How to get 95% Confidence Interval (CI) of the turning point of an inverted U-shaped curve with stata?

[Elaine Lin Shi]

Dear all,

I have obtained an inverted U-shape relationship between independent variable X and dependent variable Y with GLS and robust regressions (reg, robust) and have plotted the curve and calculated the turning point.

I need to further get the turning point's 95% CI but do not know how to do this with stata.

If any one knows how to do it, please help. Thank you!

Elaine

[Clyde Schechter]

You have shown nothing of how you have done this, so it is impossible to give a confident (no pun intended) answer. But on the assumption that you did this by fitting a quadratic model, and then calculated the turning point as -b/2a, where b is the linear coefficient and a is the quadratic coefficient, you can get both the turning point itself and the confidence interval as follows;

regression_command y ... c.x##c.x ... // PRESUMABLY YOU HAVE ALREADY DONE THIS
nlcom -_b[x]/(2*_b[x#x])

[Elaine Lin Shi]

You have shown nothing of how you have done this, so it is impossible to give a confident (no pun intended) answer. But on the assumption that you did this by fitting a quadratic model, and then calculated the turning point as -b/2a, where b is the linear coefficient and a is the quadratic coefficient, you can get both the turning point itself and the confidence interval as follows;

regression_command y ... c.x##c.x ... // PRESUMABLY YOU HAVE ALREADY DONE THIS
nlcom -_b[x]/(2*_b[x#x])

Dear Clyde,

Many thanks for the help!

Previously, I followed some prior research and used the mean of controlled variables to calculate the turning point. But I personally hardly understand and agree with this operation...

The code that you suggested solves the problem in a better way.

Thank you!

Elaine