Summation and averaging

Chapter 5.4 Combining domain-specific dissimilarities

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• Please download and unzip the replication files for Chapter 5 ( Chapter05.zip).
• Read readme.html and run 5-0_ChapterSetup.R. This will create 5-0_ChapterSetup.RData in the sub folder data/R. This file contains the data required to produce the plots shown below.
• You also have to add the function legend_large_box to your environment in order to render the tweaked version of the legend described below. You find this file in the source folder of the unzipped Chapter 5 archive.
• We also recommend to load the libraries listed in Chapter 5’s LoadInstallPackages.R

# assuming you are working within .Rproj environment
library(here)

# install (if necessary) and load other required packages
source(here("source", "load_libraries.R"))

# load environment generated in "5-0_ChapterSetup.R"
load(here("data", "R", "5-0_ChapterSetup.RData"))

In chapter 5.3, we introduce another option to account for the parallel unfolding of temporal processes: the clustering on a dissimilarity matrix that results from the summation or the averaging of pairwise dissimilarity matrices computed on separately on two (or more) pools of sequences representing the trajectories in different domains. We are now using the data.frame multidim, which contains both family formation and labour market sequences. The data come from a sub-sample of the German Family Panel - pairfam. For further information on the study and on how to access the full scientific use file see here.

Summation

We first have to construct an object X that contains the dissimilarity matrices in a sequence

X <- list(mc.fam.year.om, mc.act.year.om)

We then use the ?cbind command to combine the X object in rows and columns and generate the object Y

Y <- do.call(cbind, X)

We overwrite Y by using the ?array command to give the right dimensions to the object so that the next steps can be performed

Y <- array(Y, dim=c(dim(X[[1]]), length(X)))

We finally use the ?apply command to apply a summation function (option sum) to the two dimensions of the object Y (1 and 2). We store the resulting dissimilarity matrix in an object called mc.summation

mc.summation<-apply(Y, c(1, 2), sum, na.rm = TRUE)

Averaging

For sake of clarity, we construct another object Z that contains the dissimilarity matrices in a sequence as for the case of summation above

Z <- list(mc.act.year.om, mc.fam.year.om)

We then use the ?cbind command to combine the Z object in rows and columns and generate the object W

W <- do.call(cbind, Z)

We overwrite Y by using the ?array command to give the right dimensions to the object so that the next steps can be performed

W <- array(W, dim=c(dim(X[[1]]), length(X)))

We finally use the ?apply command to apply a averaging function (option mean) to the two dimensions of the object W (1 and 2). We store the resulting dissimilarity matrix in an object called mc.summation

mc.average<-apply(W, c(1, 2), mean, na.rm = TRUE)

Inspection of the matrices

Let’s first display the dissimilarity matrix between the first three sequences in the sample

mc.fam.year.om[1:3, 1:3]

   1  2  3
1  0 40 34
2 40  0 22
3 34 22  0

mc.act.year.om[1:3, 1:3]

   1  2  3
1  0 28 26
2 28  0 10
3 26 10  0

We now inspect the dissimilarity matrix between the first three sequences in the sample after summation….

mc.summation[1:3, 1:3]

     [,1] [,2] [,3]
[1,]    0   68   60
[2,]   68    0   32
[3,]   60   32    0

… and averaging

mc.average[1:3, 1:3]

     [,1] [,2] [,3]
[1,]    0   34   30
[2,]   34    0   16
[3,]   30   16    0