05-appendix.qmd

# Appendix {.unnumbered}

```{r}
#| label: load-pkg

library(tidyverse)
library(tidymodels)
library(knitr)
library(reshape)
library(ggplot2)
library(dplyr)
library(lme4)
library(MASS)
library(car)
library(MuMIn)
library(lmerTest)
library(ggplot2)
library(dplyr)
library(broom.mixed)
library(forcats)
library(sjPlot)

theme_set(theme_minimal(base_size = 11))
```

```{r}
#| label: load-data
#| message: false

gardnerjanson <- read_csv(here::here("processed-data/gardnerjanson.csv"))

gardnerjanson_museums <- read_csv(here::here("processed-data/gardnerjanson_museums.csv"))
```

```{r}
#| label: lmm_prep

gardnerjanson_museums_mod <- gardnerjanson_museums %>%
  filter(!startsWith(artist_name, "N/A")) %>%
  mutate(artist_race_nwi = if_else(artist_race == "White", "White", "Non-White"))

gardnerjanson_museums_mod <- gardnerjanson_museums_mod %>%
  mutate(artist_nationality_other = factor(artist_nationality_other,
    levels = c("American", "French", "Other", "British", "German", "Spanish")
  ))
```

```{r}
#| label: lmm_full

lmm_full <- lmer(log(space_ratio_per_page_total) ~ artist_race_nwi
                       + artist_ethnicity 
                       + artist_gender 
                       + artist_nationality_other
                       + moma_count_to_year
                       + whitney_count_to_year +
                         (1 | artist_name),
            data = gardnerjanson_museums_mod,
    REML = FALSE)
```

```{r}
#| label: lmm_test

lmm <- lmer(log(space_ratio_per_page_total) ~ artist_race_nwi
                       + artist_ethnicity 
                       + artist_gender 
                       + artist_nationality_other
                       + moma_count_to_year
                       + whitney_count_to_year
                       + artist_nationality_other*moma_count_to_year
                       + artist_race_nwi*moma_count_to_year
                       + artist_ethnicity*moma_count_to_year
                       + artist_race_nwi*whitney_count_to_year
                       + artist_ethnicity*whitney_count_to_year
                  + (1 | artist_name),
            data = gardnerjanson_museums_mod,
    REML = FALSE)
```

```{r}
#| label: lmm_step

final_model <- lmerTest::step(lmm)
```

```{r}
#| label: lmm

lmm <- lmer(log(space_ratio_per_page_total) ~ artist_nationality_other
                       + moma_count_to_year
                       + artist_nationality_other*moma_count_to_year
                        + (1 | artist_name),
            data = gardnerjanson_museums_mod,
    REML = FALSE)
```

## Data Dictionary

Outcome:

`space_ratio_per_page_total` = The area in centimeters squared of both the text and the figure of a particular artist in a given edition of *Janson's History of Art* or *Gardner's Art Through the Ages* divided by the area in centimeters squared of a single page of the respective edition.

Potential Predictors:

`artist_gender` = The gender of the artist.

`artist_race` = The race of the artist.

`artist_race_nwi` = The non-white indicator for artist race, meaning if an artist's race is denoted as either white or non-white.

`artist_ethnicity` = The ethnicity of the artist.

`artist_nationality_other` = The nationality of the artist. Of the total count of artists through all editions of *Gardner's Art Through the Ages* and *Janson's History of Art*, 77.32% account for French, Spanish, British, American and German. Therefore, the categorical strings of this variable are French, Spanish, British, American, German and Other.

`whitney_count_to_year` = The count of exhibitions held by The Whitney of a particular artist at a particular moment of time, as highlighted by `year`.

`moma_count_to_year` = The count of exhibitions held by the Museum of Modern Art (MoMA) of a particular artist at a particular moment of time, as highlighted by `year`.

`year` = The year of publication for a given edition of Janson or Gardner.

Other variables:

`edition_number` = The edition number of the textbook from either Janson's History of Art or Gardner's Art Through the Ages.

`book` = Which book, either Janson or Gardner the particular artist at that particular time was included.

`artist_unique_id` = A unique identifying number assigned to artists across books and editions denoted in alphabetical order.

`artist_name` = The name of the artist.

## Log Transformation: Total Space Ratio per Page

```{r}
#| label: fig-logspaceratioperpagetotal
#| fig-cap: "Distribution of the Log of Total Space Ratio per Page, n = 3162, (Source: All artists of two-dimensional works made after c. 1750 in Gardner's Art Through the Ages and Janson's History of Art, 1926-2020)."

ggplot(
  gardnerjanson_museums,
  aes(x = log(space_ratio_per_page_total))
) +
  geom_histogram(binwidth = .1) +
  labs(
    title = "Distribution of the Log of Ratio of Space 
       per Artist per Edition per Page in all Textbooks",
    x = "Ratio of Space per Page Total",
    y = "Count"
  )
```

In order to create less skew in our outcome variable, it is evident that log transforming total space ratio per page given to an artist in a particular edition gives the spread a much more mild right-skew than before. The shape is still unimodal and asymmetrical. I will be using the log transformation on the total space ratio per page, our outcome variable, in the linear mixed-effects model. This allows for the residuals to have constant variance.

\pagebreak

## Assumptions

### Residuals and Constant Variance

```{r}
#| label: fig-residuals
#| fig-cap: "Constant Variance Assumption of the Residuals"

plot(resid(lmm, type = "pearson") ~ fitted(lmm), 
     main = "Constant Variance Assumption Satisfied", 
     xlab = "Fitted", 
     ylab = "Residuals") 
```

The very low values of the predicted values have very low variability for residuals but for the bulk of the data, there is constant variability in the residuals.

\pagebreak

### Normality

```{r}
#| label: fig-density-histogram
#| fig-cap: "Normality Assumption of the Residuals"

lmm_aug <- broom.mixed::augment(lmm, gardnerjanson_museums_mod)

ggplot(lmm_aug, aes(x = .resid)) +
  geom_histogram(binwidth = .05, aes(y = after_stat(density))) +
  theme_minimal() +
  stat_function(
    fun = dnorm,
    args = list(
      mean = mean(lmm_aug$.resid),
      sd = sd(lmm_aug$.resid)
    ),
    color = "red",
    size = 2
  )+
  labs(title = "Normality Assumption Satisfied", 
       x = "Residuals", 
       y = "Density")
```

The distribution of the residuals is approximately normal.

\pagebreak

### Independence

Since we cannot assume that each row in our data set is independent from another, because we expect an artist effect, we added a random effect at the artist level. Between artists, we expect the observations to be independent.

### Collinearity

```{r}
#| label: collinearity
#| tbl-cap: "Collinearity Test"

vif(lmm)
```

Given artist nationality, MoMA Count to Year and the interaction between the two all have a corrected GVIF under 10 therefore no variables are collinear.