Vector Recycling, Lists, and Factors

Vector recycling is one of R's most distinctive features. When two vectors of different lengths are combined in an operation, R automatically repeats (recycles) the shorter vector until it matches the length of the longer one. This is extremely useful when adding a scalar to a vector or when working with data that has a natural period — for example, subtracting group means from observations. When the longer length is not a multiple of the shorter length, R issues a warning but still performs the operation. Lists in R are a generalisation of atomic vectors that can hold elements of different types, including other lists. You create a list with the list() function and access elements with double-bracket indexing ([[) by position or by name, or with the dollar-sign shorthand for named elements. Single-bracket indexing on a list returns a sub-list, not the element itself — a subtle distinction that is a common source of confusion for newcomers. Factors represent categorical data and are stored internally as integers with an associated levels attribute that holds the unique category labels. They are important for statistical modelling (as contrast-coded predictors) and for ordered comparisons. You create a factor with factor() and an ordered factor with ordered(). The table() function is particularly useful for summarising factor distributions.

Example

# Vector recycling
x <- 1:6
y <- c(10, 100)            # length 2 recycled to match length 6
x + y                      # 11 102 13 104 15 106

# Recycling with a scalar (length 1 recycles perfectly)
x * 2                      # 2 4 6 8 10 12
x - mean(x)                # centre the vector

# Warning when lengths are not multiples
# c(1,2,3,4,5) + c(1,2)   # warns: longer not multiple of shorter

# Lists: heterogeneous containers
person <- list(
    name   = "Diana",
    age    = 28,
    scores = c(90, 85, 92),
    active = TRUE
)

person[["name"]]    # "Diana"    — double bracket returns the element
person$age          # 28         — dollar-sign shorthand
person["scores"]    # a list containing the scores vector (single bracket)
person[["scores"]]  # the numeric vector itself

# Modifying list elements
person$city <- "Paris"
person[["age"]] <- 29

# Nested lists
nested <- list(a = list(b = list(c = 42)))
nested$a$b$c        # 42

# Factors
status <- factor(c("low", "med", "high", "med", "low"))
levels(status)      # "high" "low" "med"  (alphabetical by default)
nlevels(status)     # 3
table(status)       # frequency count

# Ordered factor
size <- ordered(c("S", "M", "L", "XL", "M"),
                levels = c("S", "M", "L", "XL"))
size[1] < size[3]   # TRUE  (S < L)

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