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Estimation of the covariance between the potential outcomes of two modes of response under homoscedasticity assumptions and linearity

estim_cov_12.Rd

We suppose the homoscedasticity within the first and second and between the modes of response potential outcomes. We will have an unbiased estimator if the non-informativeness, unconfoundedness and conditional mutual independence assumptions are verified ; the measure effect y_1k - y_2k follow a linear model with x_k and for some units both potential outcomes are known (which can't be under a sequential protocol). We must have at least p + 1 (p the number of covariates) units such that their measure effect are known or well estimated. The standard deviations sd1 and sd2 must be unbiased as well.

Usage

estim_cov_12(
  Y1,
  Y2,
  sd1,
  sd2,
  X,
  Yobs = NULL,
  modes = NULL,
  clamp = FALSE,
  warnClamp = TRUE,
  ...
)

Arguments

Y1

vector of the first mode outcomes (numeric vector of size N the size of the population).

Y2

vector of the second mode outcomes (numeric vector of size N).

sd1

true or estimated value of the standard deviation of the first mode of response potential outcomes (positive scalar).

sd2

true or estimated value of the standard deviation of the second mode of response potential outcomes (positive scalar).

X

design matrix (numeric matrix with N rows and p columns).

Yobs

vector of the observed outcomes. Optional. Useful if Y1 and Y2 are not given. In that case the counterfactuals of the respondents are estimated with the function estim_counterfactuals. the value is not considered and therefore can be equal to NA (numeric vector of size N the size of the population).

modes

vector of the selected mode of each unit. Optional. Used if the counterfactuals must be estimated (character vector or factor of size N).

clamp

TRUE if the estimation of the covariance must be clamped if its absolute value is superior to sd1 * sd2 (boolean).

warnClamp

TRUE if a warning must be sent when a clamp is made (boolean).

...

arguments for the function MatchIt::matchit.

Value

an estimator of the covariance between the m1 and m2 potential outcomes, unbiased under the assumptions, if sd1^2 and sd2^2 are unbiased and the counterfactuals are the true values (scalar).