Performance

What It Is

MCPower uses a native C++ backend for all computation. The C++ extension is built automatically during installation via scikit-build-core and CMake, and is required for MCPower to run. There is no pure-Python fallback.

The backend handles OLS regression (QR decomposition), data generation (Cholesky decomposition for correlations, probability integral transforms for distributions), all three mixed-model solvers (Brent’s method for random intercepts, L-BFGS-B for random slopes and nested models), and statistical distribution functions (via Boost.Math). For mixed models, the C++ solver provides roughly a 200x speedup over equivalent Python implementations, making large-scale simulations practical.

Parallelization is available through joblib. By default, MCPower parallelizes only mixed-model analyses (where the per-simulation cost justifies the overhead). Standard OLS models run sequentially because the C++ backend is already fast enough that parallelization overhead outweighs the benefit at default simulation counts.

How It Works in MCPower

Configure simulation count with set_simulations():

model.set_simulations(5000)  # higher precision
model.set_simulations(800, model_type="mixed")  # mixed models only

Configure parallelization with set_parallel():

model.set_parallel(True)            # parallel for all analyses
model.set_parallel(False)           # single core
model.set_parallel("mixedmodels")   # default: parallel only for mixed models

Guidelines

Simulation Count vs. Precision

Simulations

Precision (95% CI)

Use Case

500

+/- 3–4%

Quick exploration, model iteration

1,600 (OLS default)

+/- 1–2%

Standard analysis

800 (mixed default)

+/- 2–3%

Standard mixed-model analysis

5,000

+/- 0.5–1%

Precise estimates

10,000

+/- 0.3–0.5%

Publication-quality precision

The precision follows from the binomial standard error of the power estimate: SE = sqrt(p(1-p)/n_sims). At p = 0.80 and n_sims = 1600, SE is approximately 1%.

C++ Backend Components

Component

Library

Purpose

Linear algebra

Eigen3

QR decomposition, Cholesky, matrix operations

Distributions

Boost.Math

F, t, chi-squared, normal CDFs and PPFs

Studentized range

R port

Tukey HSD critical values (Legendre quadrature)

Optimization

LBFGSPP

L-BFGS-B for random slopes and nested LME

1D optimization

Brent’s method

Random intercept LME (profiled deviance)

RNG

std::mt19937

Data generation

Parallelization Modes

Mode

Value

When It Helps

Mixed only (default)

"mixedmodels"

Best default. Mixed models benefit; OLS stays fast single-core.

Always on

True

Useful for OLS with 5,000+ simulations.

Off

False

Debugging, reproducibility, or when overhead exceeds benefit.

Default core count: cpu_count // 2. Override with set_parallel(True, n_cores=4).

Approximate Runtimes

Model Type

Simulations

Approximate Time

OLS

1,600

1–3 seconds

OLS

10,000

5–15 seconds

Mixed (random intercept)

800

2–10 seconds

Mixed (random slopes)

800

5–30 seconds

Mixed (nested)

800

5–30 seconds

(Times depend on sample size, number of predictors, and hardware.)

Common Patterns

Tips

  • Start with defaults. Increase simulations only for final estimates.

  • Parallel for mixed models is automatic. The default "mixedmodels" mode is optimal for most users.

  • More clusters > larger clusters. Better power and faster convergence per simulation.

  • Disable progress for batch runs: find_power(..., progress_callback=False, print_results=False).

  • Scenario analysis triples runtime. Three full simulation runs (Optimistic, Realistic, Doomer).

Learn More