This year I realized as clearly as never before how important it is to show examples from A to Z.

When doing correspondence analysis, we discussed biplots with small images of company brands in them.

So, here we go.

I will replicate the beautifully arranged case presented by one of the students and re-build the picture using standard R packages.

The original case can be found here: https://rpubs.com/linalinaa/1005417

# library(datapasta)
# tribble_paste()

tabl <- tibble::tribble(
               ~V1, ~V2, ~V3, ~V4,
      "Portugal R",  7L,  2L, 26L,
      "Portugal W",  8L,  2L, 15L,
        "France R", 12L, 43L, 40L,
        "France W", 10L, 35L, 26L,
         "Italy R", 30L, 67L, 58L,
         "Italy W", 22L, 49L, 63L,
         "Spain R", 29L, 48L, 83L,
         "Spain W", 17L, 19L, 43L,
       "Georgia R", 26L, 22L, 22L,
       "Georgia W",  7L, 12L,  7L,
        "Russia R", 40L, 35L, 46L,
        "Russia W", 30L, 35L, 41L,
         "Chile W",  8L, 13L, 10L,
         "Chile R",  7L, 21L, 19L,
  "South Africa W",  5L,  5L, 10L,
  "South Africa R",  3L,  4L, 19L,
     "Argentina W",  2L,  5L,  2L,
     "Argentina R",  4L,  7L, 10L
  )
tabl1  <- as.data.frame(tabl)

Add a meaningful vector for the color of wine

Wow-wow, what do we see? Lines 1-12 are W-R, lines 13-18 are R-W, so let’s rearrange them

tabl1$color <- c(rep(seq(1, 2, 1), 6), rev(rep(seq(1, 2, 1), 3))) 
tabl1$color <- factor(tabl1$color, labels = c("red", "white"))
row.names(tabl1) <- tabl$V1
head(tabl1)
##                    V1 V2 V3 V4 color
## Portugal R Portugal R  7  2 26   red
## Portugal W Portugal W  8  2 15 white
## France R     France R 12 43 40   red
## France W     France W 10 35 26 white
## Italy R       Italy R 30 67 58   red
## Italy W       Italy W 22 49 63 white
tail(tabl1)
##                            V1 V2 V3 V4 color
## Chile W               Chile W  8 13 10 white
## Chile R               Chile R  7 21 19   red
## South Africa W South Africa W  5  5 10 white
## South Africa R South Africa R  3  4 19   red
## Argentina W       Argentina W  2  5  2 white
## Argentina R       Argentina R  4  7 10   red
tabl1$V1 <- NULL
colnames(tabl1) <- c("KB", "Lab", "AM", "color")
chisq.test(tabl1[ , 1:3])$stdres
##                         KB        Lab         AM
## Portugal R     -0.24607452 -3.6287763  3.6792871
## Portugal W      1.26375036 -2.8111457  1.6423614
## France R       -2.22998983  2.3102122 -0.3601715
## France W       -1.60177824  2.7130595 -1.2676898
## Italy R        -0.75441550  2.4611247 -1.7302022
## Italy W        -1.56855119  0.5480167  0.7779573
## Spain R        -1.17294899 -1.2681246  2.1885310
## Spain W        -0.03805425 -2.0095176  1.9559179
## Georgia R       3.23030504 -0.5466173 -2.1594430
## Georgia W       0.65443948  1.2700731 -1.7597563
## Russia R        3.19532188 -1.3451606 -1.3657038
## Russia W        1.72788893 -0.3228937 -1.1258705
## Chile W         0.56329980  0.8891029 -1.3192448
## Chile R        -1.15271941  1.5060045 -0.4847743
## South Africa W  0.36216412 -0.8960768  0.5572922
## South Africa R -1.26941724 -2.0670880  3.0337381
## Argentina W     0.03890720  1.3377738 -1.3133650
## Argentina R    -0.29631474 -0.1079913  0.3495123
library(factoextra)
library(FactoMineR)

