tidyRcheatsheet.tex

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\begin{center}
     {\Large{\textbf{Econometrics in R's \texttt{tidyverse}}}} \\
     
     {\footnotesize by Tyler Ransom, University of Oklahoma}
     
     {\footnotesize \href{https://www.twitter.com/tyleransom}{\makeatletter @tyleransom \makeatother}}
\end{center}

\section{Basics of R}
R can be thought of as a really fancy calculator

\smallskip{}

\textbf{Packages:}\\
\begin{itemize}
    \item R comes with a lot of functionality out-of-the-box
    \item Other functionality requires the user to load packages
    \item One-time installation: \verb!install.packages("tidyverse")!
    \item Each time you open R: \verb!library(tidyverse)!
\end{itemize}

\smallskip{}

\textbf{Commenting:}\\
\begin{itemize}
    \item Use \verb!#! to make a comment
    \item This tells R to ignore that code
    \item[] \verb!# My name is Tyler!
\end{itemize}

\smallskip{}

\textbf{Assignment operator:}\\
\begin{itemize}
    \item Use \verb!<-! to store a calculation, e.g. \verb!x <- 3! (``$x=3$'')
\end{itemize}

\smallskip{}

\textbf{Pipe operator:}\\
\begin{itemize}
    \item Use \verb!%>%! to ``pipe'' objects
    \item[] \verb!y <- mean(log(x))! becomes \verb!y <- x %>% log %>% mean!
    \item \verb!%<>%! pipes forward, then backwards
    \item[] \verb!x <- mean(log(x))! is same as \verb!x %<>% log %>% mean!
\end{itemize}

\section{Working with Data}
R's fundamental data object is a \textbf{data frame}

\smallskip{}

Like spreadsheets, stores data in columns and rows

\smallskip{}

\verb!tidyverse! uses \textbf{tibbles} (enhanced data frames)
\begin{itemize}
    \item[] \verb!df <- as_tibble(mtcars)!
\end{itemize}

\smallskip{}

\textbf{Reading in data}\\
\begin{itemize}
    \item Many functions for reading in different types of data
    \item[] \verb!df <- read_csv("myfile.csv")! (comma separated)
    \item[] \verb!df <- read_fwf("myfile.dat")! (fixed-width)
    \item More details: see \href{https://rawgit.com/rstudio/cheatsheets/master/data-import.pdf}{Data Importing Cheat Sheet}
    \item \verb!haven! package: import foreign files (e.g. SAS, Stata, ...)
\end{itemize}

\smallskip{}

\textbf{Accessing columns of data}\\
\begin{itemize}
    \item To reference a column in a tibble, use \verb!$!
    \item[] \verb!df$mpg!
    \item[] \verb!mean(df$mpg)! will return sample avg of \verb!mpg! variable
\end{itemize}

\smallskip{}

\textbf{Ignore missing values}\\
\begin{itemize}
    \item Missing values are indicated by \verb!NA!
    \item Some commands won't automatically ignore \verb!NA! values
    \item For these cases, use \verb!na.rm! option
    \item[] \verb!mean(df$mpg, na.rm=TRUE)!
    \item[] \verb!df$mpg %>% mean(na.rm=TRUE)! (equivalent)
    \item Otherwise, \texttt{R} would say the mean is \verb!NA!
\end{itemize}

\smallskip{}

\textbf{Removing columns and rows from a tibble}\\
\begin{itemize}
    \item To keep columns in a tibble, use \verb!select()!
    \item[] \verb!df1 <- df %>% select(mpg,disp,hp,gear,carb)!
    \item To keep rows in a tibble, use \verb!filter()!
    \item[] \verb!df1 %<>% filter(mpg>=10)!
    \item To remove columns, put a minus in front
    \item[] \verb!df1 <- df %>% select(-mpg,-disp)!
\end{itemize}

\smallskip{}

\textbf{Remove missing values from a tibble}\\
\begin{itemize}
    \item To remove \textbf{all} rows with \textit{any} \verb!NA! values, use \verb!drop_na()!
    \item[] \verb!df1 <- df %>% drop_na()!
    \item Can also drop \verb!NA!'s from particular columns:
    \item[] \verb!df1 <- df %>% drop_na(gear,carb)!
\end{itemize}

\smallskip{}

\textbf{Creating new columns in a tibble}\\
\begin{itemize}
    \item To create a new column in a tibble, use \verb!mutate()!
    \item[] \verb!df1 %<>% mutate(mpg.squared = mpg^2)!
\end{itemize}

\smallskip{}

\textbf{Manipulating values of a variable}\\
\begin{itemize}
    \item To replace (i.e. recode) values of a variable:
    \item[] \verb!df %<>% mutate(gear = replace(gear,gear==4,99))!
    \item[] Changes all 4's in \verb!gear! to be 99's
    \item[] \verb!gear==4! can be any other logical condition
    \item To specify a series of conditions, use \verb!%in%!
    \item[] \verb!df %<>% mutate(hp =!
    \item[] \verb!replace(hp,hp %in% c(110,120),99))!
    \item[] Changes all 110's or 120's in \verb!hp! to be 99's
\end{itemize}

