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First release. The package implements the estimators of Coppock, Gerber, Green, and Kern (2017) for randomized experiments with nonignorable missing outcomes.
estimator_ev(): worst-case (Manski 1990) bounds from
a single round of data collection, with a joint Imbens-Manski (2004)
confidence interval.
estimator_ds(): the double-sampling bounds of the
paper, with its analytic variance. A random sample of the initial
nonrespondents is pursued a second time, and only the subjects who
refuse twice get worst-case treatment.
estimator_ds_sens() and
sensitivity_ds(): the interpolation between worst-case
bounds and ignorability, indexed by delta, the share of
follow-up nonrespondents left unmodeled, and a sweep over
delta for delta*, the smallest value at which the
confidence interval reaches zero.
estimator_trim(): trimming bounds on the effect
among always-reporters. The design and the selection assumption are
separate choices. Which response arguments are supplied picks the
design, single sample (R) or double sampling
(R1, Attempt, R2);
monotonicity picks the assumption,
"treatment_increases_response" (Lee 2009),
"treatment_decreases_response", or "none",
which gives the sharp bounds of Imai (2008, Proposition 1) under random
assignment alone. All four combinations estimate. Standard errors come
from Lee (2009, Proposition 3) where that derivation applies, which is
the single-sample, one-group-trimmed case, and from a bootstrap
resampled within treatment arm everywhere else; asking for analytic
standard errors where they do not apply is an error rather than a silent
substitution.
estimator_ev(), estimator_ds(),
estimator_ds_sens() and sensitivity_ds() take
a strata argument for poststratification on a discrete
covariate, which targets the same identification region and estimates it
more precisely.
Every estimator returns the same six named elements in the same
order, under broom’s names: estimate_lower and
estimate_upper, the two ends of the identification region;
std.error_lower and std.error_upper, their
standard errors; and conf.low and conf.high,
the joint Imbens-Manski interval. estimator_trim() follows
them with the intermediate quantities of the path taken.
print(), summary() and
tidy() methods for every result. summary()
names the estimand and the assumptions that produced the numbers; for
trimming bounds that includes the design, the direction assumed, how
much of which group was trimmed, and where the standard errors came
from. tidy() returns a three-row tibble, a
bounds row carrying the whole vector and a row per
endpoint, so DeclareDesign::declare_estimator() can select
an endpoint with term. sensitivity_ds()
returns a classed list whose print() reports delta* and
whose tidy() returns the bounds at every value of
delta.
A formula interface on every estimator,
estimator_ds(Y ~ Z, R1 = "R1", Attempt = "Attempt", R2 = "R2", ...),
which is what declare_estimator(.method = ...) expects.
Response, attempt and stratification arguments accept an unquoted column
name, a quoted string, or a one-sided formula.
The assumed support of the outcome must cover the observed
outcomes, alpha and delta must lie in their
ranges, and every treatment group needs at least one respondent, one
follow-up attempt and one follow-up respondent (within every stratum,
when strata are supplied). Each of these is an error naming the problem
rather than a NaN or a bound that is not a bound.
A monotonicity violation in the direction assumed returns
NA bounds with a warning naming the direction the response
rates do admit. A zero trimming proportion warns that Lee’s
interior-point condition fails. Missingness rates summing to one or
more, or a trimming proportion that leaves one side of a group empty,
are errors, and the bootstrap drops the replicates in which they occur
and reports how many survived.
levendusky_replication: the replication study
reported in the paper, a two-wave survey experiment in which 536 of
1,980 subjects did not answer the second wave and 100 of them were
followed up at a higher incentive. The tibble holds the
polarized-versus-moderate contrast the paper analyzes, with columns
named for the roles they play.
data-raw/levendusky_replication.R rebuilds it from the
Harvard Dataverse deposit.
vignette("attrition") works through the design and
all five estimators on those data, reproduces Table 3 of the paper,
draws the imputation the worst-case bounds average over, and closes with
every estimator on one axis, grouped by the population each one
describes.
For anyone who installed the pre-release package from GitHub:
Output names changed. The bounding estimators returned
low_est, upp_est, low_var,
upp_var, ci_lower and ci_upper,
and estimator_trim() returned lower_bound,
upper_bound, lower_se and
upper_se. The third pair of the old names held variances;
the new std.error_lower and std.error_upper
are standard errors.
The dataset was levendusky and held all three
experimental conditions with the archive’s column names. It is now
levendusky_replication, the analyzed contrast
alone.
sensitivity_ds() returns delta_star, a
single number or NA, in place of p_star, and
its sims_df has a delta column in place of
p.
The Imbens-Manski critical value was found by a bounded optimizer
whose search interval only covered alpha near 0.05, so
confidence intervals at other levels were wrong: at
alpha = 0.01 it returned 2.000 against a correct 2.326. The
root is now found with uniroot() on a bracket derived from
alpha. Bound estimates and variances are
unaffected.
estimator_trim() with R1,
Attempt and R2 previously trimmed both groups
without a way to assume monotonicity, and with R assumed
monotonicity in one fixed direction. Both defaults are unchanged, and
the monotonicity argument now reaches the other
combinations.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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