Estimation of tphiy

Estimation of the total of the weighted potential outcomes of each mode of response \(t_{y\phi}\).

Usage

estim_tot_phi_y(Yobs, modes, pi, p1, p2, phi = rep(0.5, length(Yobs)))

Yobs: vector of the observed outcomes. (numeric vector of size N the size of the population).
modes: vector of the selected mode of each unit. The first mode of the protocol is defined as "m1", the second as "m2" (character vector or factor of size N).
pi: vector containing the first-order inclusion probabilities (numeric vector of size N).
p1: vector containing the true or estimated selection probabilities of the first mode (numeric vector of size N).
p2: vector containing the true or estimated selection probabilities of the second mode (numeric vector of size N).
phi: optional vector containing weights for the total. The values must be between 0 and 1. The more the weight is close to one, the more the first mode of reponse is important (numeric vector size N).

the estimation of the total \(t_{y\phi}\) (scalar).