simulate_stroop: Simulate Stroop Factorial Data
In dalejbarr/autocorr: Autocorrelation toolkit for multilevel data

Description Usage Arguments Details Value Examples

Simulate data from a mixed factorial design based on the Many Labs 3 (ML3) \insertCiteML3autocorr Stroop data.

simulate_stroop(
  n_subj,
  B1 = 0,
  B2 = 0,
  rivar = diag(autocorr::stroop_mod$covmx)[1],
  rsvar = diag(autocorr::stroop_mod$covmx)[2],
  verbose = FALSE
)

`n_subj`	Number of subjects.
`B1`	Fixed effect of congruency.
`B2`	Fixed effect of the between-subjects factor.
`rivar`	Random intercept variance.
`rsvar`	Random slope variance.
`verbose`	Whether to return error components (random effects and residuals).

The ML3 data was from a simple design including only the within-factor of congruency. The simulated data includes an additional between-subjects factor. The simulation parameters are taken from stroop_mod, with a random subset of residuals grafted onto the fitted values for each subject.

The simulated response latency for observation j of subject i is given by the following formula:

latency_ij = B0 + b_0i + B2 * B_i + (B1 + b_1i) * W_ij + e_ij

where B0 is stroop_mod$fixed["(Intercept)"], b_0i and b_1i are the random intercept and random slope for subject i, W_ij and B_i are deviation-coded predictors for the within- and between- subject factors respectively, B1 and B2 are the raw within- and between- subject effect sizes, and e_ij is the jth residual for subject i.

Note that whereas the original dataset had 63 observations per subject (with 2/3 in the incongruent condition and 1/3 in the congruent condition), the current dataset had 1/2 congruent and 1/2 incongruent. Also, only the first 20 of the 63 residuals were used, to eliminate discontinuities introduced at the start of each 21-trial block.

A data frame with n_subj * 20 simulated observations on 7 (or 10) variables, depending on verbose:

session_id: A factor with session_id values corresponding to the subjects whose residuals were sampled from stroop_mod[["resid"]]

trial: An integer specifying the trial number (1 to 20).
congruency: Level of within-subject factor (congruent or incongruent).
group: Level of between-subject factor (G1 or G2).
W_ij: Deviation-coded predictor for factor congruency.
B_i: Deviation-coded predictor for factor group.
Y_ij: Simulated response latency in milliseconds.
b_0i: Random effect for subject i (verbose mode only).
b_1i: Random slope for subject i (verbose mode only).
e_ij: Residual for subject i, observation j (verbose mode only).

## use parameters from Many Labs 3 model fit
dat <- simulate_stroop(48, A = stroop_mod$fixed["cong"])

mod <- lme4::lmer(Y_ij ~ W_ij + B_i + (W_ij || session_id), dat)
summary(mod)