Fake It Until You Make It

How and why to simulate research data

Lisa DeBruine

Abstract

debruine.github.io/talks/EMPSEB-fake-it-2023/

Being able to simulate data allows you to prep analysis scripts for pre-registration, calculate power and sensitivity for analyses that don’t have empirical methods, create reproducible examples when your data are too big or confidential to share, enhance your understanding of statistical concepts, and create demo data for teaching and tutorials. This workshop will cover the basics of simulation using the R package {faux}. We will simulate data with factorial designs by specifying the within and between-subjects factor structure, each cell mean and standard deviation, and correlations between cells where appropriate. This can be used to create simulated data sets to be used in preparing the analysis code for pre-registrations or registered reports. We will also create data sets for simulation-based power analyses.

Why Simulate Data?

Pre-Registration

Prep analysis scripts for pre-registration

Power

Calculate power and sensitivity for analyses that don’t have empirical methods

Reproducible Examples

Create reproducible examples when your data are too big or confidential to share

Enhance Understanding

Enhance your understanding of statistical concepts

Teaching Data

Create demo data for teaching and tutorials

Faux

Plot
Data
Code

Faux Code

sim_data <- faux::sim_design(
  within = list(version = c(V1 = "Version 1", V2 = "Version 2"), 
                condition = c(ctl = "Control", exp = "Experimental")),
  between = list(age_group = c(young = "Age 20-29", old = "Age 70-79")),
  n = 30,
  mu = c(100, 100, 100, 100, 100, 90, 110, 110),
  sd = 20,
  r = 0.5,
  dv = c(score = "Score"),
  id = c(id = "Subject ID"),
  vardesc = list(version = "Task Version", 
                 condition = "Experiment Condition", 
                 age_group = "Age Group"),
  long = TRUE
)

Faux Design Parameters

age_group	version	condition	V1_ctl	V1_exp	V2_ctl	V2_exp	n	mu	sd
young	V1	ctl	1.0	0.5	0.5	0.5	30	100	20
young	V1	exp	0.5	1.0	0.5	0.5	30	100	20
young	V2	ctl	0.5	0.5	1.0	0.5	30	100	20
young	V2	exp	0.5	0.5	0.5	1.0	30	100	20
old	V1	ctl	1.0	0.5	0.5	0.5	30	100	20
old	V1	exp	0.5	1.0	0.5	0.5	30	90	20
old	V2	ctl	0.5	0.5	1.0	0.5	30	110	20
old	V2	exp	0.5	0.5	0.5	1.0	30	110	20

Faux Design Plot

Faux Data Plot

Power Simulation: Replicate Data

sim_data <- faux::sim_design(
  within = list(version = c(V1 = "Version 1", V2 = "Version 2"), 
                condition = c(ctl = "Control", exp = "Experimental")),
  between = list(age_group = c(young = "Age 20-29", old = "Age 70-79")),
  n = 30,
  mu = c(100, 100, 100, 100, 100, 90, 110, 110),
  sd = 20,
  r = 0.5,
  dv = c(score = "Score"),
  id = c(id = "Subject ID"),
  vardesc = list(version = "Task Version", 
                 condition = "Experiment Condition", 
                 age_group = "Age Group"),
  long = TRUE,
  rep = 100
)

Power Simulation: Analysis Function

# setup options to avoid annoying afex message & run faster
afex::set_sum_contrasts()
afex::afex_options(include_aov = FALSE) 

analysis <- function(data) {
  a <- afex::aov_ez(
    id = "id", 
    dv = "score", 
    between = "age_group",
    within = c("version", "condition"),
    data = data)
  
  as_tibble(a$anova_table, rownames = "term") |>
    rename(p = `Pr(>F)`)
}

Power Simulation: Analysis Result

# test on first data set
analysis(sim_data$data[[1]])

term	num Df	den Df	MSE	F	ges	p
age_group	1	58	1,209.8	0.02	0.000	0.891
version	1	58	249.6	20.28	0.047	0.000
age_group:version	1	58	249.6	12.23	0.029	0.001
condition	1	58	174.7	5.69	0.009	0.020
age_group:condition	1	58	174.7	6.93	0.012	0.011
version:condition	1	58	154.8	0.97	0.001	0.328
age_group:version:condition	1	58	154.8	0.60	0.001	0.440

Power Simulation

power <- sim_data |>
  mutate(analysis = purrr::map(data, analysis)) |>
  select(-data) |>
  unnest(analysis) |>
  group_by(term) |>
  summarise(power = mean(p < .05))

term	power
age_group	0.11
age_group:condition	0.21
age_group:version	1.00
age_group:version:condition	0.25
condition	0.32
version	0.98
version:condition	0.32

Further Resources

Thank You!

debruine.github.io/talks/EMPSEB-fake-it-2023/

Workshop Materials: tinyurl.com/data-sim

Prerequisites: Students will need to have very basic knowledge of R and familiarity with R Markdown, and have installed R and RStudio on their laptop and installed the packages {faux}, {afex}, {broom} and {tidyverse} from CRAN.