help for utestVersion 1.2

Title

utest -- Test for a U-shaped relationship

Syntax

utest x f(x)
[, options]

min(#) Use # as lower

max(#) Use # as upper

quadratic Force quadratic specification

inverse Force inverse specification

fieller Include Fieller-interval of extreme point

level(#) Set confidence level for Fieller interval; default is
level(95)

prefix(str) Variable names are prefixed by str in the saved results

Description

utest provides the exact test of the presence of a U shaped (or
inverse U shaped) relationship on an interval.

utest is used after estimation commands to test for the presence of
a U-shaped or
inverse U-shaped relationship between an explanatory variable and the outcome
variable on
a specific interval.

The estimation must contain the level of the explanatory variable
(i.e. x)
and a non-linear term ,
either quadratic or inverse (i.e. f(x)). utest will determine which
of the two
is used
and report test results from the test of the hypothesis that the
relationship is
decreasing at the start of the interval and increasing at the end or vice
versa.

The interval is by default taken as the data range, but can be
controlled by
setting the options minimum(#) and maximum(#).

A Fieller interval for the extreme point is also provided by the
option
fieller.
This interval is correct even for finite samples.

Estimation commands that prefixes saved results by equation names can be
handled with the prefix-option. This includes estimations on multi-equation
models (e.g. mlogit) and commands with additional saved results
(e.g. nbreg).

Remarks

For full details about the test, see J. T. Lind and H. Mehlum:
With or without U? The appropriate test for a U shaped relationship.
Oxford Bulletin of Economics and Statistics 72(1): 109-18 (2010).

Examples

. utest x xsquared

. utest x xinv, min(.3) fieller

. nbreg y x xsquared
. utest x xsquared, prefix(y)

Stored results

Scalars

r(t) t-value of U-test

r(t) p-value of U-test

r(x_l) Lower boundary of interval

r(x_u) Upper boundary of interval

r(s_l) Slope at lower boundary of interval

r(s_u) Slope at upper boundary of interval

r(t_l) t-value at lower boundary of interval

r(t_u) t-value at upper boundary of interval

r(extr) Extreme point

Macros

r(shape) Shape of the relationship

Author

Contact Jo Thori Lind or
Halvor Mehlum if you observe
problems.