modi-internal: Internal Functions of modi-package

In modi: Multivariate outlier detection and imputation for incomplete survey data

Description

The modi-package contains internal functions which are normally not called directly by the user. The internal functions are specifically built for the modi-package and are mainly used to improve efficiency and speed in the main functions of the package.

Calculation of distances for Epidemic Algorithm for multivariate outlier detection and imputation: .EA.dist(data,n,p,weights,reach,transmission.function, power, distance.type, maxl)

Non-zero non-missing minimum function: .nz.min(x)

Addressing function for Epidemic Algorithm: .ind.dij(i, j, n)

Addressing function for Epidemic Algorithm: .ind.dijs(i, js, n)

Sum of weights for observations < value (if lt=T) or observations=value (if lt=F): .sum.weights(observations,weights,value,lt=TRUE)

Definition of the sweep and reverse-sweep operator: .sweep.operator(M,k,reverse=FALSE)

psi-function (defined in Little and Smith for ER algorithm): .psi.lismi(d,present,psi.par=c(2,1.25))

EM for multivariate normal data: .EM.normal(data, weights=rep(1,nrow(data)), n=sum(weights) ,p=ncol(data), s.counts, s.id, S, T.obs, start.mean=rep(0,p),start.var=diag(1,p),numb.it=10,Estep.output=F)

ER for multivariate normal data: .ER.normal(data, weights=rep(1,nrow(data)), psi.par=c(2,1.25), np=sum(weights) ,p=ncol(data), s.counts, s.id, S, missing.items, nb.missing.items, start.mean=rep(0,p),start.var=diag(1,p),numb.it=10,Estep.output=F,tolerance=1e-06)

Arguments

data	a data frame or matrix with the data
n	nrow(data)
p	ncol(data)
weights	a vector of positive sampling weights
reach	if reach="max" the maximal nearest neighbour distance is used as the basis for the transmission function, otherwise the weighted (1-(p+1)/n) quantile of the nearest neighbour distances is used.
transmission.function	form of the transmission function of distance d: "step" is a heaviside function which jumps to 1 at d0, "linear" is linearly decreasing from 1 to 0 between 0 and d0, "power" is (beta*d+1)^(-p) with p=ncol(data) as default, "root" is the function 1-(1-d/d0)^(1/maxl)
power	sets p=power
maxl	Maximum number of steps without infection
monitor	if TRUE verbose output on epidemic
x	vector of numeric values
i	index for row
j	index for column
js	vector of indices of columns
observations	Number of observations
value	an integer, indicating the threshold for the sum of weights computation
lt	if TRUE, sum of weights for observations < value is returned. If FALSE, sum of weights for observations = value is returned
M	an array, including a matrix
k	a vector giving the subscripts which the function will be applied over. E.g., for a matrix 1 indicates rows, 2 indicates columns
reverse	logical value
s.counts	counts of the different missingness patterns ordered alphabetically
s.id	indices of the last observation of each missingness pattern in the dataset ordered by missingness pattern
S	total number of different missingness patterns
T.obs	Sufficient statistics on complete observations
start.mean	starting value for mean vector
start.var	starting value for variance vector
numb.it	number of iterations
Estep.output	logical, TRUE if verbose output is desired
psi.par	further parameters passed to the psi-function
np	population size
missing.items	Indices of missing items
nb.missing.items	number of missing items
tolerance	stop iterations when change is below tolerance

Details

.EA.dist creates a vector of length n*(n-1)/2 in the global environment. To avoid memory problems this vector is not (!) passed as a function result.

Value

A list with two components: The first component output is a list with components

sample.spatial.median.index	The index of the observation with minimal sum of absolute distances to all other points
max.min.di	The maximum distance to a nearest neighbour
d0	The reach of the transmission function

The second componentn is

min.dist2nn

A vector of the distances to the nearest neighbour

Author(s)

C\'edric B\'eguin, Beat Hulliger

References

B\'eguin, C., and Hulliger, B. (2004). Multivariate oulier detection in incomplete survey data: The epidemic algorithm and transformed rank correlations. Journal of the Royal Statistical Society, A 167(Part 2.), 275-294.

modi documentation built on May 2, 2019, 6:48 p.m.