Simulation and Control Structures

Dr. Mine Dogucu

1 / 20

Goals

Probability Distribution and simulating data in R
Control structures (if/else, for and while loops and mapping)

2 / 20

Go to course organization on GitHub
Start a new repo called week-07-simulate-data-username where username represents your own username.
3 / 20

Probability Distributions - Normal

dnorm(x = -1.96, mean = 0, sd = 1)

[1] 0.05844094

pnorm(q = -1.96, mean = 0, sd = 1)

[1] 0.0249979

qnorm(p = 0.0249979, mean = 0, sd = 1, lower.tail = TRUE)

[1] -1.96

rnorm(n = 3, mean = 0, sd = 1)

[1] -1.7421388  0.2278699 -0.8605599

4 / 20

Probability Distributions - Normal

ggplot(data = data.frame(x = c(-3, 3)), aes(x)) +
  stat_function(fun = dnorm, n = 101, args = list(mean = 0, sd = 1)) + ylab("") +
  scale_y_continuous(breaks = NULL)

5 / 20

Other probability Functionsdbinom(), pbinom(), qbinom(), rbinom()
dbeta(), pbeta(), qbeta(), rbeta()
dunif(), punif(), qunif(), runif()
6 / 20

runif(1)

[1] 0.1590387

set.seed(92697)
runif(1)

[1] 0.7773408

set.seed() allows reproducibility of results when randomness is introduced.

7 / 20

while loopscount <- 0
while(count < 10) {
  count <- count + 1 
  print(count)
}

[1] 1
[1] 2
[1] 3
[1] 4
[1] 5
[1] 6
[1] 7
[1] 8
[1] 9
[1] 10
count <- 0
while(count < 10) {
  print(count)
  count <- count + 1 
}

[1] 0
[1] 1
[1] 2
[1] 3
[1] 4
[1] 5
[1] 6
[1] 7
[1] 8
[1] 9
8 / 20

if/else

if(condition) {
  ## do something
}
## Rest of the code

if(condition) {
  ## do something
} else {
  ## do something else
}

if(condition) {
  ## do something
  } else if(another condition) {
  ## do something different
  } else {
    ## do something different
}

9 / 20

count <- 0
while(count < 10) {
  if(count < 5){
    print(paste(count, "small number"))
  }
  count <- count + 1 
}

[1] "0 small number"
[1] "1 small number"
[1] "2 small number"
[1] "3 small number"
[1] "4 small number"

10 / 20

count <- 0
while(count < 10) {
  if(count %% 2 == 0){
    print(paste(count, "even number"))
  }
  count <- count + 1 
}

[1] "0 even number"
[1] "2 even number"
[1] "4 even number"
[1] "6 even number"
[1] "8 even number"

11 / 20

count <- 0
while(count < 10) {
  if(count %% 2 == 0){
    print(paste(count, "even number"))
  } else {
    print(paste(count, "odd number"))
  }
  count <- count + 1 
}

[1] "0 even number"
[1] "1 odd number"
[1] "2 even number"
[1] "3 odd number"
[1] "4 even number"
[1] "5 odd number"
[1] "6 even number"
[1] "7 odd number"
[1] "8 even number"
[1] "9 odd number"

12 / 20

for loops

for (i in 1:10){
  print(i)
}

[1] 1
[1] 2
[1] 3
[1] 4
[1] 5
[1] 6
[1] 7
[1] 8
[1] 9
[1] 10

13 / 20

for loops

sample_size <- c(30, 60, 100)
for (i in 1:3){
  print(sample_size[i])
}

[1] 30
[1] 60
[1] 100

sample_size <- c(30, 60, 100)
for (i in 1:length(sample_size)){
  print(sample_size[i])
}

[1] 30
[1] 60
[1] 100

14 / 20

apply : R Documentation

Returns a vector or array or list of values obtained by applying a function to margins of an array or matrix.

apply(X, MARGIN, FUN, ..., simplify = TRUE)

X an array, including a matrix.

MARGIN a vector giving the subscripts which the function will be applied over. E.g., for a matrix 1 indicates rows, 2 indicates columns, c(1, 2) indicates rows and columns. Where X has named dimnames, it can be a character vector selecting dimension names.

FUN the function to be applied: see ‘Details’. In the case of functions like +, %*%, etc., the function name must be backquoted or quoted.

optional arguments to FUN.

15 / 20

some_matrix <- matrix(C <- (1:30), nrow = 5, ncol = 6)
some_matrix

     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    1    6   11   16   21   26
[2,]    2    7   12   17   22   27
[3,]    3    8   13   18   23   28
[4,]    4    9   14   19   24   29
[5,]    5   10   15   20   25   30

apply(some_matrix, 1, sum) # adding rows

[1]  81  87  93  99 105

apply(some_matrix, 2, sum) # adding columns

[1]  15  40  65  90 115 140

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lapply and sapply: R Documentation

Apply a Function over a List or Vector Description

lapply returns a list of the same length as X, each element of which is the result of applying FUN to the corresponding element of X.

sapply is a user-friendly version and wrapper of lapply by default returning a vector, matrix or, if simplify = "array", an array if appropriate, by applying simplify2array(). sapply(x, f, simplify = FALSE, USE.NAMES = FALSE) is the same as lapply(x, f).

17 / 20

sapply(c(0, 1, 2), exp)

[1] 1.000000 2.718282 7.389056
lapply(c(0, 1, 2), exp)

[[1]]
[1] 1
[[2]]
[1] 2.718282
[[3]]
[1] 7.389056
18 / 20

sapply(c(0, 1, 2), exp)

[1] 1.000000 2.718282 7.389056
lapply(c(0, 1, 2), exp) %>% 
  unlist()

[1] 1.000000 2.718282 7.389056
19 / 20

This week's (long) task:

How does missing data (missing completely at random) impact bias and variance in simple linear regression?

Design a simulation to answer this question. You are in charge of developing sub-questions.

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Simulation and Control Structures

Dr. Mine Dogucu

Goals

Probability Distributions - Normal

Probability Distributions - Normal

Other probability Functions

`while` loops

if/else

for loops

for loops

apply : R Documentation

lapply and sapply: R Documentation

Goals

Help