Introduction To User Defined Functions

• Implement a function given a description of what it should do
• Describe R’s formula syntax, y ~ x
• Select rows of a data frame by index

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Defining Functions

Functions are the heart of R. Everything in R is a function. To really use R, we need to define our own functions.

Q: What’s the mathematical definition of a function?

A: Maps an input to exactly one output. input ---> output

Last homework we found the data point that was closest to the mean. Let’s implement this in a general function, closest_to_mean.

Q: 123GO - What’s a simple example we can test to verify the behavior of our function? We need an input and output.

A: There are many ways. Here’s one: closest_to_mean(c(10, 11, 12)) should output 11.

Let’s write a placeholder for the function.

#' Return the data point in `x` closest to the mean of `x`.
#'
closest_to_mean = function(x)
{
}

The empty braces {} after function(x) mean that this function doesn’t do anything yet. It’s like a skeleton or outline, ready for implementation. We can attempt to use it, and verify it doesn’t do anything:

> closest_to_mean(precip)
NULL

NULL means nothing, and we’ll talk about it in detail in a future lecture.

In the last homework, we did this calculation for precip, and we can implement our function based on this code:

diff_from_mean = abs(precip - mean(precip))
closest_index = which.min(diff_from_mean)
precip[closest_index]

The code above is written with precip as the input. We need to change it so that x is the input, and stick it in the body of the function, the part between the braces {}.

#' Return the data point in `x` closest to the mean of `x`.
#'
closest_to_mean = function(x)   # <--- function name, arguments
{                               # <--- begin body
    diff_from_mean = abs(x - mean(x))
    closest_index = which.min(diff_from_mean)
    x[closest_index]            # <--- last line of body is the return value
}

Finally, we verify that our function does what we expected.

> closest_to_mean(precip)
Cleveland
       35

> closest_to_mean(c(10, 11, 12))
[1] 11

🤑 Sweeeet.

Model Formulas

R uses ~ (tilde, pronounced “till-duh”) to specify statistical models. The most basic way to specify a model is y ~ x, which you can think of as saying “model y as a function of x”.

The R documentation goes into more detail.

?formula

The models fit by, e.g., the ‘lm’ and ‘glm’ functions are specified in a compact symbolic form. The ‘~’ operator is basic in the formation of such models. An expression of the form ‘y ~ model’ is interpreted as a specification that the response ‘y’ is modelled by a linear predictor specified symbolically by ‘model’.

Many functions accept model formula, for example, boxplot. Let’s load our data for the homework and see.

air = read.csv("http://webpages.csus.edu/fitzgerald/files/stat128/fall20/ad_viz_plotval_data.csv")

Suppose we want to see comparative boxplots of DAILY_AQI_VALUE, split into groups by COUNTY.

boxplot(DAILY_AQI_VALUE ~ COUNTY, data = air)

We see a boxplot for each county, all on the same y axis scale, so that we can easily compare them. Think about the formula DAILY_AQI_VALUE ~ COUNTY as saying, “model DAILY_AQI_VALUE as a function of COUNTY”.

Q: How can we group all the counties besides Sacramento together and do a boxplot?

A: We need a new column saying whether each row belongs to a Sacramento county or not.

air[, "Sac"] = air[, "COUNTY"] == "Sacramento"
boxplot(DAILY_AQI_VALUE ~ Sac, data = air)

Selecting Rows by Index

I’d like to reorder air so that the smallest values of DAILY_AQI_VALUE show up first. How do we do this?

Subsetting x with integers allows us to permute x, and we can use this idea to reorder our data frames. Here’s an example of randomly permuting letters.

> rand_index = sample(length(letters))
>
> rand_index
 [1] 14  6 19  2  4 16  3 10 18 13 15  8 23 11  1 12  5 26 21  7 24 25 20  9 17
[26] 22
> letters[rand_index]
 [1] "n" "f" "s" "b" "d" "p" "c" "j" "r" "m" "o" "h" "w" "k" "a" "l" "e" "z" "u"
[20] "g" "x" "y" "t" "i" "q" "v"

rand_index is a random permutation of the integers 1 to 26. letters[rand_index] selects the elements of letters corresponding to rand_index. 14 comes first in rand_index, so the 14th letter n shows up first. 6 comes next in rand_index, so the 6th letter f shows up next, and so on.

Recall general data subsetting has this form.

data[rows, columns]

We need a vector of integers that shows the sorted order of DAILY_AQI_VALUE. order will give us this.

aqi_order = order(air[, "DAILY_AQI_VALUE"])
head(aqi_order)

This means element 1065 is the smallest value in DAILY_AQI_VALUE, followed by element 582, and so on. Let’s sort the data using aqi_order and save the result.

air2 = air[aqi_order, ]

# 123GO - What do you think, same or different?
dim(air)
dim(air2)

Let’s plot them and see what happened.

plot(air[, "DAILY_AQI_VALUE"], type = "l")  # "l" for line plot

plot(air2[, "DAILY_AQI_VALUE"], type = "l")