Distribution plots

Packages: dplyr, tidyr, ggplot2, ggdist, likert, ggridges

Investigating the distribution of variables in an ESM dataset is crucial. Examining the distribution can provide insights into the data, such as whether it is normally distributed or skewed, whether it contains outliers or extreme values, whether it has floor or roof effects, and whether it has different distribution modalities (unimodal, bimodal, multimodal). Furthermore, it is important to ensure that the distribution of the data meets the assumptions of statistical models, such as normality, homogeneity of variance, and independence of observations. Histograms can help to identify deviations from these assumptions.

Different types of plots allow this investigation. For all of them, it is possible to display only one variable or multiple variables.

One variable

Two+ variables

data %>%
    ggplot(aes(y=PA1, x=factor(1))) +  # Display variable on the two axis of the plot
        geom_jitter(alpha=.1) +  # Create points on the plot and put space between them
        geom_boxplot(outlier.shape=NA, fill=NA) +  # Create the boxplot
        theme(axis.text.x=element_blank(), axis.ticks.x=element_blank(),  # Remove the x axis
              axis.title.x=element_blank())

data %>%
    gather(variable, value, PA1, PA2, PA3, NA1) %>% # Gather the PA1 to NA1 in two variables
    ggplot(aes(y=value, x=variable, color=variable)) +  # Display variable on the two axis of the plot
        geom_jitter(alpha=.1) +  # Create points on the plot and put space between them
        geom_boxplot(outlier.shape=NA, fill=NA)  # Create the boxplot

Importantly, when using ‘geom_boxplot’ in combinaison with ‘geom_jitter’, outliers from the boxplot should be removed to avoid overplotting points (using ‘outlier.shape=NA’). Additionally, the ‘fill=NA’ argument can be used to make the boxplot transparent and allow the points to be visible.

One variable

Two+ variables

data %>%
    ggplot(aes(x=PA1)) +  # Display variable on the two axis of the plot
        geom_histogram() 

data %>%
    gather(variable, value, PA1, PA2, PA3, NA1) %>% # Gather the PA1 to NA1 in two variables: variable contain the name and value contain the associated value
    ggplot(aes(x=value)) +  # Display variable on the two axis of the plot
        geom_histogram() +
        facet_wrap(.~variable)

One variable

Two+ variables

data %>% 
  ggplot (aes (x = PA1)) +
      geom_density(alpha = 0.5)

data %>%  
  gather (key = var, value = value, PA1:NA1) %>%
  ggplot (aes (x = value, color=var)) +
      geom_density(alpha = 0.5)

One variable

Two+ variables

data %>%
    ggplot(aes(y=PA1, x=factor(1))) +  # Display variable on the two axis of the plot
        geom_jitter(alpha=.1, width = .3) +  # Create points on the plot and put space between them
        geom_boxplot(width = .5, outlier.shape=NA, fill=NA) +  # Create the boxplot
        ggdist::stat_halfeye(point_colour = NA, justification = -.4,  # Add the density plot
                             .width = .6, adjust = .4) +
        theme(axis.text.x=element_blank(), axis.ticks.x=element_blank(),  # Remove the x axis
              axis.title.x=element_blank())

data %>%
    gather(variable, value, PA1, PA2, PA3, NA1) %>% # Gather the PA1 to NA1 in two variables
    ggplot(aes(y=value, x=variable, color=variable, fill=variable)) +  # Display variable on the two axis of the plot
        geom_jitter(alpha=.05, width = .2) +  # Create points on the plot and put space between them
        geom_boxplot(outlier.shape=NA, fill=NA, width = .3, size = 1.2) + # Create the boxplot
        ggdist::stat_halfeye(point_colour = NA, justification = -.5, # Add the density plot
                             .width = .6, width=.5, adjust = 1)

data %>% 
  gather (key = var, value = value, PA1:NA1) %>%
  ggplot (aes (x = value)) +
      geom_histogram(aes(y = ..density..), alpha = 0.7, fill = "#333333") + 
      geom_density(alpha = 0.5) +
      facet_wrap(vars(var), scales = "free") # Scale free is important

Conditional distributions: grouping for variables

Participants and groups

The shapes of the distributions such as modalities (e.g., unimodal, bimodal, multimodal) and others (e.g., skewed) can also be inspected for participants or groups. To do so, we can plot:

1. a unique variable and multiple participants
2. multiple variables and participants
3. a unique variable and multiple participants with density functions.

Note that the ‘filter()’ function is used to select the participants to display. Displaying all participants can be overwhelming in function of the plot type and the number of participants.

data %>% filter(id %in% c(1, 30, 50)) %>% 
    ggplot(aes(x=PA1)) +  
        geom_histogram(bins=30) +
        facet_grid(id~.)

data %>% filter(id %in% c(1, 29, 50)) %>% 
    gather(variable, value, PA1, PA2, PA3) %>% # Gather the PA1 to NA1 in two variables: variable contain the name and value contain the associated value
    ggplot(aes(x=value)) +  
        geom_histogram() +
        facet_grid(id~variable)

data %>% 
    ggplot(aes(x=PA1, color=factor(id))) +  
        geom_density(alpha = 1) +
        theme(legend.position = "none")

To investigate group differences, the participant identification variable (“id”) that we used in the previous plots can be replaced by a group variable (for instance ‘cond_perso’) for the next plots. Because groups often have multiple modes, we can unite the distributions in the same plot, as follows:

data %>%
    ggplot(aes(x=PA1, color=factor(cond_perso))) +  
        geom_histogram(aes(y = ..density.., fill=factor(cond_perso)), alpha = 0.2) +
        geom_density(alpha = 1) 

Time variables

ESM studies unfold during a period of time and questions are often asked multiple times a day. As life follows periods, it is probable that distributions of variables (e.g., positive affects, energy) can differ over time, such as between periods of the day, between days in a week or between different weeks. Again, the above plots can be used to explore such differences by grouping distributions based on time variables. For instance, the below plot allows us to investigate if there are differences in distributions at different periods of the day (i.e., morning, afternoon).

data %>%
    ggplot(aes(x=PA1)) +  # Display variable on the two axis of the plot
        geom_histogram() +
        facet_grid(period~.)

