Interpretation Confidence interval including zero

[Jack Smith]

Hi,

I'm performing a Negative binomial regression (xtnbreg), however, I found that the confidence interval of my regression includes zero.
Does this mean that I can neither accept nor reject my hypothesis?
If for example, my hypothesis is: CEO stock options are positively related to acquisition activity.

--------------------------------------------------------------------------------------
        Acquisitions |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
L_Grant_stockoptions |    .001497   .0100047     0.15   0.001    -.0181117    .0211058
         L_firm_size |   .2236534   .1122078     1.99   0.046     .0037301    .4435768
   L_stock_ownership |   .0479732   .0392127     1.22   0.001    -.0288823    .1248287
        L_other_comp |   .0733703   .0482289     1.52   0.128    -.0211566    .1678973
             CEO_age |  -.0069845   .0180781    -0.39   0.099     -.042417     .028448
          CEO_gender |   15.25186   523.3139     0.03   0.077    -1010.425    1040.928
          CEO_tenure |  -.0092427   .0184607    -0.50   0.017    -.0454251    .0269397
               _cons |  -6.097821   5.460795    -1.12   0.264    -16.80078    4.605142

Thank you!

[Carlo Lazzaro]

Jack:
when 95% CI includes 0 (or 1, if it refers to a ratio), it means that your data cannot support the evidence of an effect for that predictor (when adjusted for the other ones) on the dependent variable.
That said, in your case your 95% CI bounds are expressed on ln scale and -ln(0)- is actually undefined, whereas -ln(1)=0-.

[Jack Smith]

Thank you very much for your reply!

You're right, I'm using the natural log for this variable. I, however, don't understand what that would imply. What does undefined mean in this case? And how could I interpret the CI with regards to the log scale?

[Carlo Lazzaro]

Jack:
the conflicting indications that p-values and 95% CIs convey are possibly due to the skewed distribution for some of your predictors.
If I'm not mistaken in remembering what follows, many posts ago, Nick Cox highlighted that logging a negative skewed distribution means making its skewness even worse.
Maybe this is the case for your logged regressors.
Unfortunately I have no similar explanation for -CEO_tenure-.

[Mike Lacy]

Something still looks funny to me, perhaps reflecting some confusion on my part, since I have not used -nbreg-for many years and have never used -xtnbreg-: I thought the z-value was reported for a test of the slope differing from 0 for the raw coefficients (not the IRR where the null value would be 1.0). So, the z-value of 0.15 for the first line is the usual b/se, but how does a z value of 0.15 lead to a two-sided p of 0.001? In fact, all of the p-values above look odd relative to the z-values, but when I reality-checked some simple examples with -nbreg-, no such oddities obtained. I'd find an explanation interesting.

[Nick Cox]

Cross-posted at https://stats.stackexchange.com/ques...including-zero

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