2.1 R Data types: vector and list

‘Atomic’ vectors

• Types include integer, numeric (float-point; real), complex, logical, character, raw (bytes)

  people <- c("Lori", "Yubo", "Greg", "Nitesh", "Valerie", "Herve")
  people

  ## [1] "Lori" "Yubo" "Greg" "Nitesh" "Valerie" "Herve"

• Atomic vectors can be named

  population <- c(Buffalo=259000, Rochester=210000, `New York`=8400000)
  population

  ## Buffalo Rochester New York 
  ## 259000 210000 8400000

  log10(population)

  ## Buffalo Rochester New York 
  ## 5.413300 5.322219 6.924279

• Statistical concepts like NA ("not available")

  truthiness <- c(TRUE, FALSE, NA)
  truthiness

  ## [1] TRUE FALSE NA

• Logical concepts like ‘and’ (&), ‘or’ (|), and ‘not’ (!)

  !truthiness

  ## [1] FALSE TRUE NA

  truthiness | !truthiness

  ## [1] TRUE TRUE NA

  truthiness & !truthiness

  ## [1] FALSE FALSE NA

• Numerical concepts like infinity (Inf) or not-a-number (NaN, e.g., 0 / 0)

  undefined_numeric_values <- c(NA, 0/0, NaN, Inf, -Inf)
  undefined_numeric_values

  ## [1] NA NaN NaN Inf -Inf

  sqrt(undefined_numeric_values)

  ## Warning in sqrt(undefined_numeric_values): NaNs produced

  ## [1] NA NaN NaN Inf NaN

• Common string manipulations

  toupper(people)

  ## [1] "LORI" "YUBO" "GREG" "NITESH" "VALERIE" "HERVE"

  substr(people, 1, 3)

  ## [1] "Lor" "Yub" "Gre" "Nit" "Val" "Her"

• R is a green consumer – recylcing short vectors to align with long vectors

  x <- 1:3
  x * 2 # '2' (vector of length 1) recycled to c(2, 2, 2)

  ## [1] 2 4 6

  truthiness | NA

  ## [1] TRUE NA NA

  truthiness & NA

  ## [1] NA FALSE NA

• It’s very common to nest operations, which can be simultaneously compact, confusing, and expressive ([: subset; <: less than)

  substr(tolower(people), 1, 3)

  ## [1] "lor" "yub" "gre" "nit" "val" "her"

  population[population < 1000000]

  ## Buffalo Rochester 
  ## 259000 210000

Lists

• The list type can contain other vectors, including other lists

  frenemies = list(
   friends=c("Larry", "Richard", "Vivian"),
   enemies=c("Dick", "Mike")
  )
  frenemies

  ## $friends
  ## [1] "Larry" "Richard" "Vivian" 
  ## 
  ## $enemies
  ## [1] "Dick" "Mike"

• [ subsets one list to create another list, [[ extracts a list element

  frenemies[1]

  ## $friends
  ## [1] "Larry" "Richard" "Vivian"

  frenemies[c("enemies", "friends")]

  ## $enemies
  ## [1] "Dick" "Mike"
  ## 
  ## $friends
  ## [1] "Larry" "Richard" "Vivian"

  frenemies[["enemies"]]

  ## [1] "Dick" "Mike"

Factors

• Character-like vectors, but with values restricted to specific levels

  sex = factor(c("Male", "Male", "Female"),
   levels=c("Female", "Male", "Hermaphrodite"))
  sex

  ## [1] Male Male Female
  ## Levels: Female Male Hermaphrodite

  sex == "Female"

  ## [1] FALSE FALSE TRUE

  table(sex)

  ## sex
  ## Female Male Hermaphrodite 
  ## 1 2 0

  sex[sex == "Female"]

