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My dependent variable is a count variable that takes on the value 0 in most cases (80%) so I am applying a Negative binomial regression model. Depending on the exact model specification my independent variable of interest is significant at 5% or 1%. My model has a total of 16 predictor variables and no interaction term included. It has year and industry-fixed effects. Each observation corresponds to a Merger & Acquisition announced by US companies on some day between 2009 and 2018. For each observation (i.e., each deal) my dependent variable measures the number of press releases the acquiring company has published from one day before to one day after the acquisition was announced. So ultimately my mode examines what determines the number of press releases published by an acquiring firm around the date on which the firm announced an M&A.

Most papers I read so far take the natural log of a control variable that I also included in my model (market value of a company). This makes sense to me as the variable usually is skewed to the right. The non-transformed version of the variable is highly significant (1%) and doesn't do much to my independent variable of interest in terms of significance. However, if I include the logged version of the control my independent variable get's highly insignificant. I am not trying to push my data towards significance but want to understand if this could be an absolutely normal thing or indicates some sort of problem.

Please find below the current Stata output of my model. To improve readability I left out the estimates for the fixed effects dummies. CNS is my variable of interest that gets highly insignificant when the variable Acq_Size_MV42 is logged.

Negative binomial regression                            Number of obs =    888
                                                        Wald chi2(34) =      .
Dispersion: mean                                        Prob > chi2   =      .
Log pseudolikelihood = -577.04358                       Pseudo R2     = 0.0919

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                                                                    |               Robust
                                                      IM_Offsetting | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
--------------------------------------------------------------------+----------------------------------------------------------------
                                                         CEO_tenure |    .025844   .0138651     1.86   0.062    -.0013312    .0530192
                                                            CEO_Age |    .020748   .0121236     1.71   0.087    -.0030137    .0445097
                                                         CEO_Gender |  -.4480861   .3675936    -1.22   0.223    -1.168556    .2723841
                                                         Acq_MA_exp |  -.0114638   .0218293    -0.53   0.599    -.0542485    .0313209
                                                         Deal_Value |  -6.54e-11   2.87e-11    -2.28   0.023    -1.22e-10   -9.14e-12
                                                       Deal_AllCash |  -.2332634   .2853195    -0.82   0.414    -.7924794    .3259526
                                                         Deal_Stock |   .1867257    .310457     0.60   0.548    -.4217589    .7952103
                                                       Targ_Listing |   .0456927    .056514     0.81   0.419    -.0650726     .156458
                                                           FF12_Div |   .4330456   .1427309     3.03   0.002     .1532981     .712793
                                                      Acq_Size_MV42 |   8.18e-12   2.08e-12     3.93   0.000     4.10e-12    1.23e-11
                                                        Acq_Lev_WWU |   .0272248   .0347519     0.78   0.433    -.0408876    .0953373
                                                    Acq_TobinsQ_WWU |   .1054541    .068864     1.53   0.126    -.0295169    .2404251
                                                            Acq_FCF |   3.457239   1.930572     1.79   0.073    -.3266118    7.241091
                                                      Acq_Cash_hold |   .2302485   .5423197     0.42   0.671    -.8326787    1.293176
                                                            Acq_ROA |  -4.107877   1.856848    -2.21   0.027    -7.747232   -.4685227
                                                                CNS |   .2634295   .1097225     2.40   0.016     .0483773    .4784816

--------------------------------------------------------------------+----------------------------------------------------------------
                                                           /lnalpha |  -.7166174   .4239483                     -1.547541    .1143059
--------------------------------------------------------------------+----------------------------------------------------------------
                                                              alpha |   .4884015    .207057                      .2127706    1.121095
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    $\begingroup$ Please edit the question to provide more details about your models: how many observations, how many predictor variables, whether you have included interactions among predictors. Adding the function calls and model summaries to the question (with the {} code tool on the toolbar) would be very helpful. There are several ways this might happen, but without those details it's hard to know which might be responsible here. $\endgroup$
    – EdM
    Mar 3, 2023 at 17:31
  • $\begingroup$ Sure, thanks for pointing out! $\endgroup$
    – xxgaryxx
    Mar 3, 2023 at 17:54

1 Answer 1

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I suspect that part of the problem, at least, is your having restricted your modeling to linear associations of outcome with the continuous predictors (or linear in log-predictor). I'd recommend that you look at Chapter 2 of Frank Harrell's Regression Modeling Strategies for better ways to model continuous predictors.

If you omit a true non-linear association of a continuous predictor with outcome, you have a type of omitted-variable bias. With correlated predictors, you might end up with the coefficients of other predictors picking up some of that omitted non-linearity.

In any event, what's most important is to make sure that the model as a whole is OK. If your model with the log-transformed Acq_Size_MV42 performs more poorly overall than when that predictor is not transformed, then there isn't any need to worry about the results with its log transformation. Careful evaluation of model quality is the key.

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