RegSDChybrid {RegSDC}

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", ])