# Pipe by formula

Now that we have covered the features of first-argument piping and dot piping. In both cases, we can use . to refer to the value being piped. Sometimes, however, it may look confusing to use . to represent the value being piped. For example,

mtcars %>>%
(lm(mpg ~ ., data = .))

#
# Call:
# lm(formula = mpg ~ ., data = .)
#
# Coefficients:
# (Intercept)          cyl         disp           hp         drat
#    12.30337     -0.11144      0.01334     -0.02148      0.78711
#          wt         qsec           vs           am         gear
#    -3.71530      0.82104      0.31776      2.52023      0.65541
#        carb
#    -0.19942


The code above works correctly even though the two dots in the second line have different meanings:

• . in formula mpg ~ . represents all variables other than mpg in mtcars, as interpreted by lm().
• . in data = . represents mtcars, as interpreted by %>>%.

%>>% provides a way to reduce ambiguity. It accepts formula enclosed by parentheses like (x ~ f(x)) so that x represents the value being piped. This formula is also called lambda expression which is a general term to denote an expression that associate the symbol of an object and an expression to evaluate.

For example, the above code can be rewritten using lambda expression like

mtcars %>>%
(df ~ lm(mpg ~ ., data = df))

#
# Call:
# lm(formula = mpg ~ ., data = df)
#
# Coefficients:
# (Intercept)          cyl         disp           hp         drat
#    12.30337     -0.11144      0.01334     -0.02148      0.78711
#          wt         qsec           vs           am         gear
#    -3.71530      0.82104      0.31776      2.52023      0.65541
#        carb
#    -0.19942


where the formula tells %>>% to use df to represent mtcars so that the expression of linear model fit won't look ambiguous any more.

The following example mixes first argument piping and piping by formula.

mtcars %>>%
subset(select = c(mpg, wt, cyl)) %>>%
(x ~ lm(mpg ~ ., data = x))

#
# Call:
# lm(formula = mpg ~ ., data = x)
#
# Coefficients:
# (Intercept)           wt          cyl
#      39.686       -3.191       -1.508


One thing to notice is that the formula must be enclosed in () and cannot function in {} as we have noted before.

Since formula is, in essence, a pair of expressions connected by ~, its right-hand side can be an expression enclosed in {} which does more things. For example,

mtcars %>>%
subset(select = c(mpg, wt, cyl)) %>>%
(x ~ {
summ <- lm(mpg ~ ., data = x) %>>%
summary
list(n = nrow(x), r.squared = summ$r.squared) })  #$n
#  32
#
# \$r.squared
#  0.8302274