Colorizing equations and swapping variable names

Particularly when teaching, it can be helpful to highlight specific pieces of the equation. With {equatiomatic}, we can do this as part of the equation extraction.

For example, imagine we have a simple linear regression model, like this

library(equatiomatic)
slr <- lm(bill_length_mm ~ body_mass_g, data = penguins)

We may want to start by highlighting the independent and dependent variables. We can do this with colors. For example:

extract_eq(
  model = slr, 
  var_colors = c(
    bill_length_mm = "cornflowerblue",
    body_mass_g = "firebrick"
  )
)

$$ {\color{cornflowerblue}{\operatorname{bill\_length\_mm}}} = \alpha + \beta_{1}({\color{firebrick}{\operatorname{body\_mass\_g}}}) + \epsilon $$

and then we can use those same colors later in text, as in “The Dependent Variable is the length of the penguins bill, which is predicted by the Indepenent Variable, the body mass of the penguin.”

Note that we colorize the variables through the var_colors argument, which takes a named vector. The name is equal to the variable you’d like to change the color of, and the element is the actual color.

We could also take this further, to colorize the coefficients (the Greek notation). This argument structure is slightly different, taking either a single color, or a vector of colors. The notation includes three Greek characters, representing the model intercept, slope, and residual variance. We can just the intercept with code like this

extract_eq(
  model = slr, 
  var_colors = c(
    bill_length_mm = "cornflowerblue",
    body_mass_g = "firebrick"
  ),
  greek_colors = c(
    "#3bd100", rep("black", 2)
  )
)

$$ {\color{cornflowerblue}{\operatorname{bill\_length\_mm}}} = {\color{#3bd100}{\alpha}} + {\color{black}{\beta}}_{1}({\color{firebrick}{\operatorname{body\_mass\_g}}}) + {\color{black}{\epsilon}} $$

Or all three with something like

greek_col <- c("#1b9e77", "#d95f02", "#7570b3")

extract_eq(
  model = slr, 
  var_colors = c(
    bill_length_mm = "cornflowerblue",
    body_mass_g = "firebrick"
  ),
  greek_colors = greek_col
)

$$ {\color{cornflowerblue}{\operatorname{bill\_length\_mm}}} = {\color{#1b9e77}{\alpha}} + {\color{#d95f02}{\beta}}_{1}({\color{firebrick}{\operatorname{body\_mass\_g}}}) + {\color{#7570b3}{\epsilon}} $$

Note that all of this works with more complicated models as well. For example, consider a model with an interaction. My coloring the variable names, we can follow both the main effects and the interaction.

m_interaction <- lm(bill_length_mm ~ body_mass_g * flipper_length_mm, 
                    data = penguins)

extract_eq(
  m_interaction,
  var_colors = c(
    body_mass_g = "#ffa91f",
    flipper_length_mm = "#00d1ab"
  ),
  greek_colors = c(
    "black", "#3A21B3", "#58A1D9", "#FF7582", "black"
  ),
  wrap = TRUE,
  terms_per_line = 3
)

$$ \begin{aligned} \operatorname{bill\_length\_mm} &= {\color{black}{\alpha}} + {\color{#3A21B3}{\beta}}_{1}({\color{#ffa91f}{\operatorname{body\_mass\_g}}}) + {\color{#58A1D9}{\beta}}_{2}({\color{#00d1ab}{\operatorname{flipper\_length\_mm}}})\ + \\ &\quad {\color{#FF7582}{\beta}}_{3}({\color{#ffa91f}{\operatorname{body\_mass\_g}}} \times {\color{#00d1ab}{\operatorname{flipper\_length\_mm}}}) + {\color{black}{\epsilon}} \end{aligned} $$

Here, we’re using two different shades of blue to denote the main effects, and a pink color to denote the interaction. At the same time, we see how the variables combine. We can also change the subscripts. Perhaps we want to have them match the coefficients. The interface for the subscripts is exactly the same as the subscripts—either a single color or a vector of colors. One potentially confusing part of this, however, is that the colors still need to correspond to their position in the equation. If the term does not have a subscript, you can fill the positions with NA values or any other color (it won’t matter because there are not subscripts for those terms).

