sensitivity {twang}R Documentation

Sensitivity analysis

Description

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.

Usage

sensitivity(ps1,
            data,
            outcome,
            order.by.importance = TRUE,
            verbose = TRUE)

Arguments

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

Details

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.

Value

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)

Author(s)

Greg Ridgeway gregr@rand.org

References

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 Also

See ps for an example


[Package twang version 1.0-1 Index]