Mixed Design Simulation

library(faux)
library(dplyr)
library(tidyr)
library(broom.mixed)
library(lme4)

sim_mixed_cc

This function produces a data table for a basic cross-classified design with random intercepts for subjects and items.

For example, the following code produces the data for 100 subjects responding to 50 items where the response has an overall mean (grand_i) of 10. Subjects vary in their average response with an SD of 1, items vary in their average response with an SD of 2, and the residual error term has an SD of 3.

dat_cc <- sim_mixed_cc(
  sub_n = 100,   # subject sample size
  item_n = 50,  # item sample size
  grand_i = 10,  # overall mean of the score
  sub_sd = 1,   # SD of subject random intercepts
  item_sd = 2,  # SD of item random intercepts
  error_sd = 3  # SD of residual error
)

You can then see how changing these numbers affects the random effects in an intercept-only mixed effects model.

lme4::lmer(y ~ 1 + (1 | sub_id) + (1 | item_id), data = dat_cc) %>%
  broom.mixed::tidy() %>%
  knitr::kable(digits = 3)

effect	group	term	estimate	std.error	statistic
fixed	NA	(Intercept)	9.867	0.312	31.633
ran_pars	sub_id	sd__(Intercept)	1.157	NA	NA
ran_pars	item_id	sd__(Intercept)	2.026	NA	NA
ran_pars	Residual	sd__Observation	3.010	NA	NA

For example, changing grand_i to 0 changes the estimate for the fixed effect of the intercept (Intercept). Changing sub_sd to 1.5 and item_sd to 3 change the estimate for the SD of their corresponding random effects. Changing error_sd to 10 changes the estimate from the Residual SD.

dat_cc <- sim_mixed_cc(100, 50, 0, 1.5, 3, 10)

lme4::lmer(y ~ 1 + (1 | sub_id) + (1 | item_id), data = dat_cc) %>%
  broom.mixed::tidy() %>%
  knitr::kable(digits = 3)

effect	group	term	estimate	std.error	statistic
fixed	NA	(Intercept)	0.084	0.544	0.154
ran_pars	sub_id	sd__(Intercept)	1.223	NA	NA
ran_pars	item_id	sd__(Intercept)	3.611	NA	NA
ran_pars	Residual	sd__Observation	10.010	NA	NA

sim_mixed_df

This function uses lme4::lmer() to get subject, item and error SDs from an existing dataset and simulates a new dataset with the specified number of subjects and items with distributions drawn from the example data.

This example uses the fr4 dataset from this package to simulate 100 new subjects viewing 50 new faces.

new_dat <- sim_mixed_df(fr4, 
                        sub_n = 100, 
                        item_n = 50, 
                        dv = "rating", 
                        sub_id = "rater_id", 
                        item_id = "face_id")