draw_normal_icc: Draw normal data with fixed intra-cluster correlation.

In fabricatr: Imagine Your Data Before You Collect It

Draw normal data with fixed intra-cluster correlation.

Description

Data is generated to ensure inter-cluster correlation 0, intra-cluster correlation in expectation ICC. The data generating process used in this function is specified at the following URL: https://stats.stackexchange.com/questions/263451/create-synthetic-data-with-a-given-intraclass-correlation-coefficient-icc

Usage

draw_normal_icc(
  mean = 0,
  N = NULL,
  clusters,
  sd = NULL,
  sd_between = NULL,
  total_sd = NULL,
  ICC = NULL
)

Arguments

mean	A number or vector of numbers, one mean per cluster. If none is provided, will default to 0.
N	(Optional) A number indicating the number of observations to be generated. Must be equal to length(clusters) if provided.
clusters	A vector of factors or items that can be coerced to clusters; the length will determine the length of the generated data.
sd	A number or vector of numbers, indicating the standard deviation of each cluster's error terms – standard deviation within a cluster (default 1)
sd_between	A number or vector of numbers, indicating the standard deviation between clusters.
total_sd	A number indicating the total sd of the resulting variable. May only be specified if ICC is specified and sd and sd_between are not.
ICC	A number indicating the desired ICC.

Details

The typical use for this function is for a user to provide an ICC and, optionally, a set of within-cluster standard deviations, sd. If the user does not provide sd, the default value is 1. These arguments imply a fixed between-cluster standard deviation.

An alternate mode for the function is to provide between-cluster standard deviations, sd_between, and an ICC. These arguments imply a fixed within-cluster standard deviation.

If users provide all three of ICC, sd_between, and sd, the function will warn the user and use the provided standard deviations for generating the data.

Value

A vector of numbers corresponding to the observations from the supplied cluster IDs.

Examples

# Divide observations into clusters
clusters = rep(1:5, 10)

# Default: unit variance within each cluster
draw_normal_icc(clusters = clusters, ICC = 0.5)

# Alternatively, you can specify characteristics:
draw_normal_icc(mean = 10, clusters = clusters, sd = 3, ICC = 0.3)

# Can specify between-cluster standard deviation instead:
draw_normal_icc(clusters = clusters, sd_between = 4, ICC = 0.2)

# Can specify total SD instead:
total_sd_draw = draw_normal_icc(clusters = clusters, ICC = 0.5, total_sd = 3)
sd(total_sd_draw)

# Verify that ICC generated is accurate
corr_draw = draw_normal_icc(clusters = clusters, ICC = 0.4)
summary(lm(corr_draw ~ as.factor(clusters)))$r.squared

fabricatr documentation built on May 29, 2024, 7:22 a.m.