Compute Required Monte Carlo Replications

Uses the Burton (2003) formula to determine the minimum number of simulation replications needed to achieve a desired level of Monte Carlo precision.

Usage

irt_iterations(sigma, delta, alpha = 0.05)

Arguments

sigma

Positive numeric. The empirical standard error of the estimand across replications (or a pilot estimate thereof).

delta

Positive numeric. The acceptable Monte Carlo error (half-width of the MC confidence interval for the estimand).

alpha

Numeric in (0, 1). Two-sided significance level. Default 0.05 (i.e., 95 percent MC confidence).

Value

An integer: the minimum number of replications.

Details

The formula is: $$R = \lceil (z_{\alpha/2} \cdot \sigma / \delta)^2 \rceil$$

where \(\sigma\) is the empirical standard error of the estimand, \(\delta\) is the acceptable Monte Carlo error, and \(z_{\alpha/2}\) is the critical value for the desired confidence level.

References

Burton, A., Altman, D. G., Royston, P., & Holder, R. L. (2006). The design of simulation studies in medical statistics. Statistics in Medicine, 25(24), 4279–4292. doi:10.1002/sim.2673

See also

irt_simulate() for running the simulation with the computed number of replications.

Examples

# How many replications for MC SE of bias < 0.1
# when empirical SE of the estimand is 0.5?
irt_iterations(sigma = 0.5, delta = 0.1)
#> [1] 97

# Tighter tolerance with 99% MC confidence
irt_iterations(sigma = 0.5, delta = 0.05, alpha = 0.01)
#> [1] 664