Acknowledgements - MCPower

MCPower's engine is an independent, performance-tuned implementation written in Rust for simulation throughput. It does not wrap or embed existing statistics packages; instead it implements optimized code based on established statistical methods and the work of the projects below, and this page records what it builds on and credits the authors. Where MCPower reproduces the behaviour of another tool, it does so by following the published methods, and the original work is credited here.

Mixed-effects models

MCPower's linear and generalized linear mixed-model fitting follows the computational approach of R's lme4 (Bates, Mächler, Bolker & Walker) and Julia's MixedModels.jl (Douglas Bates and contributors). Both descend from the same line of work led by Douglas Bates, and MCPower's fitter follows the same recipe: the profiled REML/ML deviance, the Cholesky-factor (θ) "spherical" reparameterization of the random-effects covariance, sparse penalized least squares, and — for GLMMs — the PIRLS inner loop with a Laplace approximation at nAGQ = 1. The per-fit finite-difference Hessian standard errors reproduce lme4's use.hessian = TRUE default.

Those packages are themselves implementations of methods that predate them, and MCPower credits the methods directly. The fitter uses algorithms such as restricted maximum likelihood (REML — Patterson & Thompson, 1971) for the variance components, and BOBYQA (Powell, 2009), a bound-constrained derivative-free optimizer, to minimize the deviance — the same optimizer lme4 uses by default.

MCPower's mixed-model results are validated by refitting the same data with lme4 and comparing the numbers; see Validation for how that is done.

Open-source libraries

The native engine is built on the Rust numerical ecosystem — faer for dense and sparse linear algebra and rayon for data-parallel execution — and draws its simulation randomness from the Philox4x32-10 counter-based generator of the Random123 family (Salmon, Moraes, Dror & Shaw, 2011), which gives reproducible, independent streams across cores. The ports are bound to their host languages with PyO3 (Python), extendr (R), Tauri (desktop), and wasm-bindgen (browser).

References

  • Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015). Fitting Linear Mixed-Effects Models Using lme4. Journal of Statistical Software, 67(1), 1–48. https://doi.org/10.18637/jss.v067.i01
  • Bates, D., Alday, P., Kleinschmidt, D., et al. MixedModels.jl — mixed-effects models in Julia. JuliaStats. https://github.com/JuliaStats/MixedModels.jl
  • Patterson, H. D., & Thompson, R. (1971). Recovery of inter-block information when block sizes are unequal. Biometrika, 58(3), 545–554. https://doi.org/10.1093/biomet/58.3.545
  • Powell, M. J. D. (2009). The BOBYQA algorithm for bound constrained optimization without derivatives. Technical Report DAMTP 2009/NA06, Department of Applied Mathematics and Theoretical Physics, University of Cambridge.
  • Salmon, J. K., Moraes, M. A., Dror, R. O., & Shaw, D. E. (2011). Parallel random numbers: as easy as 1, 2, 3. Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC '11). https://doi.org/10.1145/2063384.2063405