I downloaded pictures of brands as .png files in my home directory

res.ca <- CA(tabl1[1:18,1:3], graph = FALSE)

The fviz_ca functionality is not bad at all but the palette is not helpful

fviz_ca_biplot(
  res.ca,
  repel = TRUE,
  col.row = tabl1$color,
  arrows = c(T,T),
  title = "CA Biplot for stores and wine"
)

Add a vector with pictures as another row

# library(here)
# here()
tabl1 <- rbind(tabl1, c("kb.png", "ab.png", "am.png", "NA"))
row.names(tabl1) <- c(tabl$V1, c("image"))
tabl1
##                    KB    Lab     AM color
## Portugal R          7      2     26   red
## Portugal W          8      2     15 white
## France R           12     43     40   red
## France W           10     35     26 white
## Italy R            30     67     58   red
## Italy W            22     49     63 white
## Spain R            29     48     83   red
## Spain W            17     19     43 white
## Georgia R          26     22     22   red
## Georgia W           7     12      7 white
## Russia R           40     35     46   red
## Russia W           30     35     41 white
## Chile W             8     13     10 white
## Chile R             7     21     19   red
## South Africa W      5      5     10 white
## South Africa R      3      4     19   red
## Argentina W         2      5      2 white
## Argentina R         4      7     10   red
## image          kb.png ab.png am.png  <NA>

Use ggplot2 to change geom to “image”.

We will need to plot two sets of points, from rows and columns

picdata1 <- as.data.frame(res.ca$row$coord)
picdata2 <- as.data.frame(res.ca$col$coord)

library(ggimage)
img <- c(tabl1$KB[19], tabl1$Lab[19], tabl1$AM[19])
label_wine <- rownames(tabl1)[1:18]

library(ggplot2)


  ggplot() +
    geom_point(
      data = picdata1,
      aes(x = `Dim 1`, y = `Dim 2`),
      color = tabl1$color[1:18]
    ) +
    geom_segment(
      aes(x = 0, y = 0, 
          xend = picdata2$`Dim 1`[1], yend = picdata2$`Dim 2`[1],
          color = "red")
    ) +
    geom_segment(
      aes(x = 0, y = 0, 
          xend = picdata2$`Dim 1`[2], yend = picdata2$`Dim 2`[2],
          color = "purple")
    ) +
    geom_segment(
      aes(x = 0, y = 0, 
          xend = picdata2$`Dim 1`[3], yend = picdata2$`Dim 2`[3],
          color = "darkred")
    ) +
    geom_image(aes(
      x = picdata2$`Dim 1`,
      y = picdata2$`Dim 2`,
      image = img
    ), size = 0.1) +
    geom_text(
      data = picdata1,
      aes(x = `Dim 1`, y = `Dim 2`, 
          label = label_wine,
          color = tabl1$color[1:18],
          vjust = -0.5, hjust = 0),
      check_overlap = T
    ) +
    scale_color_manual(values = c('white' = 'white',
                                  'red' = 'red',
                                  'purple' = 'purple',
                                  'darkred' = 'darkred')) +
    
    coord_cartesian(xlim = c(-0.75, 0.75), ylim = c(-0.5, 0.5)) +
    labs(
      title = "Wine Origin and Color by Popular Stores",
      subtitle = "Farther from the origins = more intertia, more unexpected",
      caption = "Original case: rpubs.com/linalinaa"
    ) +
    theme(
      panel.background = element_rect(
        fill = "lightsteelblue3",
        colour = "lightsteelblue3",
        linewidth = 0.5,
        linetype = "solid"
      ),
      panel.grid.major = element_line(
        linewidth = 0.5,
        linetype = 'solid',
        colour = "lavender"
      ),
      panel.grid.minor = element_line(
        linewidth = 0.25,
        linetype = 'solid',
        colour = "lightsteelblue3"
      ),
      axis.title.x = element_blank(),
      axis.title.y = element_blank(),
      legend.position = "none"
    )

See more R color names here: https://bookdown.org/hneth/ds4psy/D-3-apx-colors-basics.html

To sum up, here I built a customized biplot for correspondence analysis.

