*! version 1.2.1 07mar2013

Title

tesensitivity cpi -- Conditional partial independence analysis

Syntax

tesensitivity cpi
(ovar omvarlist) (tvar tmvarlist)
[if] [in]
[,
stat stat_options
general_options]

ovar is a continuous or binary outcome of interest.

omvarlist specifies the covariates in the outcome model.

tvar is a binary variable representing treatment.

tmvarlist specifies the covariates in the treatment-assignment model.

stat

ate Average Treatment Effect; the default

atet Average Treatment Effect on the Treated

qte Quantile Treatment Effect

cqte Conditional Quantile Treatment Effect

cate Conditional Average Treatment Effect

stat specifies the treatment effect statistic that will be analyzed

stat_options

quantile(#) treatment effect quantile for quantile statistics (qte, cqte)

median calculate conditional statistics (cqte, cate) at median; evaluted at mean by default

covsupp(cov_spec) support points of covariates for conditional stastics (cqte, cate)

qcovsupp(cov_spec) quantiles of support points of covariates for conditional stastics (cqte, cate)

stat_options specify options for the statistic selected

general_options

Main
cgrid(#) number of values in grid of c-dependence levels

creference include reference c-dependence levels from leave-one-out analysis (see below)

breakdown(#) calculate breakdown point for stat > #; default 0

nobreakdown don't calculate breakdown point

Tuning options
nodes(#) number of interpolation nodes used to approximate integrals

tol(#) maximum error in calculation of breakdown point

Display options
verbose display progress bars for long computations

Description

tesensitivity cpi estimates bounds on the treatment effect statistic selected
maintaining the assumption of conditional c-dependence. Bounds are calculated for
a uniform grid of c-dependence values from 0 to 1 with the number of point set by
the cgrid option. The breakdown point for the conclusion
that stat > breakdown is also calculated unless nobreakdown is selected.
Results of the analysis are displayed in a table and saved in e(). For details
on conditional c-dependence and the breakdown point see Remarks.

Options

Stat

stat is one of five treatment effect statistics: ate, atet,
qte, cate, or cqte. ate is the default. Only one
statistic can be specified.

ate specifies that the average treatment effect be analyzed.

atet specifies that the average treatment effect on the treated be analyzed.

qte specifies that the quantile treatment effect be analyzed.

cate specifies that the conditional average treatment effect be analyzed.

cqte specifies that the conditional quantile treatment effect be analyzed.

Stat options

stat_options apply to the particular treatment effect statistic chosen.
For conditional statistics, these set the support point of the covariates that
the treatment effect is conditional on. For quantile statistics, these set the
quantile of the treatment effect distribution.

quantile(#) specifies quantiles for (conditional) quantile treatment effects
stasitics. If no quantile is specified, the default option is 0.5.

median By default conditional statistics are calculated at the mean of the
covariates. This switches the default to the median.

covsupp(cov_spec) directly specifies covariate support points for conditional
quantile statistics. See below for input formats.

qcovsupp(cov_spec) specifies quantiles of covariate support points for
conditional quantile statistics. See below for input formats.

In the previous two options, cov_spec is a covariate specification.
This can be in three formats:

1. list of values separated with spaces

2. 1 x K unlabeled matrix

3. 1 x S matrix with column names corresponding to covariate variable names

where K is the number of covariates, and S <= K. If formats 1 or 2
are used, values must be provided for all covariates and
they must be in the same order as they were in tmvarlist and/or omvarlist.
If format 3 is used, it is not necessary to specify
the support for all covariates. Covariates not included will be evaluated at the
mean by default or at the median if the median option is selected. If format 3
is used, it is also possible to used both the covariates and qcovariates
options for different covariates.

General options

Main

cgrid(#) specifies the number of values of c in a uniform grid over [0,1].
If not specified, the default is 40.

creference if selected, also calculate bounds on stat for values of
c corresponding to the maximum propensity score deviation in the leave-one-out
analysis for each covariate. For details see Remarks.

breakdown(#) specifies the conclusion for which the breakdown point is
calculated. The conclusion is: stat > #. For details see Remarks.

nobreakdown if selected, the breakdown point is not calculated.

Tuning Parameters

nodes(#) specifies the number of Chebyschev nodes used in Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) in the computation of integrals. If it is not specified, the default number of nodes is 100. For details see Remarks.

tol(#) specifies a tolerance for the precision of the breakdown point. The breakdown point is computed using bisection algorithm, so this is a tolerance criterion for the bisection algorithm. The default value is 0.001.

Display Options

verbose prints updates on execution of the estimation and progress bars
for long computations.

Remarks

See here for links to the articles
this package is based on, more detailed documentation on the implementation in
this package, and examples of its use.

Stored results

tesensitivity cpi stores the following in e():

Scalars

e(N) number of observations

e(y_breakdown) conclusion lower bound in breakdown point analysis (stat > y_breakdown)

e(c_breakdown) breakdown point relative to the conclusion specified

Macros

e(cmd) tesensitivity

e(subcmd) cpi

e(cmdline) command as typed

e(stat) treatment effect statistic

e(tvar) treatment variable

e(properties) b

e(depvar) outcome variable

Matrices

e(b) vector of bound estimates

e(c_table) rectangular table of bound estimates and c-dependence values

e(covsupp) matrix of covariate support

e(cref) column vector of maximum deviations of covariates in leave-one-out analysis

Examples

. sysuse lalonde1986, clear

Loads LaLonde (1986) dataset included with tesensitivity package.

. tesensitivity cpi (re78 age education) (treat age education) if sample1, ate

Calculates bounds on the average treatment effect for the model specified for a grid
of 40 values of c-dependence between 0 and 1, and the breakdown point for the
conclusion that ATE > 0. Displays a table with the results and stores the
results in e().

For more examples see this vignette.