extract_eq(
  m_interaction,
  var_colors = c(
    body_mass_g = "#ffa91f",
    flipper_length_mm = "#00d1ab"
  ),
  greek_colors = c(
    "black", "#3A21B3", "#58A1D9", "#FF7582", "black"
  ),
  subscript_colors = c(
     NA_character_, "#3A21B3", "#58A1D9", "#FF7582", NA_character_
  ),
  wrap = TRUE,
  terms_per_line = 3
)

$$ \begin{aligned} \operatorname{bill\_length\_mm} &= {\color{black}{\alpha}} + {\color{#3A21B3}{\beta}}_{{\color{#3A21B3}{1}}}({\color{#ffa91f}{\operatorname{body\_mass\_g}}}) + {\color{#58A1D9}{\beta}}_{{\color{#58A1D9}{2}}}({\color{#00d1ab}{\operatorname{flipper\_length\_mm}}})\ + \\ &\quad {\color{#FF7582}{\beta}}_{{\color{#FF7582}{3}}}({\color{#ffa91f}{\operatorname{body\_mass\_g}}} \times {\color{#00d1ab}{\operatorname{flipper\_length\_mm}}}) + {\color{black}{\epsilon}} \end{aligned} $$

Again, we may want to use these colors in our explanation. For example

In the above model, both the body mass and the flipper length of penguins are used to predict their bill length. We estimate the main effect of body mass, the main effect of flipper length, and their interaction. The interaction implies that the relation between body mass and bill length depends upon flipper length. Or, equivalently, that the relation between flipper length and bill length depends upon body mass.

Finally, there’s is one additional means by which we can control colors. By default, {equatiomatic} handles categorical variables by putting the corresponding levels in subscripts (relative to the reference group, which is omitted). We can also change the color of these variable subscripts, with the var_subscript_colors argument.

m_categorical <- lm(bill_length_mm ~ species + island, data = penguins)

extract_eq(
  model = m_categorical,
  var_colors = c(
    species = "#FB2C4B",
    island = "#643B77"
  ),
  var_subscript_colors = c(
    species = "#0274B2",
    island = "#FBA640"
  )
)

$$ \operatorname{bill\_length\_mm} = \alpha + \beta_{1}({\color{#FB2C4B}{\operatorname{species}}}{\color{#0274B2}{_{\operatorname{Chinstrap}}}}) + \beta_{2}({\color{#FB2C4B}{\operatorname{species}}}{\color{#0274B2}{_{\operatorname{Gentoo}}}}) + \beta_{3}({\color{#643B77}{\operatorname{island}}}{\color{#FBA640}{_{\operatorname{Dream}}}}) + \beta_{4}({\color{#643B77}{\operatorname{island}}}{\color{#FBA640}{_{\operatorname{Torgersen}}}}) + \epsilon $$

Note that the colorization is at the variable level, not the subscript level.

extract_eq(
  model = m_interaction,
  swap_var_names = c(
    "bill_length_mm" = "Bill Length (MM)",
    "body_mass_g" = "Body Mass (grams)",
    "flipper_length_mm" = "Flipper Length (MM)"
  ),
  var_colors = c(
    flipper_length_mm = "firebrick",
    body_mass_g = "cornflowerblue"
  ),
  wrap = TRUE,
  terms_per_line = 3
)

extract_eq(
  model = m_categorical,
  swap_var_names = c(
    "bill_length_mm" = "Bill Length (MM)",
    "species" = "Species",
    "island" = "Island"
  ),
  swap_subscript_names = c(
    Chinstrap = "little buddy",
    Gentoo = "happy feet"
  ),
  var_colors = c(
    species = "#FB2C4B",
    island = "#643B77"
  ),
  var_subscript_colors = c(
    species = "#0274B2",
    island = "#FBA640"
  ),
  wrap = TRUE,
  terms_per_line = 3
)

create_eq(m_categorical) %>% 
  swap_var_names(
    "bill_length_mm" = "Bill Length (MM)",
    "species" = "Species",
    "island" = "Island"
  ) %>% 
  swap_subscript_names(
    Chinstrap = "little buddy",
    Gentoo = "happy feet"
  ) %>% 
  colorize_variables(
    species = "#FB2C4B",
    island = "#643B77"
  ) %>% 
  colorize_variable_subscripts(
    species = "#0274B2",
    island = "#FBA640"
  ) %>% 
  wrap(terms_per_line = 3)