In jmgirard/circumplex: Analysis and Visualization of Circular Data

library(tidyverse)
library(circumplex)
library(psych)

dat <- 
  jz2017 %>% 
  select(PA:NO) %>% 
  mutate(across(everything(), ~scale(.)[, 1])) %>% 
  print()

fa.parallel(dat, fa = "pc")

pca3 <- psych::pca(dat, nfactors = 3, rotate = "none")
print(pca3)
loadings <- 
  pca3$loadings[1:8,] %>% 
  as_tibble(rownames = "scale") %>% 
  mutate(veclen = sqrt(PC2^2 + PC3^2)) %>% 
  print()
circle <- tibble(
  x0 = mean(loadings$PC3), 
  y0 = mean(loadings$PC2), 
  r = mean(loadings$veclen)
)
ggplot(loadings) +
  ggforce::geom_circle(
    data = circle, 
    aes(x0 = x0, y0 = y0, r = r),
    size = 1,
    color = "grey60"
  ) +
  geom_hline(
    yintercept = circle$y0, 
    size = 1, 
    color = "grey60"
  ) +
  geom_vline(
    xintercept = circle$x0, 
    size = 1, 
    color = "grey60"
  ) +
  geom_polygon(aes(x = PC3, y = PC2), alpha = 0.5) +
  geom_point(aes(x = PC3, y = PC2), size = 2, shape = 21) +
  ggrepel::geom_label_repel(
    aes(label = scale, x = PC3, y = PC2),
    nudge_x = c(0, -.2, -.2, -.2, 0, .2, .2, .2),
    nudge_y = c(.2, .2, 0, -.2, -.2, -.2, 0, .2)
  ) +
  coord_fixed(xlim = c(-1, 1), ylim =c(-1, 1))

hyp <- matrix(
  c(1, 0.7071068, 0, -0.7071068, -1, -0.7071068, 0, 0.7071068, 
    0, -0.7071068, -1, -0.7071068, 0, 0.7071068, 1, 0.7071068), 
  ncol = 2) %>% print()
Procrustes(l)

MDS / SSA

rmat <- cor(dat) %>% print(digits = 2)
dmat <- psych::cor2dist(rmat) %>% print(digits = 2)

mds1 <- MASS::isoMDS(d = dmat, k = 1)
mds2 <- MASS::isoMDS(d = dmat, k = 2)
mds3 <- MASS::isoMDS(d = dmat, k = 3)
c(
  k1 = mds1$stress, 
  k2 = mds2$stress, 
  k3 = mds3$stress
) %>% round(5)
mds2$points %>%
  magrittr::set_colnames(c("V1", "V2")) %>% 
  as_tibble(rownames = "Scale") %>% 
  ggplot(aes(x = V2, y = V1*-1)) + 
  geom_point() +
  geom_text(aes(label = Scale)) +
  coord_fixed()