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Simulate Meta-Analytic Data from a Mixture Model with Publication Bias

Source: R/sim_mix.R
sim_mix.Rd

Simulates K published studies from the random-effects mixture model of re_mix() combined with the step-function selection model of sel_mix(). Studies are generated until K of them have passed the selection step, so the returned data set has exactly K rows.

Usage

sim_mix(
  K,
  M,
  mu,
  tau,
  steps,
  weights,
  one_sided,
  thetas = c(rep(1/M, M)),
  N_low = 25,
  N_high = 500,
  N_shape = 2,
  N_scale = 58
)

Arguments

K

number of (published) studies to return.

M

number of mixture components.

mu

numeric vector of length M: the mean true effect of each component.

tau

numeric vector of length M: the between-study standard deviation of the true effects within each component.

steps

cutoffs of the p-value intervals, in the same format as in sel_mix() (cumulative probabilities of the standard normal distribution; e.g. c(0.95, 0.975) for one-sided p-values of .05 and .025, i.e. two-sided .10 and .05 in the expected direction). Strictly increasing values in (0, 1).

weights

publication probabilities of the p-value intervals, a vector of length length(steps) + 1 with values in [0, 1]. The first element applies to the least significant interval, e.g. c(0.2, 0.5, 1).

one_sided

if TRUE selection depends on the one-sided p-value (z-statistic y/sd), if FALSE on the two-sided p-value (abs(y/sd)).

thetas

mixing weights of the components; defaults to equal weights.

N_low

lower bound on the total sample size of a primary study.

N_high

upper bound on the total sample size of a primary study.

N_shape

shape (size) of the negative binomial distribution used to generate sample sizes (see Maier et al., 2023).

N_scale

scale of the negative binomial distribution used to generate sample sizes; the success probability is 1 / (N_scale + 1) (see Maier et al., 2023).

Value

A data frame with K rows and the columns y (observed effect size) and sds (its standard error), ready to be passed to re_mix(), sel_mix() or sel_flexpb().

Details

See Maier (2026) for details of the model and the simulation design.

References

Maier, M. (2026). Addressing heterogeneity with Bayesian meta-analytic mixture modelling. PsyArXiv. doi:10.31234/osf.io/nkyqm_v2

Maier, M., Bartoš, F., & Wagenmakers, E.-J. (2023). Robust Bayesian meta-analysis: Addressing publication bias with model-averaging. Psychological Methods, 28(1), 107–122. doi:10.1037/met0000405

See also

re_mix(), sel_mix(), sel_flexpb()

Examples

set.seed(1)
# Two components (null effect and medium effect) without publication bias
dat <- sim_mix(K = 100, M = 2, mu = c(0, 0.5), tau = c(0.05, 0.1),
               steps = c(0.95, 0.975), weights = c(1, 1, 1), one_sided = TRUE)
head(dat)
#>              y       sds
#> 1  0.675906247 0.1638830
#> 2  0.083588527 0.1376880
#> 3  0.286695480 0.1898316
#> 4 -0.095939063 0.1288578
#> 5  0.675788329 0.1910095
#> 6  0.009781839 0.1898770

# Strong one-sided selection: studies that are not significant in the
# expected direction are published with probability .1 only
dat_pb <- sim_mix(K = 100, M = 1, mu = 0, tau = 0.1, steps = c(0.95, 0.975),
                  weights = c(0.1, 0.5, 1), one_sided = TRUE)
mean(dat_pb$y / dat_pb$sds > qnorm(0.975))
#> [1] 0.27