In michaelkriegsman/DiDiSTATIS: Run DiDiSTATIS and related methods

knitr::opts_chunk$set(echo = TRUE)
library(DistatisR)
library(ExPosition)
library(DiDiSTATIS)

Example: DiMDS

The data, S

For this example, I adapt the data from the chapter on DiSTATIS. Although these data are an array of distance matrices, DiSTATIS collapses the tables into a single representative table, called the compromise. This compromise is a 36 by 36 (psd) matrix of the perceived similarity between 36 pieces of classical music. Here, I denote the compromise S, where S is the input to DiMDS. (Note that in DiSTATIS, the compromise is called Splus)

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>>>>>>> origin/Testing-DiMDS
## Archived Notes
## I ran DiDiSTATIS_Composers_free_36.R (despite the name, this is a standard DiSTATIS) on 5.16.17 and saved out compromise as CompromiseForDiMDS
## S <- RvDiSTATIS_Composers.res$res4GPCA$Splus
## save("S", file = "CompromiseForDiMDS.rda")


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>>>>>>> origin/Testing-DiMDS
#read in the data, S, the compromise from DiSTATIS (from Part II of the dissertation).
load('C:/Users/Michael A. Kriegsman/Google Drive/Dissertation/DiDiSTATIS/DiDiSTATIS/vignettes/DiMDS/CompromiseForDiMDS.rda')
#round(S, 3)

The design, B

The pieces of classical music (stimuli, rows) are organized into a 2-factor completely between design. That is, each piece was composed by 1 of 3 composers, and played by 1 of 4 pianists. For the dissertation proposal, I will only investigate the effect of composer.

#create the design. B, the design matrix for the A=36 musical pieces nested in the B=3 composers.
DESIGN <- list()
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DESIGN$rows$Composers_mat <- makeNominalData(as.matrix(rep(1:3,each=12)))
colnames(DESIGN$rows$Composers_mat) <- c('Bach', 'Beethoven', 'Mozart')
B <- DESIGN$rows$Composers_mat
#B

DESIGN$rows$Composer_colors_B  <- prettyGraphsColorSelection(3, offset=3)
DESIGN$rows$Composer_colors_AB <- rep(prettyGraphsColorSelection(3, offset=3), each=12)
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Let's go!

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res_MDS <- MDS(D = S, data_are = 'CP', DESIGN_rows = B, main = 'FreeSort36 Composers')
#Feed DiMDS the goods
res_DiMDS <- DiMDS(D = S, data_are = 'CP', DESIGN_rows = B, main = 'FreeSort36 Composers')
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res_MDS <- MDS(D = S, data_are = 'CP', DESIGN_rows = B, main = 'FreeSort36 Composers')
#Feed DiMDS the goods
res_DiMDS <- DiMDS(D = S, data_are = 'CP', DESIGN_rows = B, main = 'FreeSort36 Composers')

>>>>>>> origin/Testing-DiMDS

Consider the effect size(s):

$r^2_{Total \cdot B}$

#The portion of the total barycentric space explained by the barycenters (Composers)
round(res_DiMDS$r2$total.b,3)

$r^2_{TotalTotal \cdot B}$

#The portion of the original data explained by the barycenters (Composers)
round(res_DiMDS$r2$totaltotal.b,3)

There is a large discrepency between the size of the barycentric space and the size of the original data.
This shows that the hypothesized between-group effect is small (and/or the data are highly variable).

Given the small effect, let's inspect, respectively, Fb: the group barycenters in the barycentric factor scores, F: the original data projected intot he barycentric factor space ...