{LST}: R package for Lessons in Statistical Thinking

A command template

R commands in Lessons are well exemplified by the following: generating a plot of two variables in a data frame and then annotating the plot with a simple linear model.

mtcars |> point_plot(mpg ~ hp, annot = "model")

The command illustrates several features of the style of commands in Lessons:

• The basic structure involves piping a data frame into a function. The pipeline structure is used almost exclusively in Lessons. For the reader not acquainted with the R pipe, the object on the left-hand side of the pipe token |> becomes the first argument to the function call on the right-hand side.

  • The left-hand side of the pipe—the input end of the pipe–will very often be a data frame, but a handful of other types are used in that role in Lessons. (More on this later.)
  • The right-hand side—the output end of the pipe–will always be a function call.

• Variables in the data frame are referred to by unquoted name. Such variable names are only used in the role of an un-piped argument to the right-hand side function call.

  • The $ notation is never used in any setting.
  • For situations in which there is a response variable (as in modeling or graphics), the variable names always appear in tilde expressions.

• Often, a tilde expression will be the only thing inside the parentheses that follow the function name. But sometimes additional details for the function will be added within the parentheses. In the above example command, the detail to add a statistical model as an annotation is specified by the argument `annot = “model”.

• point_plot() is a omnibus graphics command sufficient for teaching an entire statistics course that includes inference and covariation.

  • The output is {ggplot2} compatible.
  • Other such omnibus commands from {LST} seen in Lessons are model_train(), sample(), and trials().
  • Wrangling functions from {dplyr} are also occasionally used, especially mutate() and summarize().
  • Summaries of statistical models are made with the {LST} function conf_interval() and occasionally R2(). (Near the end of the course, regression_summary() and anova_summary() are introduced, but these play only a very minor, optional role in the course.)

Pipe input-ends

I’m using the term input end of a pipe to refer to the object on the left-hand side of the |> pipe token. There are only a handful of types presented to the input end of the pipe:

1. A data frame is by far the most common input type.
2. A statistical model is an input type used frequently in the second-half of the course.
3. A “data simulation” is another kind of input type.
4. Optionally, and mainly for enrichment, a data graphic frame (as produced by point_plot()) is used at the input of the pipe towards a command to add labels or to add another {ggplot2} layer.

Pipe output-ends

Just as input end refers to the object provided at the left-hand side of the pipe, the object produced by the function call on the right side is the pipe’s output. Two essential points about pipe output-ends:

1. The R command given on the right-hand side of |> will always be a function call. No exceptions. A function call consists of the name of a function (e.g., point_plot or model_train) followed by an open/closed pair of parentheses. Usually, there is something such as a tilde expression contained in the parentheses, but there are often additional named arguments such as the annot = "model" in the example command presented in @sec-command-template.

2. The function call in (a) produces an R object. For the {LST} functions, this object will always be one of the four types presented in the previous section (data frame, model, data simulation, graphics frame).

Multi-stage pipelines

The object produced by the function call at the output end of the pipe |> can provide the input, via another pipe, to another function call. This technique is often used for data wrangling or when summarizing a model. For instance, the following converts fuel “economy” (mpg) into fuel consumption (liters per 100 km), which is then used as the response variable in a model.

mtcars |> 
  dplyr::mutate(consumption = 235.2 / mpg) |>
  model_train(consumption ~ hp + wt) |> 
  conf_interval()
#> # A tibble: 3 × 4
#>   term            .lwr  .coef   .upr
#>   <chr>          <dbl>  <dbl>  <dbl>
#> 1 (Intercept) -0.486   1.48   3.45  
#> 2 hp           0.00647 0.0176 0.0287
#> 3 wt           1.92    2.70   3.48

For convenience, the add_plot_labels() function will modify the labels in a plot, taking as input a plot (as produced by point_plot(), for instance) and returning as output the modified plot. (Perhaps of interest to those familiar with {ggplot2} … add_plot_labels() is merely a wrapper on ggplot2::labs() that avoids the non-standard + pipe system.)

mtcars |> 
  point_plot(mpg ~ hp * wt) |> 
  add_plot_labels(x = "Engine power (hp)", y = "Fuel economy (mpg)")

What to do with the ultimate output of a pipeline?

The flow of computation in a pipeline runs from left to right. The output object from the last stage of the pipeline will, by default, be printed. The alternative is to store that output object under a name, using the “storage arrow”, like this:

storage_name <- pipeline

In R, the form in which an object is printed is controlled by the programmer. Graphics are typically “printed” by displaying the graphic in an appropriate place. Data frames are typically printed as text.

In addition to data frames and graphics, Lessons deals frequently with two other sorts of objects: data simulations and models.