\smallskip{}

\textbf{Working with discrete variables}\\
\begin{itemize}
    \item Discrete variables often require special treatment
    \item In R, declare discrete variables as \textbf{factors}
    \item[] \verb!df %<>% mutate(gear = as.factor(gear))!
\end{itemize}

\smallskip{}

\textbf{Other data manipulations}\\
\begin{itemize}
    \item See \href{https://www.rstudio.com/wp-content/uploads/2015/02/data-wrangling-cheatsheet.pdf}{Data Wrangling Cheat Sheet}
\end{itemize}

\section{Getting to know your data}
It's important to know what's in your data by
\begin{enumerate}
    \item Looking at summary statistics
    \item Performing cross-tabulations
    \item Visualizing certain variables
\end{enumerate}

\smallskip{}

\textbf{Summary statistics (\texttt{modelsummary} package)}\\
\begin{itemize}
    \item Report quartiles, min/max, mean, sd, and \#\verb!NA!'s:
    \item[] \verb!datasummary_skim(df, histogram=FALSE)!
    
    or
    \item[] \verb!df %>% datasummary_skim(histogram=FALSE)!
\end{itemize}

\smallskip{}

\textbf{Cross-tabulations}\\
\begin{itemize}
    \item Report frequencies of a discrete variable:
    \item[] \verb!table(df$gear)!
    \item Average $y$ by categories of a discrete $x$ variable:
    \item[] \verb!df %>% group_by(gear) %>% !
    \item[] \verb!summarize(m.mpg = mean(mpg))!
\end{itemize}

\smallskip{}

\textbf{Visualization}\\
\begin{itemize}
    \item Often helpful to look at a histogram or line graph
    \item Histogram (continuous $x$):
    \item[] \verb!ggplot(df, aes(mpg)) + geom_histogram()!
    \item Histogram (factor $x$):
    \item[] \verb!ggplot(df,aes(x=gear)) + geom_bar()!
    \item Kernel density plot:
    \item[] \verb!ggplot(df, aes(mpg)) + geom_density()!
    \item Simple scatter plot with linear fit:
    \item[] \verb!ggplot(df,aes(disp,mpg)) + geom_point() +!
    \item[] \verb!geom_smooth(method="lm")!
    \item More details: see \href{https://www.rstudio.com/wp-content/uploads/2015/03/ggplot2-cheatsheet.pdf}{ggplot2 Cheat Sheet}
\end{itemize}


\section{Regression modeling}

\smallskip{}

\textbf{Basic OLS regression}\\
\begin{itemize}
    \item Regression:
    \item[] \verb!est <- lm(mpg ~ gear + hp, data=df)!
    \item Examine regression output:
    \item[] \verb!summary(est)!
    \item[] \verb!tidy(est)!
    \item[] \verb!modelsummary(est)!
    \item Other functional forms:
    \item[] \verb!est <- lm(mpg ~ gear + I(gear^2), data=df)!
    \item[] \verb!est <- lm(log(mpg) ~ gear + I(gear^2), data=df)!
    \item Factor variables automatically get separate intercepts
\end{itemize}

\smallskip{}

\textbf{$t$-statics and $F$-statistics}\\
\begin{itemize}
    \item $t$-stats, $p$-values reported in regression output
    \item $F$-test:
    \item[] \verb!linearHypothesis(est,c("gear","hp"))!
    \item[] tests $H_0: \beta_{gear} = 0, \beta_{hp}=0$
    \item[] \verb!linearHypothesis(est,c("gear=5","hp=-1"))!
    \item[] tests $H_0: \beta_{gear} = 5, \beta_{hp}=-1$
    \item Robust $F$-test (see next section):
    \item[] \verb!linearHypothesis(est.rob,c("gear","hp"))!
\end{itemize}

\smallskip{}

\textbf{Robust standard errors (\texttt{estimatr} and \texttt{sandwich} packages)}\\
\begin{itemize}
    \item Correct for heteroskedasticity:
    \item[] \verb!est.rob <- lm_robust(mpg ~ gear + hp, data=df)!
    \item[] \verb!modelsummary(est.rob)!
    \item[]
    \item Correct for serial correlation:
    \item[] \verb!est <- lm(mpg ~ gear + hp, data=df)!
    \item[] \verb!modelsummary(est, vcov=sandwich::NeweyWest(est))!
    \item[]
    \item Correct for clustering:
    \item[] \verb!est.clust <- lm_robust(mpg ~ gear + hp, data=df,!
    \item[] \verb!clusters=df$carb)!
    \item[] \verb!modelsummary(est.clust)!
\end{itemize}




