{smcl}
{* 28 August 2002/14 October 2005}{...}
{hline}
help for {hi:cipolate}
{hline}

{title:Cubicly interpolate values}

{p 8 17 2}{cmd:cipolate} {it:yvar} {it:xvar} [{cmd:if} {it:exp}] [{cmd:in}
{it:range}] {cmd:,} {cmdab:g:enerate}{cmd:(}{it:newvar}{cmd:)} 

{p 4 4 2}{cmd:by} {it:...} {cmd::} may be used with {cmd:cipolate}; see help 
{help by}.


{title:Description}

{p 4 4 2}
{cmd:cipolate} creates {it:newvar} by averaging non-missing values of
{it:yvar} and cubicly interpolating missing values of
{it:yvar}, given {it:xvar}. That is, provided that {it:xvar} is not
missing, 

{p 4 4 2}1. When {it:yvar} is not missing, {it:newvar} is the mean of
{it:yvar} over observations with the same value of {it:xvar}. If a value of 
{it:xvar} is unique, then each mean is just the same as the value of
{it:yvar} at that point. 

{p 4 4 2}2. When {it:yvar} is missing, {it:newvar} is filled in with
cubicly interpolated values of {it:yvar}.  

{p 4 4 2}Interpolated values are based on exact fitting of a cubic curve 
to two data points before and two data points after each observation 
for which {it:yvar} is missing. {cmd:cipolate} will thus produce 
missing values whenever fewer than two data points are present 
on either side. Note that this is not a spline method.  

{p 4 4 2}Extrapolation is not provided, mainly because of reservations about 
the general (and even particular) wisdom of extrapolating cubics into 
the unknown. Some users may wish to extrapolate any remaining missing values 
linearly using {help ipolate}. 


{title:Options}

{p 4 8 2}{cmd:generate()} is not optional; it specifies the name of the new
variable to be created.


{title:Examples}

{p 4 8 2}{cmd:. cipolate y x, gen(yprime)}{p_end}

{p 4 8 2}{cmd:. by panel : cipolate response year, gen(iresponse)}


{title:Author}

{p 4 4 2}Nicholas J. Cox, Durham University, U.K.{break}  
    n.j.cox@durham.ac.uk


{title:References}

{p 4 8 2}Hamming, R.W. 1973. {it:Numerical methods for scientists and engineers.}
New York: McGraw-Hill. See pp.235-236. 

{p 4 8 2}Morton, B.R. 1964. {it:Numerical approximation}. London: Routledge 
and Kegan Paul. See p.38. 

{p 4 8 2}Press, W.H., S.A. Teukolsky, W.T. Vetterling, B.P. Flannery. 1992. 
{it:Numerical recipes in C: the art of scientific computing.} 
Cambridge: Cambridge University Press. See pp.108-110. 


{title:Also see}

{p 4 13 2}Manual:  {hi:[D] ipolate}

{p 4 13 2}On-line:  help for {help ipolate}{p_end}