RegSDChybrid: Regression-based SDC Tools - Generalized microaggregation

In RegSDC: Information Preserving Regression-Based Tools for Statistical Disclosure Control

Regression-based SDC Tools - Generalized microaggregation

Description

Implementation of the methodology in section 6 in the paper

Usage

RegSDChybrid(
  y,
  clusters = NULL,
  xLocal = NULL,
  xGlobal = NULL,
  clusterPieces = NULL,
  xClusterPieces = NULL,
  groupedClusters = NULL,
  xGroupedClusters = NULL,
  alternative = NULL,
  alpha = NULL,
  ySim = NULL,
  returnParts = FALSE,
  epsAlpha = 1e-07,
  makeunique = TRUE,
  tolerance = sqrt(.Machine$double.eps)
)

Arguments

y	Matrix of confidential variables
clusters	Vector of cluster coding
xLocal	Matrix of x-variables to be crossed with clusters
xGlobal	Matrix of x-variables NOT to be crossed with clusters
clusterPieces	Vector of coding of cluster pieces
xClusterPieces	Matrix of x-variables to be crossed with cluster pieces
groupedClusters	Vector of coding of grouped clusters
xGroupedClusters	Matrix of x-variables to be crossed with grouped clusters
alternative	One of "" (default), "a", "b" or "c"
alpha	Possible to specify parameter used internally by alternative "c"
ySim	Possible to specify the internally simulated data manually
returnParts	Alternative output six matrices: y1 and y2 (fitted), e3s and e4s (new residuals), e3 and e4 (original residuals)
epsAlpha	Precision constant for alpha calculation
makeunique	Parameter to be used in GenQR
tolerance	Parameter to Cdiff used within the algorithm

Details

Input matrices are subjected to EnsureMatrix. Necessary constant terms (intercept) are automatically included. That is, a column of ones is not needed in the input matrices.

Value

Generated version of y

Author(s)

Øyvind Langsrud

Examples

#################################################
# Generate example data for introductory examples
################################################# 
y <- matrix(rnorm(30) + 1:30, 10, 3)
x <- matrix(1:10, 10, 1)  # x <- 1:10 is equivalent

# Same as RegSDCipso(y)
yOut <- RegSDChybrid(y)

# With a single cluster both are same as RegSDCipso(y, x)
yOut <- RegSDChybrid(y, xLocal = x)
yOut <- RegSDChybrid(y, xGlobal = x)

# Define two clusters
clust <- rep(1:2, each = 5)

# MHa and MHb in paper
yMHa <- RegSDChybrid(y, clusters = clust, xLocal = x)
yMHb <- RegSDChybrid(y, clusterPieces = clust, xLocal = x)

# An extended variant of MHb as mentioned in paper paragraph below definition of MHa/MHb
yMHbExt <- RegSDChybrid(y, clusterPieces = clust, xClusterPieces = x)

# Identical means within clusters
aggregate(y, list(clust = clust), mean)
aggregate(yMHa, list(clust = clust), mean)
aggregate(yMHb, list(clust = clust), mean)
aggregate(yMHbExt, list(clust = clust), mean)

# Identical global regression results
summary(lm(y[, 1] ~ x))
summary(lm(yMHa[, 1] ~ x))
summary(lm(yMHb[, 1] ~ x))
summary(lm(yMHbExt[, 1] ~ x))

# MHa: Identical local regression results
summary(lm(y[, 1] ~ x, subset = clust == 1))
summary(lm(yMHa[, 1] ~ x, subset = clust == 1))

# MHb: Different results
summary(lm(yMHb[, 1] ~ x, subset = clust == 1))

# MHbExt: Same estimates and different std. errors
summary(lm(yMHbExt[, 1] ~ x, subset = clust == 1))

###################################################
#  Generate example data for more advanced examples
###################################################
x <- matrix((1:90) * (1 + runif(90)), 30, 3)
x1 <- x[, 1]
x2 <- x[, 2]
x3 <- x[, 3]
y <- matrix(rnorm(90), 30, 3) + x
clust <- paste("c", rep(1:3, each = 10), sep = "")

