Sensitivity to User-Specified Perturbations

The more standard sensitivity and sensitivity_pathwise functions support sensitivity analysis to violations in assumptions restricted to specific mediator-outcome pairs. For more general violations, this function allows arbitrary modification of the default, diagonal covariance matrix structure across both mediators and outcomes. This makes it possible to ask what happens when mediators are correlated with one another or when more some pairs of mediator-outcome pairs have much stronger correlation than others.

Usage

sensitivity_perturb(
  model,
  exper,
  perturb,
  nu_seq = NULL,
  n_bootstrap = 100,
  progress = TRUE
)

Arguments

model

A multimedia object containing the fitted models for sensitivity analysis. Note that since our approach relies on correlating simulated residual error, it is only applicable to models of class lm_model(), glmnet_model() and rf_model().

exper

The original mediation_data class object used to fit model. These observations will be resampled to support bootstrap confidence interval construction of the sensitivity curve.

perturb

A matrix towards which the original mediator-outcome covariance should be perturbed. Must have dimension (n_mediators + n_outcomes) x (n_mediators + n_outcomes).

nu_seq

The strength of the perturbation towards the matrix perturb.

n_bootstrap

The number of bootstrap resamples used to build confidence bands around the sensitivity curves. Defaults to 100.

progress

A logical indicating whether to show a progress bar.

Value

A date.frame giving the outputs of indirect_overall across many values of the correlation rho.

Details

Specifically, it defines a new covariance matrix across mediators and outcomes according to diag(sigma^2_mediator, sigma^2_outcome) + nu * perturb. The estimates sigma^2 are taken from the residuals in the original mediation and outcome models, and perturb and nu are provided by the user.

Examples

xy_data <- demo_spline()
exper <- mediation_data(
    xy_data, starts_with("outcome"), "treatment", "mediator"
)
model <- multimedia(
    exper,
    outcome_estimator = glmnet_model(lambda = 1e-2)
) |>
    estimate(exper)
nu_seq <- c(-0.2, 0.2)
perturb <- matrix(
    c(
        0, 3, 0,
        3, 0, 0,
        0, 0, 0
    ),
    nrow = 3, byrow = TRUE
)
sensitivity_perturb(model, exper, perturb, nu_seq, n_bootstrap = 2)
#> Error in mvrnorm(nrow(exper), rep(0, Nm + Ny), Sigma = (covariance_matrix(model) +     nu * perturb)): 'Sigma' is not positive definite