vignettes/paper.md

In moderndive: Tidyverse-Friendly Introductory Linear Regression

title: "Take a moderndive into introductory linear regression with R" author: "Albert Y. Kim, Chester Ismay, and Max Kuhn" date: "2021-07-13" tags: - R - Rstats - tidyverse - regression - moderndive - modeling - modelling - kaggle authors: - name: Albert Y. Kim orcid: 0000-0001-7824-306X affiliation: 1 - name: Chester Ismay orcid: 0000-0003-2820-2547 affiliation: 2 - name: Max Kuhn orcid: 0000-0003-2402-136X affiliation: 3 affiliations: - name: Assistant Professor of Statistical and Data Sciences, Smith College, Northampton, MA, USA. index: 1 - name: Data Science Evangelist, DataRobot, Portland, OR, USA. index: 2 - name: Software Engineer, RStudio, USA. index: 3 bibliography: paper.bib output: rticles::joss_article: keep_md: yes number_sections: yes

Summary

We present the moderndive{target="blank"} R package of datasets and functions for tidyverse-friendly introductory linear regression [@tidyverse2019]. These tools leverage the well-developed tidyverse and broom packages to facilitate 1) working with regression tables that include confidence intervals, 2) accessing regression outputs on an observation level (e.g. fitted/predicted values and residuals), 3) inspecting scalar summaries of regression fit (e.g. $R^2$, $R^2{adj}$, and mean squared error), and 4) visualizing parallel slopes regression models using ggplot2-like syntax [@R-ggplot2; @R-broom]. This R package is designed to supplement the book "Statistical Inference via Data Science: A ModernDive into R and the Tidyverse" [@ismay2019moderndive]. Note that the book is also available online at https://moderndive.com and is referred to as "ModernDive" for short.

Statement of Need

Linear regression has long been a staple of introductory statistics courses. While the curricula of introductory statistics courses has much evolved of late, the overall importance of regression remains the same [@ASAGuidelines]. Furthermore, while the use of the R statistical programming language for statistical analysis is not new, recent developments such as the tidyverse suite of packages have made statistical computation with R accessible to a broader audience [@tidyverse2019]. We go one step further by leveraging the tidyverse and the broom packages to make linear regression accessible to students taking an introductory statistics course [@R-broom]. Such students are likely to be new to statistical computation with R; we designed moderndive with these students in mind.

Introduction

Let's load all the R packages we are going to need.

library(moderndive)
library(ggplot2)
library(dplyr)
library(knitr)
library(broom)

Let's consider data gathered from end of semester student evaluations for a sample of 463 courses taught by 94 professors from the University of Texas at Austin [@diez2015openintro]. This data is included in the evals data frame from the moderndive package.

In the following table, we present a subset of 9 of the 14 variables included for a random sample of 5 courses^[For details on the remaining 5 variables, see the help file by running ?evals.]:

1. ID uniquely identifies the course whereas prof_ID identifies the professor who taught this course. This distinction is important since many professors taught more than one course.
2. score is the outcome variable of interest: average professor evaluation score out of 5 as given by the students in this course.
3. The remaining variables are demographic variables describing that course's instructor, including bty_avg (average "beauty" score) for that professor as given by a panel of 6 students.^[Note that gender was collected as a binary variable at the time of the study (2005).]

| ID| prof_ID| score| age| bty_avg|gender |ethnicity |language |rank | |---:|-------:|-----:|---:|-------:|:------|:------------|:--------|:-------| | 129| 23| 3.7| 62| 3.000|male |not minority |english |tenured | | 109| 19| 4.7| 46| 4.333|female |not minority |english |tenured | | 28| 6| 4.8| 62| 5.500|male |not minority |english |tenured | | 434| 88| 2.8| 62| 2.000|male |not minority |english |tenured | | 330| 66| 4.0| 64| 2.333|male |not minority |english |tenured |

Regression analysis the "good old-fashioned" way

Let's fit a simple linear regression model of teaching score as a function of instructor age using the lm() function.

score_model <- lm(score ~ age, data = evals)

Let's now study the output of the fitted model score_model "the good old-fashioned way": using summary() which calls summary.lm() behind the scenes (we'll refer to them interchangeably throughout this paper).

summary(score_model)
## 
## Call:
## lm(formula = score ~ age, data = evals)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9185 -0.3531  0.1172  0.4172  0.8825 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.461932   0.126778  35.195   <2e-16 ***
## age         -0.005938   0.002569  -2.311   0.0213 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5413 on 461 degrees of freedom
## Multiple R-squared:  0.01146,    Adjusted R-squared:  0.009311 
## F-statistic: 5.342 on 1 and 461 DF,  p-value: 0.02125

Regression analysis using moderndive

As an improvement to base R's regression functions, we've included three functions in the moderndive package that take a fitted model object as input and return the same information as summary.lm(), but output them in tidyverse-friendly format [@tidyverse2019]. As we'll see later, while these three functions are thin wrappers to existing functions in the broom package for converting statistical objects into tidy tibbles, we modified them with the introductory statistics student in mind [@R-broom].

