Clusters of Effects Curves in Quantile Regression Models

Clustering of curves based on a dissimilarity that combines the concordance of their shapes and their closeness, as proposed by Sottile and Adelfio (2019) . The method can be applied to the effects curves of quantile regression coefficients models fitted with 'qrcm', with univariate or multivariate responses, and to curves observed in time, as in functional data analysis. The package also implements the clustering of waveforms by trimmed k-means of functional principal component scores (Adelfio, Chiodi, D'Alessandro and Luzio, 2011).

clustEff

'clustEff' clusters curves with the shape-distance dissimilarity of Sottile and Adelfio (2019): the effects curves of quantile regression coefficients models (fitted with 'qrcm', with one or more responses) and curves observed in time. It also implements the FPCAC algorithm (trimmed k-means of functional principal component scores) for waveforms.

Installation

install.packages("clustEff")
# development version
remotes::install_github("gianluca-sottile/clustEff")

Example

library(clustEff)
set.seed(1234)
tt <- seq(0, 1, length.out = 100)
W <- cbind(sapply(1:5, function(i) sin(3 * pi * tt) + rnorm(100, 0, 0.1)),
           sapply(1:5, function(i) cos(3 * pi * tt) + rnorm(100, 0, 0.1)),
           sapply(1:5, function(i) sin(3 * pi * tt) * cos(pi * tt) + rnorm(100, 0, 0.1)))
fit <- clustEff(W, p = tt, k = c(2, 5), smooth = TRUE)
fit
#> 
#> Call:
#> clustEff(curves = W, p = tt, k = c(2, 5), smooth = TRUE)
#> 
#> Clusters of curves: 3 clusters of sizes 5, 5, 5
#> Dissimilarity: step = "both", alpha = 0.5, derivative = 2, combine = "product"
#> Agglomeration method: ward.D2   criterion: height
#> 
fit$clusters
#>  X1  X2  X3  X4  X5  X6  X7  X8  X9 X10 X11 X12 X13 X14 X15 
#>   1   1   1   1   1   2   2   2   2   2   3   3   3   3   3

References

Sottile, G. and Adelfio, G. (2019). Clusters of effects curves in quantile regression models. Computational Statistics, 34, 551-569. https://doi.org/10.1007/s00180-018-0817-8
Adelfio, G., Chiodi, M., D'Alessandro, A. and Luzio, D. (2011). FPCA algorithm for waveform clustering. Journal of Communication and Computer, 8, 494-502.