\section{Instrumental Variables}

\smallskip{}

\begin{itemize}
    \item Let \verb!drat! be the endogenous covariate
    \item Let \verb!wt! be the instrument
    \item Let \verb!qsec! and \verb!gear! be exogenous covariates
    \item[] \verb!est.iv <- ivreg(mpg ~ drat + qsec + gear | !
    \item[] \verb!wt + qsec + gear, data=df)!
    \item Instruments come after the \verb!|! symbol
    \item Endogenous covariates come before the \verb!|! symbol
    \item Exogenous covariates appear on both sides of the \verb!|!
    \item First-stage regression:
    \item[] \verb!est.1 <- lm(drat ~ wt + qsec + gear, data=df)!
    \item[] \verb!df %<>% mutate(drat.hat = est.1$fitted.values)!
    \item Second-stage regression:
    \item[] \verb!est.2 <- lm(mpg ~ drat.hat + qsec+ gear,data=df)!
    \item Can also use \verb!estimatr! for robust SEs:
    \item[] \verb!est.ivr <- iv_robust(mpg ~ drat + qsec + gear | !
    \item[] \verb!wt + qsec + gear, data=df)!
\end{itemize}




\section{Working with time series data}

\smallskip{}

\begin{itemize}
    \item Declare a time series data frame
    \item[] \verb!df.ts <- as_tsibble(df, key=id, index=year)!
    \item Time series line plot:
    \item[] \verb!ggplot(df.ts, aes(year, inf)) + geom_line()!
    \item Simple AR(1) model:
    \item[] \verb!est <- lm(inf ~ lag(inf,1), data=df.ts)!
    \item First-differences model:
    \item[] \verb!est.diff <- lm(difference(inf) ~ unem,!
    \item[] \qquad\qquad\qquad\verb!data = df.ts)!
    \item ADF test for unit root:
    \item[] \verb!adf.test(df1.ts$inf, k=1)!
    \item ARIMA model:
    \item[] \verb!est.arima <- auto.arima(df.ts$inf)!
    \item Plot $h$-period-ahead forecast intervals
    \item[] \verb!autoplot(forecast(est.arima, h=2))!
    \item Extended date and time functions available in \href{https://evoldyn.gitlab.io/evomics-2018/ref-sheets/R_lubridate.pdf}{\texttt{lubridate} package}
\end{itemize}




\section{Working with panel data}

\smallskip{}

\begin{itemize}
    \item Report number of units and time periods
    \item[] \verb!pdim(df)!
    \item Pooled OLS model
    \item[] \verb!est.pols <- plm(lwage ~ exper + I(exper^2) +! 
    \item[] \verb!year, data = df, index = c("id","year"),! 
    \item[] \verb!model = "pooling")!
    \item Random effects model
    \item[] \verb!est.re <- plm(lwage ~ exper + I(exper^2) +! 
    \item[] \verb!year, data = df, index = c("id","year"),! 
    \item[] \verb!model = "random")!
    \item Fixed effects model
    \item[] \verb!est.fe <- plm(lwage ~ exper + I(exper^2) +! 
    \item[] \verb!year, data = df, index = c("id","year"),! 
    \item[] \verb!model = "within")!
    \item First differences model
    \item[] \verb!est.fd <- plm(lwage ~ exper + I(exper^2) +! 
    \item[] \verb!year, data = df, index = c("id","year"),! 
    \item[] \verb!model = "fd")!
\end{itemize}




\section{Limited dependent variable models}

\smallskip{}

\textbf{Linear probability model (LPM):}\\
\begin{itemize}
    \item If $y$ is a factor, format it as a numeric
    \item[] \verb!est.lpm <- lm(as.numeric(y) ~ x1 + x2, data=df)!
\end{itemize}

\textbf{Logit and Probit:}\\

\smallskip{}

In this case, $y$ should be formatted as a factor

\smallskip{}

\begin{itemize}
    \item Logit:
    \item[] \verb!est.logit <- glm(y ~ x1 + x2,!
    \item[] \verb!family=binomial(link="logit"),data=df)!
    \item Probit:
    \item[] \verb!est.probit <- glm(y ~ x1 + x2,!
    \item[] \verb!family=binomial(link="probit"),data=df)!
\end{itemize}


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\section{List of packages}
The document requires the following packages:

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\begin{multicols}{4}
\verb!tidyverse!  \\
\verb!magrittr!  \\
\verb!broom!  \\
\verb!modelsummary! \\
\verb!car!  \\
\verb!estimatr!  \\
\verb!lmtest!  \\
\verb!clubSandwich!  \\
\verb!sandwich!  \\
\verb!AER!  \\
\verb!tsibble!  \\
\verb!tseries!  \\
\verb!lubridate!  \\
\verb!forecast!  \\
\verb!plm!  \\
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