1. Get a tidy regression table with confidence intervals:

   ```r get_regression_table(score_model)

   # A tibble: 2 x 7

   term estimate std_error statistic p_value lower_ci upper_ci

   1 intercept 4.46 0.127 35.2 0 4.21 4.71

   2 age -0.006 0.003 -2.31 0.021 -0.011 -0.001

   ``` 2. Get information on each point/observation in your regression, including fitted/predicted values and residuals, in a single data frame:

   ```r get_regression_points(score_model)

   # A tibble: 463 x 5

   ID score age score_hat residual

   1 1 4.7 36 4.25 0.452

   2 2 4.1 36 4.25 -0.148

   3 3 3.9 36 4.25 -0.348

   4 4 4.8 36 4.25 0.552

   5 5 4.6 59 4.11 0.488

   6 6 4.3 59 4.11 0.188

   7 7 2.8 59 4.11 -1.31

   8 8 4.1 51 4.16 -0.059

   9 9 3.4 51 4.16 -0.759

   10 10 4.5 40 4.22 0.276

   # ... with 453 more rows

   ``` 3. Get scalar summaries of a regression fit including $R^2$ and $R^2_{adj}$ but also the (root) mean-squared error:

   ```r get_regression_summaries(score_model)

   # A tibble: 1 x 9

   r_squared adj_r_squared mse rmse sigma statistic p_value df

   1 0.011 0.009 0.292 0.540 0.541 5.34 0.021 1

   # ... with 1 more variable: nobs

   ```

Furthermore, say you would like to create a visualization of the relationship between two numerical variables and a third categorical variable with $k$ levels. Let's create this using a colored scatterplot via the ggplot2 package for data visualization [@R-ggplot2]. Using geom_smooth(method = "lm", se = FALSE) yields a visualization of an interaction model where each of the $k$ regression lines has their own intercept and slope. For example in \autoref{fig:interaction-model}, we extend our previous regression model by now mapping the categorical variable ethnicity to the color aesthetic.

# Code to visualize interaction model:
ggplot(evals, aes(x = age, y = score, color = ethnicity)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE) +
  labs(x = "Age", y = "Teaching score", color = "Ethnicity")

\begin{figure}

{\centering \includegraphics[width=1\linewidth]{paper_files/figure-latex/interaction-model-1}

}

\caption{Visualization of interaction model.}\label{fig:interaction-model} \end{figure}

However, many introductory statistics courses start with the easier to teach "common slope, different intercepts" regression model, also known as the parallel slopes model. However, no argument to plot such models exists within geom_smooth().

Evgeni Chasnovski{target="_blank"} thus wrote a custom geom_ extension to ggplot2 called geom_parallel_slopes(); this extension is included in the moderndive package. Much like geom_smooth() from the ggplot2 package, you add geom_parallel_slopes() as a layer to the code, resulting in \autoref{fig:parallel-slopes-model}.

# Code to visualize parallel slopes model:
ggplot(evals, aes(x = age, y = score, color = ethnicity)) +
  geom_point() +
  geom_parallel_slopes(se = FALSE) +
  labs(x = "Age", y = "Teaching score", color = "Ethnicity")

\begin{figure}

{\centering \includegraphics[width=1\linewidth]{paper_files/figure-latex/parallel-slopes-model-1}

}

\caption{Visualization of parallel slopes model.}\label{fig:parallel-slopes-model} \end{figure}

Repository README

In the GitHub repository README, we present an in-depth discussion of six features of the moderndive package:

1. Focus less on p-value stars, more confidence intervals
2. Outputs as tibbles
3. Produce residual analysis plots from scratch using ggplot2
4. A quick-and-easy Kaggle predictive modeling competition submission!
5. Visual model selection: plot parallel slopes & interaction regression models
6. Produce metrics on the quality of regression model fits

Furthermore, we discuss the inner-workings of the moderndive package:

1. It leverages the broom package in its wrappers
2. It builds a custom ggplot2 geometry for the geom_parallel_slopes() function that allows for quick visualization of parallel slopes models in regression.

Author contributions

Albert Y. Kim and Chester Ismay contributed equally to the development of the moderndive package. Albert Y. Kim wrote a majority of the initial version of this manuscript with Chester Ismay writing the rest. Max Kuhn provided guidance and feedback at various stages of the package development and manuscript writing.

Acknowledgments

Many thanks to Jenny Smetzer \@smetzer180{target="_blank"}, Luke W. Johnston \@lwjohnst86{target="_blank"}, and Lisa Rosenthal \@lisamr{target="_blank"} for their helpful feedback for this paper and to Evgeni Chasnovski \@echasnovski{target="_blank"} for contributing the geom_parallel_slopes() function via GitHub pull request{target="_blank"}. The authors do not have any financial support to disclose.

References

moderndive documentation built on Sept. 11, 2024, 9:26 p.m.