Regression-based SDC Tools - Component score correlation control
Source:R/RegSDCcomp.R
RegSDCcomp.RdImplementation of equation 8 in the paper.
Usage
RegSDCcomp(
y,
compCorr = NA,
x = NULL,
doSVD = FALSE,
makeunique = TRUE,
ensureIntercept = TRUE
)Arguments
- y
Matrix of confidential variables
- compCorr
Required component score correlations (possibly recycled)
- x
Matrix of non-confidential variables
- doSVD
SVD when TRUE and QR when FALSE
- makeunique
Parameter to be used in GenQR
- ensureIntercept
Whether to ensure/include a constant term. Non-NULL x is subjected to
EnsureIntercept
Details
NA component score correlation means independent random. Input matrices are subjected to EnsureMatrix.
Examples
x <- matrix(1:10, 10, 1)
y <- matrix(rnorm(30) + 1:30, 10, 3)
# Same as IPSO (RegSDCipso)
RegSDCcomp(y, NA, x)
#> [,1] [,2] [,3]
#> [1,] 0.8317548 10.52484 21.38367
#> [2,] 2.2396118 11.34822 22.75468
#> [3,] 4.6698188 13.12409 22.96191
#> [4,] 4.2293614 14.15172 25.04092
#> [5,] 5.9821308 14.56800 26.79894
#> [6,] 4.9595102 16.49727 26.99543
#> [7,] 5.3957966 16.19149 27.70459
#> [8,] 7.0159493 17.51957 26.58577
#> [9,] 7.1895163 19.88291 28.35850
#> [10,] 9.2620562 20.52317 29.21500
# Using QR and SVD
yQR <- RegSDCcomp(y, c(0.1, 0.2, NA), x)
ySVD <- RegSDCcomp(y, c(0.1, 0.2, NA), x, doSVD = TRUE)
# Calculation of residuals
r <- residuals(lm(y ~ x))
rQR <- residuals(lm(yQR ~ x))
rSVD <- residuals(lm(ySVD ~ x))
# Correlations for two first components as required
diag(cor(GenQR(r)$Q, GenQR(rQR)$Q))
#> [1] 0.1000000 0.2000000 0.1373426
diag(cor(GenQR(r, doSVD = TRUE)$Q, GenQR(rSVD, doSVD = TRUE)$Q))
#> [1] 0.1000000 0.2000000 0.5668663
# Identical covariance matrices
cov(yQR) - cov(ySVD)
#> [,1] [,2] [,3]
#> [1,] -4.440892e-15 -1.065814e-14 -7.105427e-15
#> [2,] -1.065814e-14 -2.131628e-14 -1.421085e-14
#> [3,] -7.105427e-15 -1.421085e-14 -7.105427e-15
cov(rQR) - cov(rSVD)
#> [,1] [,2] [,3]
#> [1,] -4.440892e-16 -1.484923e-15 -4.024558e-16
#> [2,] -1.484923e-15 -3.330669e-16 -1.630640e-16
#> [3,] -4.024558e-16 -1.630640e-16 2.664535e-15
# Identical regression results
summary(lm(y[, 1] ~ x))
#>
#> Call:
#> lm(formula = y[, 1] ~ x)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.5674 -0.4055 0.1461 0.3306 1.1205
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 1.01990 0.61025 1.671 0.133
#> x 0.75594 0.09835 7.686 5.82e-05 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.8933 on 8 degrees of freedom
#> Multiple R-squared: 0.8807, Adjusted R-squared: 0.8658
#> F-statistic: 59.08 on 1 and 8 DF, p-value: 5.818e-05
#>
summary(lm(yQR[, 1] ~ x))
#>
#> Call:
#> lm(formula = yQR[, 1] ~ x)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.0724 -0.6544 -0.2782 0.6340 1.2333
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 1.01990 0.61025 1.671 0.133
#> x 0.75594 0.09835 7.686 5.82e-05 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.8933 on 8 degrees of freedom
#> Multiple R-squared: 0.8807, Adjusted R-squared: 0.8658
#> F-statistic: 59.08 on 1 and 8 DF, p-value: 5.818e-05
#>
summary(lm(ySVD[, 1] ~ x))
#>
#> Call:
#> lm(formula = ySVD[, 1] ~ x)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.9801 -0.5008 -0.2042 0.1629 2.0462
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 1.01990 0.61025 1.671 0.133
#> x 0.75594 0.09835 7.686 5.82e-05 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.8933 on 8 degrees of freedom
#> Multiple R-squared: 0.8807, Adjusted R-squared: 0.8658
#> F-statistic: 59.08 on 1 and 8 DF, p-value: 5.818e-05
#>