Min.Max.Multivar.PCA {EffectTreat}

Minimum and maximum values for the multivariate predictive causal association (PCA) in the continuous-continuous case

Description

The function Min.Max.Multivar.PCA computes the minimum and maximum values for the multivariate predictive causal association (PCA) in the continuous-continuous case.

Usage

Min.Max.Multivar.PCA(gamma, Sigma_SS, Sigma_T0T0, Sigma_T1T1)

Arguments

gamma

The vector of regression coefficients for the S by treatment interactions.

Sigma_SS

The variance-covariance matrix of the pretreatment predictors. For example, when there are 2 pretreatment predictors \bold{\Sigma}_{SS}=\left(\begin{array}{cc}\sigma_{S1S1} & \sigma_{S1S2} \\ \sigma_{S1S2} & \sigma_{S2S2}\end{array}\right).

Sigma_T0T0

The variance of T in the control treatment group.

Sigma_T1T1

The variance of T in the experimental treatment group.

Author(s)

Wim Van der Elst & Ariel Alonso

References

Alonso, A., & Van der Elst, W. (submitted). Evaluating multivariate predictors of therapeutic success: a causal inference approach.

Examples

# Specify vector of S by treatment interaction coefficients 
gamma <- matrix(data = c(-0.006, -0.002, 0.045), ncol=1)
# Specify variances
Sigma_SS = matrix(data=c(882.352, 49.234, 6.420,
49.234, 411.964, -26.205, 6.420, -26.205, 95.400),
byrow = TRUE, nrow = 3)
Sigma_T0T0 <- 82.274
Sigma_T1T1 <- 96.386

# Compute min and max PCA
Min.Max.Multivar.PCA(gamma=gamma, Sigma_SS=Sigma_SS, 
Sigma_T0T0=Sigma_T0T0, Sigma_T1T1=Sigma_T1T1)