By default, models are printed as text. There is a wide variety of formats corresponding to the large number of people who have communally put together the modeling systems in R. Rather than the hodge-podge of printed model formats, I encourage users to print specific summaries of models such as graphs of the model function (use model_plot()). The numerical model summaries in {LST} are always printed in data-frame format. Most of the time in Lessons, models are summarized with coefficients and confidence intervals, a format produced by conf_interval(). I strongly recommend that model coefficients always be shown in the context of a confidence interval; conf_interval() imposes this policy. Another sometimes useful format of summary is provided by R2(). Toward the end of the course, the ANOVA generalization of R² is introduced. anova_summary() is useful for comparing two or more models. regression_summary() shows a standard regression report, but conf_interval() is, I think, a superior format. (If you feel obliged to show a p-value, use the show_p = TRUE argument to conf_interval(). But I recommend focussing on whether the confidence interval includes zero, using the level = argument if you aren’t happy with 0.05.)

Data simulations are printed as text showing the causal formulas relating one variable to the others. Like this:

sim_06
#> $names
#> $names[[1]]
#> a
#> 
#> $names[[2]]
#> b
#> 
#> $names[[3]]
#> c
#> 
#> $names[[4]]
#> d
#> 
#> 
#> $calls
#> $calls[[1]]
#> rnorm(n)
#> 
#> $calls[[2]]
#> a + rnorm(n)
#> 
#> $calls[[3]]
#> b + rnorm(n)
#> 
#> $calls[[4]]
#> c + a + rnorm(n)
#> 
#> 
#> attr(,"class")
#> [1] "list"    "datasim"

Instructions for constructing data simulations are given in the Simulating data with Directed Acyclic Graphs vignette of this package. Many pre-built simulations are provided with this {LST} package. New ones can be constructed using datasim_make(). Except in the most straightforward cases, such construction is an instructor-level task.

Trials and the pipe

A popular feature of the {mosaic} package is the do() function, which provides syntax and logic for repeating a command multiple times, accumulating the results into a data frame. For instance:

mosaic::do(3) * sum(runif(5))

{LST} has updated this functionality to take advantage of the R built-in pipe notation and the style of arranging model summaries as data frames. The functionality is provided by the trials() function. To use it, place trials() at the end of a pipeline:

mtcars |> 
  sample(replace = TRUE) |> # resampling here!
  model_train(mpg ~ hp) |> 
  conf_interval() |> 
  filter(term == "hp") |>
  trials(5) 
#>   .trial term        .lwr       .coef        .upr
#> 1      1   hp -0.05884886 -0.04350439 -0.02815991
#> 2      2   hp -0.07123911 -0.05567061 -0.04010210
#> 3      3   hp -0.10945900 -0.08387168 -0.05828437
#> 4      4   hp -0.11131359 -0.08981114 -0.06830869
#> 5      5   hp -0.08612844 -0.06705820 -0.04798795

You can, of course, take the data frame produced by trials() to use for later wrangling or graphics.

It’s natural to think of the pipeline leading up to the trials() stage as creating a single output. But trials() has a seemingly magical ability to grab the whole pipeline and run it over and over again. (The “magic” is provided by the “non-standard evaluation” facilities in R, an advanced programming construct.)

An excellent way to develop the statement to be repeated: write the pipeline excluding the final trials() stage. Each time you run the truncated pipeline, you will receive one object. When this object has the format you seek, add the final trials() stage back in.

Graphics in {LST}

Instructors may feel obliged by convention to introduce the menagerie of plotting modalities, such as bar charts, line charts, histograms, etc. Lessons was written to use only a single primary graphic modality: the point plot (a.k.a. “scatter plot”) as produced by point_plot(). Three other modalities—confidence intervals, confidence bands, and violin plots of density—are provided by the annotation feature of point_plot(). These are annot = "violin" and "annot = "model".

The output of point_plot() is a {ggplot2} graphical object. Consequently, you can use the various {ggplot2} functions to set a graphics theme, label axes, and so on. Unfortunately, {ggplot2} functions use the + pipe rather than |>. This can be confusing and frustrating for students.

I recommend use of the {ggformula} package which re-packages the {ggplot2} facilities in a way that can be used with the R pipe |> and which employe tilde-expressions for specifying response and explanatory variables.

{LST}, {mosaic}, and {ggformula}

The MOSAIC suite of packages—including {mosaic} and {ggformula}—are widely used in teaching statistics with R. Many of the pedagogical principles behind {LST} are shared with {mosaic} and {ggformula}. You are of course welcome to use {mosaic} and {ggformula} along with {LST}, particularly if you want to teach other graphics modalities than those provided by LST::point_plot().

Other than shared pedagogical principles, there is no connection of {LST} with either {mosaic} and {ggformula}. One reason for this is the pipe |>, which prominently features in Lessons. {mosaic} is not pipe-ready because many functions require a data = argument.

Another reason concerns recent developments in deploying R computing via web pages. The system that provides within-a-web-page R computing is not yet compatible with {mosaic} or {ggformula}. For {LST} to work with R embedded in web pages, {LST} cannot make any use of {mosaic}/{ggformula}. This situation may change in the future, at which point {LST} will be able to acknowledge its aunts and uncles.