simulate_smd {pema}

Simulates a meta-analytic dataset

Description

This function simulates a meta-analytic dataset based on the random-effects model. The simulated effect size is Hedges' G, an estimator of the Standardized Mean Difference (Hedges, 1981; Li, Dusseldorp, & Meulman, 2017). The functional form of the model can be specified, and moderators can be either normally distributed or Bernoulli-distributed. See Van Lissa, in preparation, for a detailed explanation of the simulation procedure.

Usage

simulate_smd(
  k_train = 20,
  k_test = 100,
  mean_n = 40,
  es = 0.5,
  tau2 = 0.04,
  alpha = 0,
  moderators = 5,
  distribution = "normal",
  model = "es * x[, 1]"
)

Arguments

k_train

Atomic integer. The number of studies in the training dataset. Defaults to 20.

k_test

Atomic integer. The number of studies in the testing dataset. Defaults to 100.

mean_n

Atomic integer. The mean sample size of each simulated study in the meta-analytic dataset. Defaults to 40. For each simulated study, the sample size n is randomly drawn from a normal distribution with mean mean_n, and sd mean_n/3.

es

Atomic numeric vector. The effect size, also known as beta, used in the model statement. Defaults to .5.

tau2

Atomic numeric vector. The residual heterogeneity. For a range of realistic values encountered in psychological research, see Van Erp, Verhagen, Grasman, & Wagenmakers, 2017. Defaults to 0.04.

alpha

Vector of slant parameters, passed to sn::rsn.

moderators

Atomic integer. The number of moderators to simulate for each study. Make sure that the number of moderators to be simulated is at least as large as the number of moderators referred to in the model parameter. Internally, the matrix of moderators is referred to as "x". Defaults to 5.

distribution

Atomic character. The distribution of the moderators. Can be set to either "normal" or "bernoulli". Defaults to "normal".

model

Expression. An expression to specify the model from which to simulate the mean true effect size, mu. This formula may use the terms "es" (referring to the es parameter of the call to simulate_smd), and ⁠"x\[, \]"⁠ (referring to the matrix of moderators, x). Thus, to specify that the mean effect size, mu, is a function of the effect size and the first moderator, one would pass the value model = "es * x\[ , 1\]". Defaults to ⁠"es * x\[ , 1\]"⁠.

Value

List of length 4. The "training" element of this list is a data.frame with k_train rows. The columns are the variance of the effect size, vi; the effect size, yi, and the moderators, X. The "testing" element of this list is a data.frame with k_test rows. The columns are the effect size, yi, and the moderators, X. The "housekeeping" element of this list is a data.frame with k_train + k_test rows. The columns are n, the sample size n for each simulated study; mu_i, the mean true effect size for each simulated study; and theta_i, the true effect size for each simulated study.

Examples

set.seed(8)
simulate_smd()
simulate_smd(k_train = 50, distribution = "bernoulli")
simulate_smd(distribution = "bernoulli", model = "es * x[ ,1] * x[ ,2]")