{smcl}
{* *!version 1.0.0 16dec2011}{...}
{cmd: help margintegrate}
{hline}

{title:Title}
{phang}
{bf: margintegrate} {hline 2} Estimate generalized additive non-parametric functions of two dependent variables; output
graphical representation of {bf: E(yvar|xvar1)}.

{title:Syntax}
{phang}
{cmd:margintegrate} yvar xvar1 xvar2 {ifin} {opt ,} {opt bw(numlist)} [{it:options}]
{p_end}

{title:Description}
{pstd}
{cmd:margintegrate} estimates a non-parametric regression of {it:yvar} on {it:xvar1} and {it:xvar2}, treating the 
expectation of {bf:yvar|xvar1} as the quantity of interest. It integrates out the effect of the "nuisance" variable 
xvar2 by means of marginal integration, following the methods outlined in Linton and Neilsen (1996), Tjostheim
and Auestad (1994); see also Li and Racine (2007, 283-289).


{title:Required Argument}
{phang}
{opt bw(numlist)} must contain two values, bw_1 and bw_2, the bandwidths for xvar1 and xvar2, respectively. The 
literature on generalized additive models has suggested using a multiple of the standard deviation as the 
bandwidth each independent variable of interest (i.e. .7, .9, 1.1 times sd); this solution is not optimal in the
mean squared error sense, but visual inspection can provide a good guide to appropriate levels of smoothing. 

{title:Options}
{phang}
{opt n(integer 50)} contains the number of points at which the estimation will be executed. The maximum is 800; default
is 50. The marginal integration estimator requires {it: n x n} regression smoothes to get predicted values, so {opt n(100)}
estimates 10,000 regression smoothes. Points are chosen according to percentile values of the data sorted by xvar1
and xvar2. 

{phang}
{opt gen:erate(varlist)} can contain up to two variable names, the first for the predicted value of the estimator,
the second for the pointwise estimate of the variance.

{phang}
{opt ci(level)} shows pointwise confidence intervals at specified level, assuming asymptotic normal distribution of
the expected value. If {opt boot} is not specified, the estimator uses asymptotic variance (see Li and Racine 
(2007, p.285)) to construct confidence intervals; this expression can be fragile, especially if the support for 
either of the independent variables is not compact.

{phang}
{opt boot(integer)} estimates confidence intervals by bootstrapping original data {it:integer} number of times. 

{phang}
{opt trim(real)} specifies that a total of {it: real} percent of the data will be trimmed for the purposes of estimation;
trims {it: real/2} percent at top and bottom of the data sorted by xvar1.

{phang}
{opt nograph} specifies no graphical output: predicted values will be calculated and stored if {opt gen:erate(varlist)}
is specified; use to incorporate your own graph preferences.


{title:Examples}
{pstd}
Estimate a locally linear regression of y on x1 and x2 and use the asymptotic variance to show 95% confidence 
intervals. Use 100 points to in the distribution of x1 and x2 to derive estimates.

{phang2}
{cmd: . margintegrate y x1 x2, bw(4 5) n(100) ci(95)}


{pstd}
Estimate a locally linear regression of y on x1 and x2 without producing any graphical output, but using
the bootstrap procedure to estimate pointwise variances. Use 100 points to in the distribution of x1 and x2 to derive 
estimates.
{phang2}
{cmd: . margintegrate y x1 x2, bw(4 5) n(100) boot(50) nograph}