{smcl}
{* 28Feb2011}{...}
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help for {hi:_grmargd}{right:28Feb2011}
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{title:Marginal effects and their differences in binary regressions using the delta method for inference}

{p 8 15 2}{cmd:_grmargd} [{cmd:if} exp] [{cmd:in} range] [{cmd:,}
{cmd:x(}{it:variables_and_values}{cmd:)}
{cmdab:r:est(}{it:stat}{cmd:)}
{cmdab:noba:se}
{cmd:all}
{cmdab:l:evel(}{it:#}{cmd:)}
{cmdab:s:ave}
{cmdab:d:iff}
{cmd:dydxmat(}{it:matrix_kxk}{cmd:)}]

{p 4 4 2}
where {it:variables_and_values} is an alternating list of variables
and either numeric values or mean, median, min, max, upper, lower,
previous.

{p 4 4 2}
{it:stat} is either mean, median, min, max, upper, lower,
previous, grmean(group mean), mrmedian, grmin, grmax.


{title:Description}

{p 4 4 2}
After estimating a binary regression model, {cmd:_grmargd} computes the
predicted marginal effects at specific values of the independent variables, 
or differences in marginal effects at two different x vectors. confidence 
intervals are available using the {help delta} method with closed form 
analytic solutions. This low utility program also provides retued matrices (see below).

{title:Options}

{p 4 8 2}
{cmd:save}  saves current values of independent variables and predictions (marginal effects)
for computing changes using the diff option.

{p 4 8 2}
{cmd:diff}  computes difference between current predictions (marginal effects) and those
that were saved.

{p 4 8 2}
{cmd:level()} sets the {help level} of the confidence interval for predicted
values or marginal effects for the commands for which these are provided. The
default is 95.

{p 4 8 2}
{cmd:x()} sets the values of independent variables for calculating
predicted values.  The list must alternate variable names and values.
The values may be either numeric values or can be mean, median, min,
max, previous, upper, or lower.  The latter cannot be used if rest()
specifies a group summary statistic (e.g., grmean).

{p 4 8 2}
{cmd:rest()} sets the independent variables not specified in x()
to their {cmd:mean} (default), {cmd:minimum}, {cmd:maximum}, {cmd:median}
when calculating predicted values. {cmd:grmean} sets these independent
variables to the mean conditional on the variables and values specified
in x(); {cmd:grmedian},{cmd:grmax}, and {cmd:grmin} can also be used.

{p 4 8 2}
{cmd:nobase} suppresses inclusion of the base values of x in the output.

{p 4 8 2}
{cmd:all} specifies that any calculations of means, medians, etc.,
should use the entire sample instead of the sample used to estimate
the model.

{p 4 8 2}
{cmd:dydxmat(}{it:matrix_kxk}{cmd:)} supplies a matrix by users of dy/dx or 
dxb/dx, where there is polynomial or interaction terms.

{title:Returned Matrices}

{p 4 8 2}
r(marg):    saves marginal effects.

{p 4 8 2}
r(margci):  saves confidence intervals for marginal effects

{p 4 8 2}
r(margvar): saves variance-covariance matrix for marginal effects

{p 4 8 2}
r(margse):  saves standard errors for marginal effects

{p 4 8 2}
r(dmarg):   saves differences in marginal effects when {cmd:diff} option is used

{p 4 8 2}
r(dmargci): saves confidence intervals for differences in marginal effects when {cmd:diff} option is used.


{title:Examples}

{p 4 4 2}
To compute the predicted marginal effects and confidence intervals using delta method
for a logit in which all independent variables are held at the mean.

{p 4 8 2}{cmd:.logit vote black educ income}

{p 4 8 2}{cmd:._grmargd, x(black=1 educ=16) save}

{p 4 8 2}{cmd:._grmargd, x(black=0 educ=16) diff}

{p 4 4 2}
What if there is interaction terms or polynomial terms? Here is an example.

{p 4 8 2}{cmd:.gen age2=age*age}

{p 4 8 2}{cmd:.logit lfp age age2 k5 inc }

{p 4 8 2}{cmd:._grmargd, x(age=20 age2=400) dydxmat(1, 20, 0, 0, 0 \ 0, 1, 0, 0, 0 \ 0, 0, 1, 0, 0 \ 0, 0, 0, 1, 0 \ 0, 0, 0, 0, 1)}

 :::

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{p 2 4 2}Authors: Jun Xu{p_end}