sensitivity {twang} | R Documentation |
Produces a table to help the user assess the extent to which a hidden bias might remove any differences observed in the propensity score analysis.
sensitivity(ps1, data, outcome, order.by.importance = TRUE, verbose = TRUE)
ps1 |
a ps object as returned from ps |
data |
the data frame used to fit ps1 |
outcome |
a character string indicating the name of the variable in
data to use as the outcome |
order.by.importance |
if TRUE then the variables are sorted by
their relative influence in the gbm.object used
to create ps1 |
verbose |
if TRUE, lots of information will be printed to monitor the the progress of the fitting |
This function implements the sensitivity analysis described in Ridgeway (2006), Section 5.5. This analysis helps the user assess the extent to which a hidden bias might remove any differences observed in the propensity score analysis.
If there is an important unobserved factor the odds than the correct
propensity score weight is not w(x_i), as the propensity score model
predicts, but actually w(x_i, z_i) where z represents the
unobserved factor. Let a_i=w(x_i, z_i)/w(x_i). These a_i's give
an estimate of g(a), the distribution of the multiplicative errors that
we observe in the weights when excluding z_i. Changing the values of
the a_i's will affect the treatment effect estimate if a is
correlated with y, the outcome. The stronger the correlation the more
sensitive the results will be to the hidden bias. sensitivity
computes
over control group subjects a modified estimate of E(Y_0|t=1).
(sum a_i*w_i*y_i)/(sum a_i*w_i)
subject to the constraint that a_i ~ g(a) and cor(a_i, y_i) = rho.
Several g(a)'s are considered by removing each variable from the propensity score model in turn and computing the ratio of the original weights to the weights with the variable removed. Several choices for rho are also considered, making rho as large as possible, as small as possible, and solving for the ``break even'' rho, the rho that eliminates any treatment effect.
Returns a list where each component contains the sensitivity analysis
for each stop.method
used in fitting ps1
. Each component
contains a data frame with a row for each variable in the original propensity
score model. The columns are
var |
the name of the variable excluded from the model |
E0 |
the estimated E(Y_0|t=1) with var excluded from the
propensity score model |
a.min,a.max |
the smallest and largest values of a observed |
a.cor |
the observed correlation between a and y |
a.mincor,a.maxcor |
the smallest and largest values of rho possible |
minE0,maxE0 |
the smallest and largest values of estimated E(Y_0|t=1) possible |
breakeven.cor |
the break even correlation (see Details section) |
Greg Ridgeway gregr@rand.org
G. Ridgeway (2006). “Assessing the effect of race bias in post-traffic stop outcomes using propensity scores,” Journal of Quantitative Criminology 22(1):1-29.
See ps
for an example