaro]

Moshin:
once Nick Cox wrote (in an English much better than mine)something in the line of: "We are all beginners. Some of us are only more experienced". I do hope I can feel this way forever and learn from the other Listers.

[Mohsin Khan]

True that!