Draw discrete variables including binary, binomial count, poisson count, ordered, and categorical

Source: R/variable_creation_functions.R

Drawing discrete data based on probabilities or latent traits is a common task that can be cumbersome. Each function in our discrete drawing set creates a different type of discrete data: draw_binary creates binary 0/1 data, draw_binomial creates binomial data (repeated trial binary data), draw_categorical creates categorical data, draw_ordered transforms latent data into observed ordered categories, draw_count creates count data (poisson-distributed). draw_likert is an alias to draw_ordered that pre-specifies break labels and offers default breaks appropriate for a likert survey question.

draw_binomial(
  prob = link(latent),
  trials = 1,
  N = length(prob),
  latent = NULL,
  link = "identity",
  quantile_y = NULL
)

draw_categorical(
  prob = link(latent),
  N = NULL,
  latent = NULL,
  link = "identity",
  category_labels = NULL
)

draw_ordered(
  x = link(latent),
  breaks = c(-1, 0, 1),
  break_labels = NULL,
  N = length(x),
  latent = NULL,
  strict = FALSE,
  link = "identity"
)

draw_count(
  mean = link(latent),
  N = length(mean),
  latent = NULL,
  link = "identity",
  quantile_y = NULL
)

draw_binary(
  prob = link(latent),
  N = length(prob),
  link = "identity",
  latent = NULL,
  quantile_y = NULL
)

draw_likert(
  x,
  type = 7,
  breaks = NULL,
  N = length(x),
  latent = NULL,
  link = "identity",
  strict = !is.null(breaks)
)

draw_quantile(type, N)

Arguments

prob

A number or vector of numbers representing the probability for binary or binomial outcomes; or a number, vector, or matrix of numbers representing probabilities for categorical outcomes. If you supply a link function, these underlying probabilities will be transformed.
trials

for draw_binomial, the number of trials for each observation
N

number of units to draw. Defaults to the length of the vector of probabilities or latent data you provided.
latent

If the user provides a link argument other than identity, they should provide the variable latent rather than prob or mean
link

link function between the latent variable and the probability of a positive outcome, e.g. "logit", "probit", or "identity". For the "identity" link, the latent variable must be a probability.
quantile_y

A vector of quantiles; if provided, rather than drawing stochastically from the distribution of interest, data will be drawn at exactly those quantiles.
category_labels

vector of labels for the categories produced by draw_categorical. If provided, must be equal to the number of categories provided in the prob argument.
x

for draw_ordered or draw_likert, the latent data for each observation.
breaks

vector of breaks to cut a latent outcome into ordered categories with draw_ordered or draw_likert
break_labels

vector of labels for the breaks to cut a latent outcome into ordered categories with draw_ordered. (Optional)
strict

Logical indicating whether values outside the provided breaks should be coded as NA. Defaults to FALSE, in which case effectively additional breaks are added between -Inf and the lowest break and between the highest break and Inf.
mean

for draw_count, the mean number of count units for each observation
type

Type of Likert scale data for draw_likert. Valid options are 4, 5, and 7. Type corresponds to the number of categories in the Likert scale.

Value

A vector of data in accordance with the specification; generally numeric but for some functions, including draw_ordered, may be factor if break labels are provided.

Details

For variables with intra-cluster correlations, see draw_binary_icc and draw_normal_icc

Examples


# Drawing binary values (success or failure, treatment assignment)
fabricate(N = 3,
   p = c(0, .5, 1),
   binary = draw_binary(prob = p))

#>   ID   p binary
#> 1  1 0.0      0
#> 2  2 0.5      0
#> 3  3 1.0      1

# Drawing binary values with probit link (transforming continuous data
# into a probability range).
fabricate(N = 3,
   x = 10 * rnorm(N),
   binary = draw_binary(latent = x, link = "probit"))

#>   ID          x binary
#> 1  1 12.1515166      1
#> 2  2  0.4221889      0
#> 3  3  3.9740704      1

# Repeated trials: `draw_binomial`
fabricate(N = 3,
   p = c(0, .5, 1),
   binomial = draw_binomial(prob = p, trials = 10))

#>   ID   p binomial
#> 1  1 0.0        0
#> 2  2 0.5        6
#> 3  3 1.0       10

# Ordered data: transforming latent data into observed, ordinal data.
# useful for survey responses.
fabricate(N = 3,
   x = 5 * rnorm(N),
   ordered = draw_ordered(x = x,
                          breaks = c(-Inf, -1, 1, Inf)))

#>   ID          x ordered
#> 1  1 -0.7245082       2
#> 2  2 -1.6222348       1
#> 3  3 -0.8628245       2

# Providing break labels for latent data.
fabricate(N = 3,
   x = 5 * rnorm(N),
   ordered = draw_ordered(x = x,
                          breaks = c(-Inf, -1, 1, Inf),
                          break_labels = c("Not at all concerned",
                                           "Somewhat concerned",
                                           "Very concerned")))

#>   ID          x              ordered
#> 1  1 -6.1803146 Not at all concerned
#> 2  2 -9.5115210 Not at all concerned
#> 3  3 -0.4725201   Somewhat concerned

# Likert data: often used for survey data
fabricate(N = 10,
          support_free_college = draw_likert(x = rnorm(N),
                                             type = 5))

#>    ID support_free_college
#> 1  01 Don't Know / Neutral
#> 2  02 Don't Know / Neutral
#> 3  03                Agree
#> 4  04 Don't Know / Neutral
#> 5  05                Agree
#> 6  06 Don't Know / Neutral
#> 7  07             Disagree
#> 8  08             Disagree
#> 9  09             Disagree
#> 10 10 Don't Know / Neutral

# Count data: useful for rates of occurrences over time.
fabricate(N = 5,
   x = c(0, 5, 25, 50, 100),
   theft_rate = draw_count(mean=x))

#>   ID   x theft_rate
#> 1  1   0          0
#> 2  2   5          5
#> 3  3  25         26
#> 4  4  50         51
#> 5  5 100         88

# Categorical data: useful for demographic data.
fabricate(N = 6, p1 = runif(N), p2 = runif(N), p3 = runif(N),
          cat = draw_categorical(cbind(p1, p2, p3)))

#>   ID         p1         p2        p3 cat
#> 1  1 0.09022236 0.22092086 0.1625581   2
#> 2  2 0.23832468 0.06540764 0.5351122   2
#> 3  3 0.25913474 0.64489713 0.5850109   1
#> 4  4 0.02566954 0.31255200 0.3186254   2
#> 5  5 0.17555081 0.63886730 0.4680848   3
#> 6  6 0.61982165 0.97387534 0.6392598   1