This tutorial shows how to put a picture instead of a point, add arrows, and reminds how to plot two data frames in one ggplot.

More resources:

library(ggpattern)
bmd <- data.frame(treatment = c("control", "R as calculator", "R for fun"),
                  outcome = c(2.3, 1.9, 3.2))
ggplot(bmd,
       aes(treatment, outcome)) +
  geom_col_pattern(
    pattern = 'placeholder',
    pattern_type = 'kitten',
    color = 'black'
  ) +
  theme_bw(16) +
  labs(
    title = "Thank you for this class!",
    subtitle = "Best of luck with data analysis"
  ) +
  theme(legend.position = "none") +
  coord_fixed(ratio = 1/2)

---
title: "R Hidden Gem 2023"
author: "Anna Shirokanova"
date: "`r Sys.Date()`"
output:
  html_document:
    code_download: true
    toc: true
    toc_depth: 3
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, warning = F, message = F)
```

This year I realized as clearly as never before how important it is to show examples from A to Z.

When doing correspondence analysis, we discussed biplots with small images of company brands in them.

So, here we go.

I will replicate the beautifully arranged case presented by one of the students and re-build the picture using standard R packages.


The original case can be found here: <https://rpubs.com/linalinaa/1005417>

```{r}
# library(datapasta)
# tribble_paste()

tabl <- tibble::tribble(
               ~V1, ~V2, ~V3, ~V4,
      "Portugal R",  7L,  2L, 26L,
      "Portugal W",  8L,  2L, 15L,
        "France R", 12L, 43L, 40L,
        "France W", 10L, 35L, 26L,
         "Italy R", 30L, 67L, 58L,
         "Italy W", 22L, 49L, 63L,
         "Spain R", 29L, 48L, 83L,
         "Spain W", 17L, 19L, 43L,
       "Georgia R", 26L, 22L, 22L,
       "Georgia W",  7L, 12L,  7L,
        "Russia R", 40L, 35L, 46L,
        "Russia W", 30L, 35L, 41L,
         "Chile W",  8L, 13L, 10L,
         "Chile R",  7L, 21L, 19L,
  "South Africa W",  5L,  5L, 10L,
  "South Africa R",  3L,  4L, 19L,
     "Argentina W",  2L,  5L,  2L,
     "Argentina R",  4L,  7L, 10L
  )
tabl1  <- as.data.frame(tabl)
```


Add a meaningful vector for the color of wine

Wow-wow, what do we see? Lines 1-12 are W-R, lines 13-18 are R-W, so let's rearrange them

```{r}
tabl1$color <- c(rep(seq(1, 2, 1), 6), rev(rep(seq(1, 2, 1), 3))) 
tabl1$color <- factor(tabl1$color, labels = c("red", "white"))
row.names(tabl1) <- tabl$V1
head(tabl1)
tail(tabl1)
tabl1$V1 <- NULL
```



```{r}

colnames(tabl1) <- c("KB", "Lab", "AM", "color")
chisq.test(tabl1[ , 1:3])$stdres
```

```{r}
library(factoextra)
library(FactoMineR)
```


I downloaded pictures of brands as `.png` files in my home directory

```{r}
res.ca <- CA(tabl1[1:18,1:3], graph = FALSE)
```

The `fviz_ca` functionality is not bad at all but the palette is not helpful

```{r}
fviz_ca_biplot(
  res.ca,
  repel = TRUE,
  col.row = tabl1$color,
  arrows = c(T,T),
  title = "CA Biplot for stores and wine"
)
```

Add a vector with pictures as another row

```{r}
# library(here)
# here()
tabl1 <- rbind(tabl1, c("kb.png", "ab.png", "am.png", "NA"))
row.names(tabl1) <- c(tabl$V1, c("image"))
tabl1
```

Use `ggplot2` to change geom to "image".

We will need to plot two sets of points, from rows and columns