  ## [1] Female
  ## Levels: Female Male Hermaphrodite

2.2 Classes: data.frame and beyond

Variables are often related to one another in a highly structured way, e.g., two ‘columns’ of data in a spreadsheet

x = rnorm(1000) # 1000 random normal deviates
y = x + rnorm(1000) # another 1000 deviates, as a function of x
plot(y ~ x) # relationship bewteen x and y

Convenient to manipulate them together

• data.frame(): like columns in a spreadsheet

  df = data.frame(X=x, Y=y)
  head(df) # first 6 rows

  ## X Y
  ## 1 0.03638925 0.5489812
  ## 2 -0.41545524 0.1326022
  ## 3 -0.07465566 -0.5745222
  ## 4 -0.54492524 1.0485564
  ## 5 1.09338400 -0.4200256
  ## 6 0.95695268 1.6142163

  plot(Y ~ X, df) # same as above

• See all data with View(df). Summarize data with summary(df)

  summary(df)

  ## X Y 
  ## Min. :-3.907163 Min. :-4.897088 
  ## 1st Qu.:-0.671598 1st Qu.:-0.969528 
  ## Median : 0.005968 Median : 0.078811 
  ## Mean : 0.014603 Mean : 0.002155 
  ## 3rd Qu.: 0.700852 3rd Qu.: 0.991753 
  ## Max. : 3.133759 Max. : 3.973073

• Easy to manipulate data in a coordinated way, e.g., access column X with $ and subset for just those values greater than 0

  positiveX = df[df$X > 0,]
  head(positiveX)

  ## X Y
  ## 1 0.03638925 0.5489812
  ## 5 1.09338400 -0.4200256
  ## 6 0.95695268 1.6142163
  ## 7 1.97637428 0.9102277
  ## 9 2.26707137 1.0087697
  ## 10 1.26675817 1.5059712

  plot(Y ~ X, positiveX)

• R is introspective – ask it about itself

  class(df)

  ## [1] "data.frame"

  dim(df)

  ## [1] 1000 2

  colnames(df)

  ## [1] "X" "Y"

• matrix() a related class, where all elements have the same type (a data.frame() requires elements within a column to be the same type, but elements between columns can be different types).

A scatterplot makes one want to fit a linear model (do a regression analysis)

• Use a formula to describe the relationship between variables

• Variables found in the second argument

  fit <- lm(Y ~ X, df)

• Visualize the points, and add the regression line

  plot(Y ~ X, df)
  abline(fit, col="red", lwd=3)

• Summarize the fit as an ANOVA table

  anova(fit)

  ## Analysis of Variance Table
  ## 
  ## Response: Y
  ## Df Sum Sq Mean Sq F value Pr(>F) 
  ## X 1 1063.5 1063.55 1058 < 2.2e-16 ***
  ## Residuals 998 1003.2 1.01 
  ## ---
  ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

• N.B. – ‘Type I’ sums-of-squares, so order of independent variables matters; use drop1() for ‘Type III’. See DataCamp Quick-R

• Introspection – what class is fit? What methods can I apply to an object of that class?

  class(fit)

  ## [1] "lm"

  methods(class=class(fit))

  ## [1] add1 alias anova case.names coerce confint 
  ## [7] cooks.distance deviance dfbeta dfbetas drop1 dummy.coef 
  ## [13] effects extractAIC family formula hatvalues influence 
  ## [19] initialize kappa labels logLik model.frame model.matrix 
  ## [25] nobs plot predict print proj qr 
  ## [31] residuals rstandard rstudent show simulate slotsFromS3 
  ## [37] summary variable.names vcov 
  ## see '?methods' for accessing help and source code

2.3 Help!

Help available in Rstudio or interactively

• Check out the help page for rnorm()

  ?rnorm

• ‘Usage’ section describes how the function can be used

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

• Arguments, some with default values. Arguments matched first by name, then position

• ‘Arguments’ section describes what the arguments are supposed to be

• ‘Value’ section describes return value

• ‘Examples’ section illustrates use

• Often include citations to relevant technical documentation, reference to related functions, obscure details

• Can be intimidating, but in the end actually very useful