{smcl}
{* 08dec2009 }{...}
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help for {hi:gradip} {right:- v001 08dec2009 jx }
{hline}

{title: Compute averaged differences in predicted probabilities in binary regressions}

{p 8 15 2}{cmd:gradip} varname [if] [in] {cmd:,}
[{cmdab:f:rom(}{it:#}{cmd:)}
{cmdab:t:o(}{it:#}{cmd:)}]
[{cmd:x(}{it:variables_and_values}{cmd:)}
{cmdab:r:est(}{it:stat}{cmd:)}
{cmd:all}
{cmdab:rep:s(}{it:#}{cmd:)}
{cmdab:si:ze(}{it:#}{cmd:)}
{cmdab:g:roup(}{it:varname}{cmd:)}
{cmdab:do:ts}}]


{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), grmedian, grmin, grmax.

{title: Description}

{p 4 4 2}
{cmd:gradip} computes average differences in predicted probabilities over a range
of a continuous variable c from v1 to v2 between Group 1 and 0 using the {help bootstrap} method. The formula in logit model is:
{b_c*(v2-v1)}^(-1){[ln(exp(xb|g=1,c=v2)+1)-ln(exp(xb|g=0,c=v2)+1] - [ln(exp(xb|g=1,c=v1)+1)-ln(exp(xb|g=0,c=v1)+1]}.

{title: Options}

{p 4 8 2}
{cmd:from()} and {cmd:to()} specify the values over which varname
should vary when calculating differences in predicted probabilities.  

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

{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:reps(}{it:#}{cmd:)} specifies the number of bootstrap replications
to be performed.  The default is 1000.

{p 4 8 2}
{cmd: size(}{it:#}{cmd:)} specifies the size of the samples to be drawn.
The default is e(N), the same size as the estimation sample.

{p 4 8 2}
{cmd:dots} requests a dot be placed on the screen at the beginning of each
replication, thus providing entertainment when a large number of reps() are
requested. It also prints out the percent replications finished.

{p 4 8 2}
{cmdab:g:roup} identifies a group indicator variable. This variable needs to be in the 
estimation. One group is coded as 1 and the other group is coded as 0 (G1-G0). 
To compare two groups when we have multiple groups, we need to be also specify
0's for other group indicator variables. For example, we have three groups, Asians, Blacks, 
and Whites. If we want to compare Asians with Whites, and Asian is the omitted category. Then
in the rest option, we need to set Blacks to be zero, and in this {cmdab:g:roup} option,
we just need to specify Whites. 

{title: Returned Matrices}

{p 4 8 2}
r(adipmat):    saves summed differences in predicted probabilities between two groups. Note that to
get average differences in predicted probabilities, users need to divide the matrix by taking the 
differences between {cmd:from()} and {cmd:to()}.

{title:Examples}

{p 4 4 2}
To compute the average difference in predicted probabilities and confidence intervals using bootstrap method
for a logit model with all other variables set at their means except for black (between black=1 and black=1) 
and education (from 12 to 20).

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

{p 4 8 2}{cmd: gradip educ, group(black) from(12) to(20) reps(1000) dots}

{p 4 8 2}
 :::

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