```{r}
picdata1 <- as.data.frame(res.ca$row$coord)
picdata2 <- as.data.frame(res.ca$col$coord)

library(ggimage)
img <- c(tabl1$KB[19], tabl1$Lab[19], tabl1$AM[19])
label_wine <- rownames(tabl1)[1:18]

library(ggplot2)


  ggplot() +
    geom_point(
      data = picdata1,
      aes(x = `Dim 1`, y = `Dim 2`),
      color = tabl1$color[1:18]
    ) +
    geom_segment(
      aes(x = 0, y = 0, 
          xend = picdata2$`Dim 1`[1], yend = picdata2$`Dim 2`[1],
          color = "red")
    ) +
    geom_segment(
      aes(x = 0, y = 0, 
          xend = picdata2$`Dim 1`[2], yend = picdata2$`Dim 2`[2],
          color = "purple")
    ) +
    geom_segment(
      aes(x = 0, y = 0, 
          xend = picdata2$`Dim 1`[3], yend = picdata2$`Dim 2`[3],
          color = "darkred")
    ) +
    geom_image(aes(
      x = picdata2$`Dim 1`,
      y = picdata2$`Dim 2`,
      image = img
    ), size = 0.1) +
    geom_text(
      data = picdata1,
      aes(x = `Dim 1`, y = `Dim 2`, 
          label = label_wine,
          color = tabl1$color[1:18],
          vjust = -0.5, hjust = 0),
      check_overlap = T
    ) +
    scale_color_manual(values = c('white' = 'white',
                                  'red' = 'red',
                                  'purple' = 'purple',
                                  'darkred' = 'darkred')) +
    
    coord_cartesian(xlim = c(-0.75, 0.75), ylim = c(-0.5, 0.5)) +
    labs(
      title = "Wine Origin and Color by Popular Stores",
      subtitle = "Farther from the origins = more intertia, more unexpected",
      caption = "Original case: rpubs.com/linalinaa"
    ) +
    theme(
      panel.background = element_rect(
        fill = "lightsteelblue3",
        colour = "lightsteelblue3",
        linewidth = 0.5,
        linetype = "solid"
      ),
      panel.grid.major = element_line(
        linewidth = 0.5,
        linetype = 'solid',
        colour = "lavender"
      ),
      panel.grid.minor = element_line(
        linewidth = 0.25,
        linetype = 'solid',
        colour = "lightsteelblue3"
      ),
      axis.title.x = element_blank(),
      axis.title.y = element_blank(),
      legend.position = "none"
    )

```

See more R color names here: <https://bookdown.org/hneth/ds4psy/D-3-apx-colors-basics.html>

**To sum up**, here I built a customized biplot for correspondence analysis.

This tutorial shows how to put a picture instead of a point, add arrows, and reminds how to  plot two data frames in one ggplot.

_More resources:_

- Emojis in a ggplot <https://www.r-bloggers.com/2019/09/using-emojis-and-png-as-icons-in-your-ggplot/>

- Check out the party penguins <https://rpubs.com/shirokaner/bar> and plotting logo <https://rpubs.com/shirokaner/logo>

- Fill in bars with wild topics (fun + exploration - data:ink) <https://coolbutuseless.github.io/package/ggpattern/articles/pattern-placeholder.html>

```{r}
library(ggpattern)
bmd <- data.frame(treatment = c("control", "R as calculator", "R for fun"),
                  outcome = c(2.3, 1.9, 3.2))
ggplot(bmd,
       aes(treatment, outcome)) +
  geom_col_pattern(
    pattern = 'placeholder',
    pattern_type = 'kitten',
    color = 'black'
  ) +
  theme_bw(16) +
  labs(
    title = "Thank you for this class!",
    subtitle = "Best of luck with data analysis"
  ) +
  theme(legend.position = "none") +
  coord_fixed(ratio = 1/2)
```

