library(knitr) options(knitr.kable.NA = "") knitr::opts_chunk$set( comment = ">", message = FALSE, warning = FALSE, out.width = "100%", dpi = 300 ) options(digits = 2) if (!requireNamespace("parameters", quietly = TRUE) || !requireNamespace("poorman", quietly = TRUE) || !requireNamespace("see", quietly = TRUE) || !requireNamespace("ggplot2", quietly = TRUE) || !requireNamespace("lme4", quietly = TRUE) || !requireNamespace("gamm4", quietly = TRUE)) { knitr::opts_chunk$set(eval = FALSE) } else { library(gamm4) } set.seed(333)
Sometimes, for instance for visualization purposes, we want to extract a reference grid (or data grid) of our dataset, that we will call a visualisation matrix. This reference grid usually contains the same variables than the original dataset, but reorganized in a particular, balanced, way. For instance, it might contain all the combinations of factors, or equally spread points of a continuous variable. These reference grids are often used as data for predictions of statistical models, to help us represent and understand them.
NOTE: the
visualisation_matrix()
function showcased in this vignette is now an alias (another name) for theget_datagrid()
function in the insight package.
For instance, let's fit a simple linear model that models the relationship
between Sepal.Width
and Sepal.Length
.
library(parameters) model <- lm(Sepal.Width ~ Sepal.Length, data = iris) model_parameters(model)
The most obvious way of representing this model is to plot the data points and
add the regression line using the geom_smooth
function from ggplot2
:
library(ggplot2) library(see) library(poorman) ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width)) + geom_point() + geom_smooth(method = "lm") + theme_modern()
But how to "access" the data of this regression line? One good option is to select
some values of of the predictor (Sepal.Length
), and predict (using the
base R predict()
method for now) the response (Sepal.Width
) using the model.
Using these x and y points, we can then create the regression line.
Let's try the visualisation_matrix
function from the modelbased
package (note that this function is the same as insight::get_datagrid()
, just with a different name).
library(modelbased) visualisation_matrix(iris["Sepal.Length"])
If we pass a numeric column to the function, it will return a vector of
equally spread points (having the same range, i.e., the same minimum and
maximum, than the original data). The default length is 10, but we can
adjust that through the length
argument. For instance, for linear relationships
(i.e., a straight line), two points are in theory sufficient. Let's generate
predictions using this reference grid of the predictor.
vizdata <- visualisation_matrix(iris["Sepal.Length"], length = 2) vizdata$Predicted <- predict(model, vizdata) vizdata
Now that we have our x and y values, we can plot the line as an overlay to the actual data points:
ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width)) + geom_point() + geom_line(data = vizdata, aes(y = Predicted), size = 1, color = "red") + theme_modern()
As we can see, it is quite similar to the previous plot. So, when can this be useful?
Data grids are useful to represent more complex models. For instance, in the models above, the negative relationship between the length and width of the sepals is in fact biased by the presence of three different species. One way of adjusting the model for this grouping structure is to add it as a random effect in a mixed model. In the model below, the "fixed" effects (the parameters of interest) will be adjusted ("averaged over") to the random effects.
library(lme4) model <- lmer(Sepal.Width ~ Sepal.Length + (1 | Species), data = iris) model_parameters(model)
As we can see, when adjusting for the species, the relationship between the two variables has become positive!
We can represent it using the same procedure as above, but note that instead of
using the base R predict()
function, we will be using get_predicted(),
from the insight package, which is a more robust and user-friendly version
of predict()
.
vizdata <- visualisation_matrix(iris["Sepal.Length"]) vizdata$Predicted <- insight::get_predicted(model, vizdata) ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width)) + geom_point(aes(color = Species)) + geom_line(data = vizdata, aes(y = Predicted), size = 1) + theme_modern()
The above way of constructing the reference grid, i.e., by providing a single column of data to the function, is almost equivalent to the following:
vizdata <- visualisation_matrix(iris, at = "Sepal.Length") vizdata
However, the other variables (present in the dataframe but not selected as
at
) are "fixed", i.e., they are maintained at specific values. This is
useful when we have other variables in the model in whose effect we are not
interested.
By default, factors are fixed by their "reference" level and numeric variables are fixed at their mean. However, this can be easily changed:
vizdata <- visualisation_matrix(iris, at = "Sepal.Length", numerics = "min") vizdata
If more than one target variable is selected, visualisation_matrix
will return
the combination of them (i.e., all unique values crossed together). This
can be useful in the case of an interaction between a numeric variable and a
factor.
