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

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, link = "identity", quantile_y = NULL) 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", quantile_y = NULL) draw_quantile(type = NULL, N = NULL)

## 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 postiive 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) |

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 15.169750 1 #> 2 2 9.526467 1 #> 3 3 -5.088359 0# 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 4 #> 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 -4.470176 1 #> 2 2 3.509748 3 #> 3 3 -1.477712 1# 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 1.755604 Very concerned #> 2 2 5.182757 Very concerned #> 3 3 1.420082 Very 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 Agree #> 3 03 Strongly Agree #> 4 04 Agree #> 5 05 Agree #> 6 06 Strongly Disagree #> 7 07 Strongly Agree #> 8 08 Disagree #> 9 09 Agree #> 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 9 #> 3 3 25 25 #> 4 4 50 51 #> 5 5 100 102# 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 0.1604869 0.5617880 0.03923126 2 #> 2 2 0.2274149 0.6039721 0.62940734 3 #> 3 3 0.4889994 0.1923918 0.52326970 3 #> 4 4 0.2662559 0.3716696 0.39310540 1 #> 5 5 0.9868869 0.1200995 0.87789330 3 #> 6 6 0.6590275 0.3957093 0.28824992 2