Negative predicted values with an implausible variable

[John Fasano]

Dear StataList,

I am running regressions in Stata and I got the following table below from predicted margins. The thing is that the variable is time and time cannot be negative - so it looks pretty bad in the graphs :/ How is that possible? How could justify that?

Many many thanks in advance

           margins timex, post noestimcheck

            
        Delta-method
    Margin    Std. Err.    z    P>z    [95% Conf.    Interval]
                        
timex    
-8/-10    163.964    5.348    30.66    0.000    153.483    174.445
  -4/-6    118.091    34.397    3.43    0.001    50.674    185.508
     -2    122.463    36.124    3.39    0.001    51.661    193.264
      0    11.913     36.115    0.33    0.742    -58.871    82.697
    +2    41.892     37.119    1.13    0.259    -30.859    114.644
 +4/+6    74.276     37.856    1.96    0.050    0.079    148.474

[Clyde Schechter]

Which negative values are you referring to? Are you referring to the negative numbers like -8/-10 that appear in the first row and first column of the table? Or are you referring to the negative values that appear in the 95% confidence intervals?

If the former, as best I can tell from what you show, you created these negative values of timex yourself. The values shown in the leftmost column, given how -margins- works can only be value labels applied to the actual integer values of variable timex. So you (or whoever created the data set) developed these value labels and used them. So revisit that decision, or take it up with that other person.

If you are referring to the values in the 95% confidence intervals, there is absolutely nothing wrong here. The 95% confidence interval is based on the normal theory approximation and the lower limit is just the main estimate (margin) - 1.96*std.err. There is no reason that that can't be negative, even if the variable itself never takes on negative values. Now, the occurrence of a negative confidence limit on a variable that can never be negative may be an indication that the normal-theory approximation is not very good. But that doesn't invalidate the calculation. Also, the defining property of a 95% confidence interval algorithm is that when applied to a large number of random samples, 95% of the confidence intervals it produces will in fact contain the true value. (This is usually referred to as the 95% coverage probability.) If your variable cannot take on negative values, then you can simply replace the negative limits by zero without changing the coverage probability. From a statistical perspective, it makes no difference in this context. If you, or your prospective audience, are uncomfortable with seeing the negative confidence limits, then feel free to do that.

[John Fasano]

Thank you so much Clyde. I was referring to the second part you highlighted. And I will follow your instructions Thanks!