What this report shows

MCPower generates a binary dataset from a formula, then fits it back to recover the coefficients. This report checks the fitting half: given one fixed dataset, does MCPower’s own solver return the same numbers a trusted, independent R fit returns?

For each formula we take the exact bytes MCPower saved (the same design matrix and 0/1 outcome, byte-for-byte), fit them two ways —

• R (the reference): stats::glm(family = binomial()) through the origin on the design matrix, the textbook maximum-likelihood logistic fit.
• MCPower: the engine’s own load_data() path, which runs the same iterative IRLS solver the power simulation uses.

— and compare the fitted coefficients, the test statistics, and the decision threshold. Because both fit the identical bytes, sampling noise cancels: any difference is a solver discrepancy, and the allowed differences are small.

How the check works

1. Provenance. Re-generate the dataset from the committed seed and confirm its content hash matches the saved file — proof the bytes haven’t drifted.
2. B (R) vs C (MCPower) on those bytes: coefficients, the Wald z statistics (β̂/se), and the critical value qnorm(1 − α/2) ≈ 1.96.
3. C vs A (a readable sanity overlay): MCPower’s recovered coefficients next to the formula’s true values (on the log-odds scale).

The thresholds

These are the B↔C gates from tolerances.R. GLM is an iterative IRLS fit, so its agreement with R is looser than OLS’s closed-form solution: it gets the estimate_rel_iter band (typically ~1e-6 to 1e-9 for well-converged IRLS), not the tight OLS estimate_rel_ols. The per-formula tables below show each formula’s actual margin.

All GLM formulas pass: MCPower’s IRLS solver matches R’s glm well inside the iterative band on every saved dataset, and every file reproduces from its seed.

png 2

Each point is one fitted quantity on one saved dataset; the red line is the gate. The iterative IRLS fit agrees with R’s glm comfortably inside the band on every quantity.

log-odds(y = 1) = logit(0.30) + 0.5·x1

R formula y ~ x1 · logistic regression (binary outcome) · n=600, seed=2137. File reproduces from seed: yes.

log-odds(y = 1) = logit(0.50) + 0.8·x1

R formula y ~ x1 · logistic regression (binary outcome) · n=600, seed=2138. File reproduces from seed: yes.

log-odds(y = 1) = logit(0.30) + 0.5·x1 + 0.3·x2

R formula y ~ x1 + x2 · logistic regression (binary outcome) · n=800, seed=2137. File reproduces from seed: yes.

log-odds(y = 1) = logit(0.50) + 0.8·x1 + 0.5·x2

R formula y ~ x1 + x2 · logistic regression (binary outcome) · n=800, seed=2138. File reproduces from seed: yes.

log-odds(y = 1) = logit(0.30) + 0.5·x1 + 0.4·g[2] + 0.8·g[3]

R formula y ~ x1 + g · logistic regression (binary outcome) · n=1000, seed=2137. File reproduces from seed: yes.

log-odds(y = 1) = logit(0.50) + 0.8·x1 + 0.5·g[2] + 0.8·g[3]

R formula y ~ x1 + g · logistic regression (binary outcome) · n=1000, seed=2138. File reproduces from seed: yes.

log-odds(y = 1) = logit(0.30) + 0.5·x1 + 0.3·x2 + 0.3·x1:x2

R formula y ~ x1*x2 · logistic regression (binary outcome) · n=1000, seed=2137. File reproduces from seed: yes.

log-odds(y = 1) = logit(0.50) + 0.8·x1 + 0.5·x2 + 0.4·x1:x2

R formula y ~ x1*x2 · logistic regression (binary outcome) · n=1000, seed=2138. File reproduces from seed: yes.

Reproduce: Rscript mcpower/validation/data_generation.r then rmarkdown::render("mcpower/validation/validation_GLM_solving.rmd", output_dir = "mcpower/web/documentation/validation").