Lecture 5: More functions

Last time

assess_coverage <- function(n, nsim, beta0, beta1, noise_dist){
  results <- rep(NA, nsim)

  for(i in 1:nsim){
    x <- runif(n, min=0, max=1)
    noise <- noise_dist(n)
    y <- beta0 + beta1*x + noise

    lm_mod <- lm(y ~ x)
    ci <- confint(lm_mod, "x", level = 0.95)
    results[i] <- ci[1] < beta1 & ci[2] > beta1
  }
  return(mean(results))
}

Function defaults

assess_coverage <- function(n, nsim, beta0, beta1, noise_dist){
  ...
}

assess_coverage(n = 100, nsim = 1000, beta0 = 0.5, beta1 = 1,
                noise_dist = rexp)

[1] 0.951

What if I wanted noise_dist to be the \(N(0, 1)\) distribution instead?

Function defaults

assess_coverage <- function(n, nsim, beta0, beta1, noise_dist){
  ...
}

assess_coverage(n = 100, nsim = 1000, beta0 = 0.5, beta1 = 1,
                noise_dist = rnorm)

[1] 0.951

What if I wanted noise_dist to be the \(\chi^2_1\) distribution?

Function defaults

assess_coverage <- function(n, nsim, beta0, beta1, noise_dist){
  ...
}

assess_coverage(n = 100, nsim = 1000, beta0 = 0.5, beta1 = 1,
                noise_dist = rchisq)

Error in noise_dist(n): argument "df" is missing, with no default

Function defaults

?rexp

Description

Density, distribution function, quantile function and random generation for the exponential distribution with rate rate (i.e., mean 1/rate).

Usage

rexp(n, rate = 1)

• The default value of rate is 1!

Function defaults

rexp(n, rate = 1)

The default value of rate is 1!

Same results:

set.seed(93)
rexp(n=1)

[1] 1.188317

set.seed(93)
rexp(n=1, rate=1)

[1] 1.188317

Different result:

set.seed(93)
rexp(n=1, rate=2)

[1] 0.5941585

Function defaults

?rnorm

Description

Density, distribution function, quantile function and random generation for the normal distribution with mean equal to mean and standard deviation equal to sd.

Usage

rnorm(n, mean = 0, sd = 1)

Function defaults

?rchisq

Usage

rchisq(n, df, ncp = 0)

• There is no default for df in the rchisq function!

assess_coverage(n = 100, nsim = 1000, beta0 = 0.5, beta1 = 1,
                noise_dist = rchisq)

Error in noise_dist(n): argument "df" is missing, with no default

• How can we use a \(\chi^2_1\) for noise_dist?

Two options

Option 1: Create a new function

set.seed(73)

chisq_1 <- function(m){
  return(rchisq(m, df=1))
}
assess_coverage(n = 100, nsim = 1000, beta0 = 0.5, beta1 = 1,
                noise_dist = chisq_1)

[1] 0.962

Option 2: Anonymous functions

set.seed(73)

assess_coverage(n = 100, nsim = 1000, beta0 = 0.5, beta1 = 1,
                noise_dist = function(m) {return(rchisq(m, df=1))})

[1] 0.962

Anonymous functions

We use anonymous functions when we don’t need a name for them.

Example:

integrate(function(x) {sin(x)^2}, 0, pi)

1.570796 with absolute error < 1.7e-14

Function scoping

What value will the following code return?

g01 <- function(x = 10) {
  return(x)
}

g01()

Function scoping

What value will the following code return?

g01 <- function(x = 10) {
  return(x)
}

g01()

[1] 10

What if I try to look at x?

x

Function scoping

What value will the following code return?

g01 <- function(x = 10) {
  return(x)
}

g01()

[1] 10

What if I try to look at x?

x

Error in eval(expr, envir, enclos): object 'x' not found

• Variables created within functions don’t exist outside the function!

Function scoping

Variables created within functions don’t exist outside the function!

g01 <- function() {
  x <- 10
  return(x)
}

g01()

[1] 10

x

Error in eval(expr, envir, enclos): object 'x' not found

Function scoping

What will the following code return?

x <- 10

g01 <- function(){
  return(x)
}

g01()

Function scoping

x <- 10

g01 <- function(){
  return(x)
}

g01()

[1] 10

x

[1] 10

• If a variable is not defined in a function, R looks outside the function (the global environment)

Name masking

What value will the following code return?

x <- 10
g01 <- function() {
  x <- 20
  return(x)
}

g01()
x

Name masking

What value will the following code return?

x <- 10
g01 <- function() {
  x <- 20
  return(x)
}

g01()

[1] 20

x

[1] 10

• Names defined inside a function mask names defined outside a function
• Variables created within a function don’t exist outside

Summary

• Anonymous functions can be used if we don’t need to name them
• Variables created within a function don’t exist outside
• If a variable is not defined in a function, R looks outside the function
• Names defined inside a function mask names defined outside a function

Class activity

https://sta279-f23.github.io/class_activities/ca_lecture_5.html

• If finished early, you may work on homework
• Solutions will be posted on course website