clustEff-package: Clusters of effects

In gianluca-sottile/clustEff: Clusters of effects in pseudo multi-type response model

Description

This package implements a general algorithm to cluster curves of effects obtained from a quantile regression (qrcm; Frumento and Bottai, 2015) in which the coefficients are described by flexible parametric functions of the order of the quantile. This algorithm can be also used for clustering of curves observed in time, as in functional data analysis.

Details

Package:	clustEff
Type:	Package
Version:	1.0
Date:	2017-03-06
License:	GPL-2

The function clustEff allows to specify the type of the curves to apply the proposed clustering algorithm. The function extract.object extracts the matrices, in case of multivariate response, through the quantile regression coefficient modeling, useful to run the main algorithm. The auxiliary functions summary.clustEff and plot.clustEff can be used to extract information from the main algorithm.

Author(s)

Gianluca Sottile

Maintainer: Gianluca Sottile <[e-mail]>

References

Sottile, G and Adelfio, G (2017). Clustering of effects through quantile regression. Proceedings International Workshop of Statistical Modeling.

Frumento, P., and Bottai, M. (2015). Parametric modeling of quantile regression coefficient functions. Biometrics, doi: 10.1111/biom.12410.

Examples

# use simulated data
# CURVES EFFECTS CLUSTERING

set.seed(1234)
n <- 1000
q <- 2
k <- 5
x1 <- runif(n, 0, 5)
x2 <- runif(n, 0, 5)

X <- cbind(x1, x2)
rownames(X) <- 1:n
colnames(X) <- paste0("X", 1:q)

theta1 <- matrix(c(1, 1, 0, 0, 0, .5, 0, .5, 1, 2, .5, 0, 2, 1, .5),
                 ncol=k, byrow=TRUE)

theta2 <- matrix(c(1, 1, 0, 0, 0, -.3, 0, .5, 1, .5, -1.5, 0, -1, -.5, 1),
                 ncol=k, byrow=TRUE)

theta3 <- matrix(c(1, 1, 0, 0, 0, .3, 0, -.5, -1, 2, -.5, 0, 1, -.5, -1),
                 ncol=k, byrow=TRUE)

rownames(theta3) <- rownames(theta2) <- rownames(theta1) <-
    c("(intercept)", paste("X", 1:q, sep=""))
colnames(theta3) <- colnames(theta2) <- colnames(theta1) <-
    c("(intercept)", "qnorm(p)", "p", "p^2", "p^3")

Theta <- list(theta1, theta2, theta3)

B <- function(p, k){matrix(cbind(1, qnorm(p), p, p^2, p^3), nrow=k, byrow=TRUE)}
Q <- function(p, theta, B, k, X){rowSums(X * t(theta %*% B(p, k)))}

s <- matrix(1, q+1, k)
s[2:(q+1), 2] <- 0
s[1, 3:k] <- 0

Y <- matrix(NA, nrow(X), 15)
for(i in 1:15){
  if(i <= 5) Y[, i] <- Q(runif(n), Theta[[1]], B, k, cbind(1, X))
  if(i <= 10 & i > 5) Y[, i] <- Q(runif(n), Theta[[2]], B, k, cbind(1, X))
  if(i <= 15 & i > 10) Y[, i] <- Q(runif(n), Theta[[3]], B, k, cbind(1, X))
}

XX <- extract.object(Y, X, intercept=TRUE, formula.p= ~ I(p) + I(p^2) + I(p^3))
seqP <- XX$p

obj <- clustEff(XX$X$X1, seqP, Beta.lower=XX$Xl$X1, Beta.upper=XX$Xr$X1)
summary(obj)
plot(obj, xvar="clusters", add=TRUE)
plot(obj, xvar="clusters", add=FALSE)
plot(obj, xvar="dendrogram")
plot(obj, xvar="boxplot")

# CURVES CLUSTERING IN FUNCTIONAL DATA ANALYSIS

set.seed(1234)
n <- 1000
x <- 1:n/n

Y <- matrix(0, n, 30)

sigma2 <- 4*pmax(x-.2, 0) - 8*pmax(x-.5, 0) + 4*pmax(x-.8, 0)

mu <- sin(3*pi*x)
for(i in 1:10) Y[, i] <- mu + rnorm(length(x), 0, pmax(sigma2, 0))

mu <- cos(3*pi*x)
for(i in 11:23) Y[,i] <- mu + rnorm(length(x), 0, pmax(sigma2,0))

mu <- sin(3*pi*x)*cos(pi*x)
for(i in 24:28) Y[, i] <- mu + rnorm(length(x), 0, pmax(sigma2, 0))

mu <- 0 #sin(1/3*pi*x)*cos(2*pi*x)
for(i in 29:30) Y[, i] <- mu + rnorm(length(x), 0, pmax(sigma2, 0))

obj2 <- clustEff(Y, x, cluster.effects=FALSE)
summary(obj2)

plot(obj2, xvar="clusters", add=TRUE)
plot(obj2, xvar="clusters", add=FALSE)
plot(obj2, xvar="dendrogram")
plot(obj2, xvar="boxplot")

gianluca-sottile/clustEff documentation built on May 8, 2019, 9:22 a.m.