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MultiLevelOptimalBayes 0.1.0.0

This release corrects the implementation of the regularized Bayesian estimator so that it follows the derivation in Dashuk et al. (2025a, 2025b). Estimates and standard errors of beta_b change; results from earlier versions can be reproduced with MultiLevelOptimalBayes 0.0.4.0 from the CRAN archive. (GitHub branch v0.0.5.0 has the same estimator family, with additional bug fixes.)

Bug fixes in the Bayesian estimator

• The gamma approximations described the between-group mean square MSA / n (mean tau + sigma / n) instead of (MSA - MSD) / n (mean tau). The mean and variance of both estimators are now computed exactly in closed form.
• Changed the scale parameters of the gamma approximations to improve the search window.
• Fixed dependence of the estimate on the units of the predictor.
• The standard errors of beta_b (Bayesian and ML) use the same corrected moments. Where the variance of the ML ratio does not exist under the gamma approximation (k_B <= 2), a first-order approximation is reported.
• Improved the computation of the standard errors of the covariate coefficients (gamma).

Other changes

• Estimates of beta_b are now exactly equivariant to the units of x and y (multiplying x by s divides beta_b and its standard error by s).
• Estimation no longer builds (nJ + J + 1)-dimensional covariance matrices, so mlob() (and especially jackknife = TRUE) is much faster and works for large data sets. The pracma dependency is removed.
• Example 1 in ?mlob used conf.level = 0.01 (a 1% interval); it now uses 0.99.

MultiLevelOptimalBayes 0.0.5.0

Bug fixes

• mlob() now gives correct results when the rows of a group are not contiguous in data.
• mlob() now gives an explicit warning when the estimated between-group variance of the predictor is negative. Previously this was only hinted at later by messages such as “Please check grouping” or “Singularities in the between-group estimation”.
• Added an early check for near-zero between- and within-group (co)variances.

Testing

• Added a simulation-based test fixture (simulate_alcd_cv()) for the test suite only (not exported; implements the data-generating process from the supplementary material of Dashuk et al. (2025a, 2025b)).
• Added numeric tests on seeded simulated data:
  • ML estimates agree with an independent anova(lm()) implementation of the estimator (with and without control variables) and with variance components from REML fits in lme4.
  • The Bayes estimate equals the regularized ratio at the grid-search optimum, and confidence intervals and p-values are consistent with the reported estimates and standard errors.
  • Results are invariant to row order, group labels and shifts of the variables, and equivariant to rescaling of the response and covariates.
  • Reference values guard against unintended changes in output.
  • The Bayes estimator has a lower standard error and lower mean squared error than ML across replications.

Documentation

• The ChickWeight example in ?mlob, which demonstrates all S3 methods, is now wrapped in \donttest{} to keep example run time within CRAN limits.
• Fixed a stray comment marker that caused #' to be rendered literally in the ?mlob examples section.

Internal

• Added lme4 to Suggests (used in tests only).

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.