Implementation of equation 4 in the paper.
Arguments
- y
Matrix of confidential variables
- x
Matrix of non-confidential variables
- ensureIntercept
Whether to ensure/include a constant term. Non-NULL x is subjected to
EnsureIntercept
Details
Input matrices are subjected to EnsureMatrix.
Examples
x <- matrix(1:5, 5, 1)
y <- matrix(rnorm(15) + 1:15, 5, 3)
ySynth <- RegSDCipso(y, x)
# Identical regression results
summary(lm(y[, 1] ~ x))
#>
#> Call:
#> lm(formula = y[, 1] ~ x)
#>
#> Residuals:
#> 1 2 3 4 5
#> -1.1012 0.9930 0.8082 -0.1907 -0.5093
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 0.7162 1.0743 0.667 0.5527
#> x 0.8419 0.3239 2.599 0.0804 .
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 1.024 on 3 degrees of freedom
#> Multiple R-squared: 0.6925, Adjusted R-squared: 0.59
#> F-statistic: 6.756 on 1 and 3 DF, p-value: 0.08044
#>
summary(lm(ySynth[, 1] ~ x))
#>
#> Call:
#> lm(formula = ySynth[, 1] ~ x)
#>
#> Residuals:
#> 1 2 3 4 5
#> -0.6954 0.1954 1.4436 -0.6917 -0.2519
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 0.7162 1.0743 0.667 0.5527
#> x 0.8419 0.3239 2.599 0.0804 .
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 1.024 on 3 degrees of freedom
#> Multiple R-squared: 0.6925, Adjusted R-squared: 0.59
#> F-statistic: 6.756 on 1 and 3 DF, p-value: 0.08044
#>
# Identical covariance matrices
cov(y) - cov(ySynth)
#> [,1] [,2] [,3]
#> [1,] -8.881784e-16 -1.776357e-15 -3.108624e-15
#> [2,] -1.776357e-15 -1.776357e-15 -4.440892e-15
#> [3,] -3.108624e-15 -4.440892e-15 -8.881784e-15
cov(residuals(lm(y ~ x))) - cov(residuals(lm(ySynth ~ x)))
#> [,1] [,2] [,3]
#> [1,] -1.110223e-16 -3.400058e-16 5.828671e-16
#> [2,] -3.400058e-16 5.551115e-16 1.665335e-16
#> [3,] 5.828671e-16 1.665335e-16 -3.608225e-16