{smcl}
{* 28jan2001}{...}
{hline}
help for {hi:wherext}{right:(STB-60: sg161)}
{hline}

{title:Computes the extreme of the effect of a linear and quadratic predictor}

{p 8 44}
{cmd:wherext} {it:linear-var} {it:quadratic-var }
[{cmd:,}
  {cmd:eq(}{it:str}{cmd:)}
  {cmdab:b:ootstrap}
  {cmdab:r:eps}{cmd:(}{it:#}{cmd:)}
  {cmdab:k:density}[{cmd:(}{it:options}{cmd:)}]
  {cmdab:l:evel}{cmd:(}{it:#}{cmd:)}
]


{title:Description}

{p}{cmd:wherext} is a post-estimation command after estimating a model that
includes both a linear effect and quadratic term in a predictor variable
{it:v}. {cmd:wherext} displays the range of {it:v}, the value of {it:v}
(called {it:argext}) at which the linear + quadratic terms are extreme, and
the standard error and confidence interval of {it:argext}.

{p}The quadratic term may take the general form a+b*v+c*v^2; {cmd:wherext}
verifies that {it:quadratic-var} is indeed quadratic in {it:linear-var}.

{p}The standard error and confidence interval of {it:argext} are computed via the
"delta method", and, optionally, by a parametric bootstrap.


{title:Options}

{p 0 4}
{cmd:eq(}{it:str}{cmd:)} specifies the name of the equation in which the
  variables occur. If not specified, the first equation is assumed.

{p 0 4}
{cmd:bootstrap} specifies that a bootstrap estimate of the confidence interval
  of {it:argext} is computed.  This parametric simulator assumes that the coefficients
  of the linear and quadratic terms are distributed as bivariate normal with mean
  and variance obtained from the estimation command.

{p 0 4}
{cmd:reps(}{it:#}{cmd:)} specifies the number of Monte Carlo simulations to be
  performed. The default is 10000.

{p 0 4}
{cmd:kdensity}[{cmd:(}{it:options}{cmd:)}] specifies that a kernel density
 estimate of the distribution of {it:argext} is displayed. This graph is overlaid
 with a normal distribution based on the delta method.

{p 4 4}
  Options for the {cmd:kdensity} command can be provided as an argument to the
  {cmd:kdensity} option of {cmd:wherext}, without the comma.  Example:
  {cmd:kdensity(parzen)} specifies that option {cmd:parzen} is issued when
  invoking {cmd:kdensity}.

{p 0 4}
{cmd:level(}{it:#}{cmd:)} specifies the confidence level, in percent, for
  confidence intervals. The default is {cmd:level(95)} or as set by
  {help set level}.


{title:Examples}

{p 8 12}{inp:. regress income edu exp exp2}{p_end}
{p 8 12}{inp:. wherext exp exp2}{p_end}
{p 8 12}{inp:. wherext exp exp2, boot kdensity}{p_end}

{p}A nonparametric bootstrap estimate of the confidence interval of {it:argext} can
be obtained via {help bs}. For instance,

{p 8 12}{inp:. bs "regress income edu exp exp2" "-0.5*_b[exp]/_b[exp2]", rep(1000)}{p_end}


{title:Saved results}

{cmd:wherext} saves in

{p 8 20}{cmd:r(argext)}{space  5}value at which linear+quadratic takes extreme{p_end}
{p 8 20}{cmd:r(Vargext)}{space 4}variance of argext (delta method){p_end}
{p 8 20}{cmd:r(extreme)}{space 4}maximum or minimum{p_end}

{p}In addition, if {cmd:bootstrap} was specified, the {cmd:r()} results of
{cmd:bstat} are added.


{title:Author}

	Jeroen Weesie
	Dept of Sociology/ICS
	Utrecht University
	J.Weesie@fss.uu.nl


{title:Also See}

 Manual:  {hi:[R] bstrap}
{p 0 9}On-line:{space 2}help for {help bs}, {help graphf}{p_end}