Let's visualise the regression line for each of the levels of Species
:
model <- lm(Sepal.Width ~ Sepal.Length * Species, data = iris) vizdata <- visualisation_matrix(iris, at = c("Sepal.Length", "Species"), length = 5) vizdata$Predicted <- insight::get_predicted(model, vizdata) vizdata ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width, color = Species)) + geom_point() + geom_line(data = vizdata, aes(y = Predicted), size = 1) + theme_modern()
However, it is generally not a good practice to extend the regression lines
beyond the range of its original data, as it is the case here for the red
line. The preserve_range
option allows to remove observations that are
"outside" the original dataset (however, the length should be increased to
improve the precision toward the edges):
vizdata <- visualisation_matrix(iris, at = c("Sepal.Length", "Species"), length = 100, preserve_range = TRUE ) vizdata$Predicted_Sepal.Width <- insight::get_predicted(model, vizdata) ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width, color = Species)) + geom_point() + geom_line(data = vizdata, aes(y = Predicted_Sepal.Width), size = 1) + theme_modern()
model <- lm(Sepal.Length ~ Petal.Length * Petal.Width, data = iris) model_parameters(model)
This idea can also be used to visualise interactions between two numeric variables, aka the nightmare of every scientist. One possibility is to basically represent the relationship between the response and one predictor at a few representative values of the second predictor.
In this case, we will represent the regression line between Sepal.Length
and
Petal.Length
and a 5 equally spaced values of Petal.Length
, to get a feel for
the interaction.
We can obtain the right reference grid quite easily by chaining two
visualisation_matrix
together as follows:
vizdata <- iris %>% visualisation_matrix(c("Petal.Length", "Petal.Width"), length = 10) %>% visualisation_matrix("Petal.Width", length = 5, numerics = "all")
What did we do here? We started by generating a reference grid containing all
the combinations between the 10 equally spread values of the two target
variables, creating 10 * 10 = 100
rows. The next step was to reduce
Petal.Length
to a set of 5 values, but without touching the other variables
(i.e., keeping the 10 values created for Petal.Length
). This was achieved
using numerics = "all"
.
We can then visualise it as follows:
vizdata$Predicted <- insight::get_predicted(model, vizdata) iris %>% ggplot(aes(x = Petal.Length, y = Sepal.Length, color = Petal.Width)) + geom_point() + geom_line(data = vizdata, aes(y = Predicted, group = Petal.Width), size = 1) + scale_color_viridis_c() + theme_modern()
Such plot can be more clear by expressing the interaction variable in terms of deviations from the mean (as a standardized variable).
# Express values in an abstract way vizdata$Petal.Width <- effectsize::format_standardize(vizdata$Petal.Width, reference = iris$Petal.Width) ggplot(iris, aes(x = Petal.Length, y = Sepal.Length)) + # Only shapes from 21 to 25 have a fill aesthetic geom_point2(aes(fill = Petal.Width), color = "white", shape = 21, size = 5) + geom_line(data = vizdata, aes(y = Predicted, color = Petal.Width), size = 1) + scale_color_viridis_d(direction = -1) + scale_fill_viridis_c(guide = "none") + theme_modern()
As the Petal.Width
increases (becomes yellow), the coefficient between
Petal.Length
and Sepal.Length
increases (the slope is more steep). Although,
as we can guess, this in fact captures the underlying effect of species... but
we'll leave discussing the meaningfulness of your models to you :)
visualization_matrix()
also runs directly on model objectsTo illustrate this, let's set up a general additive mixed model (GAMM),
where we are going to specify a smooth term (a non-linear relationship;
specified by s()
function) and some random effects structure.
library(gamm4) model <- gamm4::gamm4( formula = Petal.Length ~ Petal.Width + s(Sepal.Length), random = ~ (1 | Species), data = iris )
One can directly extract the visualization matrix for this model by entering the entire object into the function:
visualisation_matrix(model, length = 3, include_random = FALSE)
We also skip the smooth term if we are interested only in the fixed effects:
visualisation_matrix(model, length = 3, include_random = FALSE, include_smooth = FALSE)
We can also include random effects:
visualisation_matrix(model, length = 5, include_random = TRUE)
Although the plot above is nice, and all, we would like the standardized changes in SD to be smoother (e.g., by increments of 1 SD). This can be achieved by first requesting the values that we want, and then unstandardizing it.
Let's use the same model as above, and then obtain a data grid with specific values for Petal.Width
.
vizdata <- lm(Sepal.Length ~ Petal.Length * Petal.Width, data = iris) %>% visualisation_matrix(at = c("Petal.Length", "Petal.Width = seq(-3, 3)")) %>% unstandardize(vizdata, select = "Petal.Width") %>% estimate_relation(vizdata) vizdata$Petal.Width <- effectsize::format_standardize(vizdata$Petal.Width, reference = iris$Petal.Width) # 6. Plot ggplot(iris, aes(x = Petal.Length, y = Sepal.Length)) + geom_point2(aes(fill = Petal.Width), shape = 21, size = 5) + geom_line(data = vizdata, aes(y = Predicted, color = Petal.Width), size = 1) + scale_color_viridis_d(direction = -1) + scale_fill_viridis_c(guide = "none") + theme_modern()
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