Package: betaregscale 3.0.0

Audience and scope | 1) Reproducible simulation and data checks | 2) Fixed-effects candidate set and model ranking | 3) Inference stack: Wald + bootstrap + AME | 4) Prediction layer on analyst scale | 5) Out-of-sample validation | 6) Escalation to mixed models | 6.1 Simulate clustered data with random intercept + slope | 6.2 Fit evolutionary sequence | 6.3 Model choice by LLR/LRT (ANOVA) | 7) Random-effects study (numeric + visual) | 8) A Monte Carlo study (design of Lopes, 2023, ch. 3) | 9) Practical decision checklist | References

Overview | Mathematical foundations | Complete likelihood by censoring type | Model-comparison metrics | Average marginal effects (AME) | Score-scale probabilities | Cross-validation log score | Reproducible workflow | 1) Simulate data and fit candidate models | 2) Compare models in one table | 3) Estimate average marginal effects | 4) Predict score probabilities | 5) ggplot2 diagnostics | 6) Repeated k-fold cross-validation | Practical interpretation | References

Overview | Installation | The score scale and ncuts | Likelihood and censoring types | Interval construction | Data preparation with brs_prep() | Mode 1: Score only (automatic) | Mode 2: Score + explicit censoring indicator | Mode 3: Interval endpoints with NA patterns | Mode 4: Analyst-supplied intervals | Using brs_prep with brs() | Example 1: Fixed dispersion model | Simulating data | Fitting the model | Estimation and fit diagnostics | Goodness of fit | Comparing link functions | Residual diagnostics | Predictions | Confidence intervals | Censoring structure | Example 2: Variable dispersion model | Accessing coefficients by submodel | Comparing link functions (variable dispersion) | Diagnostics for variable dispersion | Advanced analyst functions | Parametric bootstrap confidence intervals | Average marginal effects (AME) | Score probabilities on the original scale | Repeated k-fold cross-validation | S3 methods reference | Reparameterizations | References

Overview | Mathematical model | Linear predictors | Beta parameterization | Conditional contribution by censoring type | Random-effects distribution | Group marginal likelihood | Laplace approximation used by brsmm() | Other integration methods and estimation details | Simulating clustered scale data | Fitting brsmm() | Random intercept + slope example | Additional studies of random effects (numerical and visual) | Core methods | Coefficients and random effects | Variance-covariance, summary and likelihood criteria | Fitted values, prediction and residuals | Diagnostic plotting methods | Prediction with newdata | Statistical tests and validation workflow | Wald tests (from summary) | Evolutionary scheme and Likelihood Ratio (LR) test selection | Residual diagnostics (quick checks) | Parameter recovery experiment | How this maps to automated package tests | References