Sensitivity analysis for unit and item nonresponse ($\theta =[n_R{\hat{p}}_R+n_I{p}_I+n_U{p}_U]/n$)

Vary the unobserved outcome probabilities for item and unit nonresponders, and any unknown auxiliary-variable mixture, over scientifically plausible ranges. Recompute the population estimate and identify values at which substantive conclusions change. This probes untestable transport or missing at random assumptions; it is distinct from sampling uncertainty represented by a confidence interval. Letting each missing-outcome probability vary from zero to one gives worst-case identification bounds.