Categorical and Likert scales

In addition to the widespread utilization of slider scales in ESM studies, it is important to note that categorical and Likert scales (ranging from 1 to 7) are also frequently employed. Especially for Likert scales, the Likert package can be employed. This package provides convenient functionalities to generate visually appealing distribution plots of Likert scale responses, helping to gain insights into the patterns and distributions of participants’ ratings across the scale items.

Firstly, we have to do a quick preprocessing of the categorical or Likert items we want to plot. They need to be in a factor format and the levels must be ordered and named. In our example the labels are: “never”, “rarely”, “occasionally”, “sometimes”, “frequently”, “often”, “always”. Here, the order perfectly fits the Likert scale values used: from 1 (“never”) to 7 (“always”).

data = data %>%
  mutate(across(likert1:likert3,
                function(x) factor(x, labels = c("never", "rarely", "occasionally", "sometimes", "frequently", "often", "always"),
                                  ordered=TRUE)))

Different types of distribution plots can be built based on Likert items:

Warning

After the ‘gather’ function, it is required to transform the ‘value’ column into a factor and specify the levels order based on the original Likert scale. You will probably need to adapt the labels and the levels to your own Likert scale.

data %>%
  gather(key = "var", value = "value", likert1:likert3) %>%
  mutate(value = factor(value, levels=c("never", "rarely", "occasionally", "sometimes", "frequently", "often", "always"))) %>%
  ggplot(aes(x = var, y = ..count.., fill = value)) +
    geom_bar(stat = "count", position = "stack") + 
    scale_fill_brewer(palette = "RdBu") # Set the color palette

yscale = seq(0,100,20) # Define the scale of the y axis
data %>%
  gather(key = "var", value = "value", likert1:likert3) %>%
  mutate(value = factor(value, levels=c("never", "rarely", "occasionally", "sometimes", "frequently", "often", "always"))) %>% 
  group_by(var, value) %>%
  summarise(count = n()) %>% # Count the number of each value
  mutate(percentage = count / sum(count) * 100) %>% # Compute the percentage
  ggplot(aes(x = var, y = percentage, fill = value, 
             label = sprintf("%.1f%%", percentage))) + # Add the percentage labels
    geom_bar(stat = "identity", position = "stack") +
    geom_text(position = position_stack(vjust = 0.5), size = 3) + # Add the percentage labels on the bars
    scale_y_continuous(breaks = yscale, labels = paste0(yscale, "%")) + # Set the scale of the y axis
    scale_fill_brewer(palette = "RdBu", direction=-1) # Set the color palette

library(likert)
vars_likert = c("likert1","likert2","likert3")

plot(likert(data[,vars_likert]), 
     type="bar")

library(likert)
vars_likert = c("likert1","likert2","likert3")

plot(likert(data[,vars_likert]),
      type="heat")

library(likert)
vars_likert = c("likert1","likert2","likert3")

plot(likert(data[,vars_likert]), 
     type="density",facet = TRUE, bw = 0.5)

The ‘likert’ function also offers the capability to partition the distribution plots based on grouping variables. It helps to explore potential variations and differences in the ratings based on specific factors of interest within their dataset. In the exemple, we split the distribution according to the ‘cond_perso’ variable.

library(likert)
vars_likert = c("likert1","likert2","likert3")

plot(likert(data[,vars_likert], grouping = data[,"cond_perso"]), legend.position="right",
     type="bar")

Further plots

Many functions from many packages allow creating distribution plots, each with specificities. Rather than making an exhaustive list, here are some useful functions that we found.

When visualizing time series data, incorporating marginal density or histogram plots alongside the main series offers a swift means to examine the distribution of values across the scale. We propose two methods:

• ‘ggMarginal()’ from the ‘ggExtra’ package: it allows to add marginal density or histogram plots to a ggplot2 scatterplot.
• ‘geom_rug()’ from the ‘ggplot2’ package: display the distribution of the variables with thin overlapping lines next to the x- or y-axis as a projection of the variables displayed in the plot.

library(ggExtra)
p = data %>% filter(id == 3) %>% 
  ggplot(aes(x=obsno, y=PA1)) +
    geom_line() +
    geom_point()
ggMarginal(p, margins = "y", type = "histogram")

data %>% filter(id == 3) %>% 
  ggplot(aes(x=obsno, y=PA1)) +
    geom_line() +
    geom_point() +
    geom_rug(position="jitter", alpha = .3, show.legend = FALSE, sides = "l")

The ‘geom_density_ridges()’ function helps to split the distribution according to a grouping variable (using the y and fill arguments).

library(ggridges)
data %>%
  ggplot(aes(x=PA1, y=factor(cond_perso), fill=factor(cond_perso))) +
    geom_density_ridges(stat = "binline", bins = 25, scale = .9,
                        draw_baseline = FALSE, show.legend = FALSE)