Dear Stata comunity,

I was wondering whether there is any statistical test and command in Stata to test for S-shapes -- analogue to the Utest command which Lind and Mehlum developed for quadratic relationships.

I am currently working on a paper where we hypothesize an S-shaped relationship. The IV of interest is a certain firm_strategy, and the DV is firm_performance.

Of course I can just check whether the normal, the squared, and the cubic term are all significant (and whether the signs of the three variables are negative/positive/negative).
I.e., I would look at: firm_strategy, firm_strategy_squared, firm_strategy_cubed

Now I have been advised by a colleague that when hypothesizes for a U-shaped (quadratic) relationship, just looking at the term of firm_strategy and firm_strategy_squared is not enough. Apparently the Utest of Lind and Mehlum is more elaborate, as it combines a number of different tests in one test .For example, the Utest of Lind and Mehlum also tests whether the turning points are well within the data range, or whether the curves are steep enough around the turning points, etc.

http://fmwww.bc.edu/repec/bocode/u/utest.html

Now I have never heard about the existence of a similar test for S-shaped (cubic) relationships. And I could not find any such test when googling for it.

Yet I assume that potentially lots of the "additional things" that the Utest of Lind and Mehlum takes into consideration for U-shaped relationships could also be of importance when studying S-shaped cubic relationships. I.e., just looking at the significance and signs of firm_strategy, firm_strategy_squared, firm_strategy_cubed might not be enough.

Now I was wondering whether anyone in this community might indeed have heard of the existence of such a Stata command/ statistical test.

Thanks a lot.

Franz