Simulate a latent class model

Draws a latent class for each observation from proportions, then draws every indicator independently from that class's category probabilities (the usual local-independence assumption of latent class analysis).

Usage

simulate_lca(
  n,
  probabilities,
  proportions = NULL,
  class_labels = NULL,
  category_labels = NULL,
  seed = NULL,
  batch = NULL
)

Arguments

n

Number of observations. A single whole number of at least 2.

probabilities

Item probabilities as an array with dimensions class, indicator and category, or as a tidy data frame with columns class, indicator, category and probability. Category probabilities must sum to one within each class and indicator. The dimnames (the class, indicator and category values of a tidy table) name the classes, the indicator columns and the categories.

proportions

Latent-class proportions, one positive value per class; they are rescaled to sum to one. NULL (the default) makes every class equally likely.

class_labels, category_labels

Optional labels, one unique value per class and per category, overriding the names given in probabilities. Without names there, class_labels defaults to "Class 1", "Class 2" and so on, and category_labels to the integers 1:categories. The category labels are the values written into the indicator columns.

seed

Optional random seed.

batch

Optional single positive whole number. When given, the simulator runs batch times and returns a plain list of batch results, each exactly what the same call without batch returns. With a seed, every dataset gets its own seed drawn from seed, so the whole batch is reproducible; without one the datasets are consecutive draws from the session's random-number stream. The default NULL returns a single result.

Value

A simulab_sim base data.frame with one row per observation and columns id, latent_class (the true class label) and one column per indicator holding the sampled value of category_labels. A parameters component holds one row per class-by-indicator-by-category combination with columns latent_class, indicator, category, probability and proportion.

Examples

# `probabilities` is a class x indicator x category array. Values fill the
# class dimension fastest, so each pair below is one category across the two
# classes: P(indicator = 1) then P(indicator = 2).
probabilities <- array(
  c(0.8, 0.2,   0.7, 0.3,     # category 1, for each class and indicator
    0.2, 0.8,   0.3, 0.7),    # category 2, for each class and indicator
  dim = c(2, 2, 2),
  dimnames = list(
    class = c("Class 1", "Class 2"),
    indicator = c("item_1", "item_2"),
    category = c("no", "yes")
  )
)

# Only the `indicator` dimnames name the output columns, so the class and
# category labels are passed explicitly.
result <- simulate_lca(
  n = 200,
  probabilities = probabilities,
  proportions = c(0.6, 0.4),
  category_labels = c("no", "yes"),
  seed = 1
)
head(result)
#> <simulab_sim:lca> 6 rows x 4 columns
#>   id latent_class item_1 item_2
#> 1  1      Class 1     no     no
#> 2  2      Class 1     no     no
#> 3  3      Class 1     no    yes
#> 4  4      Class 2    yes     no
#> 5  5      Class 1     no    yes
#> 6  6      Class 2    yes     no
#> 
#> Truth (parameters):
#>   latent_class indicator category probability proportion
#> 1      Class 1    item_1       no         0.8        0.6
#> 2      Class 2    item_1       no         0.2        0.4
#> 3      Class 1    item_2       no         0.7        0.6
#> 4      Class 2    item_2       no         0.3        0.4
#> 5      Class 1    item_1      yes         0.2        0.6
#> 6      Class 2    item_1      yes         0.8        0.4
#> 7      Class 1    item_2      yes         0.3        0.6
#> 8      Class 2    item_2      yes         0.7        0.4
as.data.frame(result, what = "parameters")
#>   latent_class indicator category probability proportion
#> 1      Class 1    item_1       no         0.8        0.6
#> 2      Class 2    item_1       no         0.2        0.4
#> 3      Class 1    item_2       no         0.7        0.6
#> 4      Class 2    item_2       no         0.3        0.4
#> 5      Class 1    item_1      yes         0.2        0.6
#> 6      Class 2    item_1      yes         0.8        0.4
#> 7      Class 1    item_2      yes         0.3        0.6
#> 8      Class 2    item_2      yes         0.7        0.4