######## Run main algorithm
z0 <- RegSDChybrid(y, clusters = clust, xLocal = x3, xGlobal = cbind(x1, x2))

# Corresponding models by lm
lmy <- lm(y ~ clust + x1 + x2 + x3:clust)
lm0 <- lm(z0 ~ clust + x1 + x2 + x3:clust)

# Preserved regression coef (x3 within clusters)
coef(lmy) - coef(lm0)

# Preservation of x3 coef locally can also be seen by local regression
coef(lm(y ~ x3, subset = clust == "c2")) - coef(lm(z0 ~ x3, subset = clust == "c2"))

# Covariance matrix preserved
cov(resid(lmy)) - cov(resid(lm0))

# But not preserved within clusters
cov(resid(lmy)[clust == "c2", ]) - cov(resid(lm0)[clust == "c2", ])

######## Modification (a)
za <- RegSDChybrid(y, clusters = clust, xLocal = x3, xGlobal = cbind(x1, x2), alternative = "a")
lma <- lm(za ~ clust + x1 + x2 + x3:clust)

# Now covariance matrices preserved within clusters
cov(resid(lmy)[clust == "c2", ]) - cov(resid(lma)[clust == "c2", ])

# If we estimate coef for x1 and x2 within clusters, 
# they become identical and identical to global estimates
coef(lma)
coef(lm(za ~ clust + x1:clust + x2:clust + x3:clust))

######## Modification (c) with automatic calculation of alpha 
# The result depends on the randomly generated data
# When the result is that alpha=1, modification (b) is equivalent
zc <- RegSDChybrid(y, clusters = clust, xLocal = x3, xGlobal = cbind(x1, x2), alternative = "c")
lmc <- lm(zc ~ clust + x1 + x2 + x3:clust)

# Preserved regression coef as above
coef(lmy) - coef(lmc)

# Again covariance matrices preserved within clusters
cov(resid(lmy)[clust == "c2", ]) - cov(resid(lmc)[clust == "c2", ])

# If we estimate coef for x1 and x2 within clusters, 
# results are different from modification (a) above
coef(lmc)
coef(lm(zc ~ clust + x1:clust + x2:clust + x3:clust))


####################################################
# Make groups of clusters (d) and cluster pieces (e)
####################################################
clustGr <- paste("gr", ceiling(rep(1:3, each = 10)/2 + 0.1), sep = "")
clustP <- c("a", "a", rep("b", 28))

######## Modifications (c), (d) and (e)
zGrP <- RegSDChybrid(y, clusters = clust, clusterPieces = clustP, groupedClusters = clustGr,
                     xLocal = x3, xGroupedClusters = x2, xGlobal = x1, alternative = "c")

# Corresponding models by lm
lmGrP <- lm(zGrP ~ clust:clustP + x1 + x2:clustGr + x3:clust - 1)
lmY <- lm(y ~ clust:clustP + x1 + x2:clustGr + x3:clust - 1)

# Preserved regression coef
coef(lmY) - coef(lmGrP)

# Identical means within cluster pieces
aggregate(y, list(clust = clust, clustP = clustP), mean)
aggregate(zGrP, list(clust = clust, clustP = clustP), mean)

# Covariance matrix preserved
cov(resid(lmY)) - cov(resid(lmGrP))

# Covariance matrices preserved within clusters
cov(resid(lmY)[clust == "c2", ]) - cov(resid(lmGrP)[clust == "c2", ])

# Covariance matrices not preserved within cluster pieces
cov(resid(lmY)[clustP == "a", ]) - cov(resid(lmGrP)[clustP == "a", ])

RegSDC documentation built on Aug. 19, 2022, 9:08 a.m.