bossanova.internal

Auto-generated index of all exports from bossanova.internal. Each module’s __all__ is introspected to list classes, functions, and constants with their first-line docstrings.

Summary¶

Module	Classes	Functions	Attributes	Total
`structs.data`	3	0	0	3
`structs.display`	2	0	0	2
`structs.explore`	6	0	0	6
`structs.fit`	1	0	0	1
`structs.formula`	1	0	0	1
`structs.inference`	4	0	0	4
`structs.marginal`	1	0	0	1
`structs.mixed`	3	0	0	3
`structs.prediction`	2	0	0	2
`structs.simulation`	1	0	0	1
`structs.specs`	4	0	4	8
`schemas`	1	0	37	38
`validators`	0	25	0	25
`builders`	0	30	0	30
`compare`	0	2	0	4
`design`	2	24	0	26
`fit`	1	24	1	26
`formula`	3	5	0	9
`infer`	1	24	0	25
`marginal`	4	33	0	37
`rendering`	0	5	0	5
`simulation`	2	20	0	22
`backend`	1	7	1	9
`batching`	0	2	0	2
`config`	0	5	0	5
`convergence`	1	2	0	3
`differentiation`	0	5	0	5
`distributions`	6	12	0	18
`family`	1	50	3	59
`inference`	6	45	0	51
`linalg`	5	7	0	12
`predict`	0	3	0	3
`rng`	1	1	0	2
`rounding`	0	2	0	2
`solvers`	3	16	0	20
`tolerances`	0	13	4	17
`transforms`	8	1	1	10
`variance`	0	1	0	1
`weights`	1	2	0	3
`viz`	0	21	1	22

containers¶

structs.data¶

Name	Kind	Description
`DataBundle`	class	Validated model data (valid observations only)
`REInfo`	class	Random effects metadata
`RankInfo`	class	Rank deficiency information for a design matrix

structs.display¶

Name	Kind	Description
`MathDisplay`	class	Display wrapper for model equation with IPython rich display
`TermInfo`	class	Parsed information about a single model term

structs.explore¶

Name	Kind	Description
`Condition`	class	A conditioning specification in explore formula
`ContrastExpr`	class	Bracket contrast expression: `Drug[A - B, C - D]`
`ContrastItem`	class	A single contrast: left operand minus right operand
`ContrastOperand`	class	One side of a bracket contrast item
`ExploreFormulaError`	class	Error in explore formula syntax
`ExploreFormulaSpec`	class	Parsed explore formula

structs.fit¶

Name	Kind	Description
`FitState`	class	Immutable fitting result

structs.formula¶

Name	Kind	Description
`FormulaSpec`	class	Learned formula encoding — everything needed to replay on new data

structs.inference¶

Name	Kind	Description
`CVState`	class	Cross-validation results for model evaluation
`InferenceState`	class	Inference results that augment params or estimates
`JointTestState`	class	Joint hypothesis test results for model terms
`ResamplesState`	class	Unified resampling results from bootstrap or permutation inference

structs.marginal¶

Name	Kind	Description
`MeeState`	class	Marginal effects / estimated marginal means results

structs.mixed¶

Name	Kind	Description
`ProfileState`	class	Profile likelihood state for variance component CIs
`VaryingSpreadState`	class	Variance components for mixed models
`VaryingState`	class	Random effects (BLUPs) for mixed models

structs.prediction¶

Name	Kind	Description
`PredictionConfig`	class	Configuration that produced a PredictionState
`PredictionState`	class	Prediction results with optional intervals

structs.simulation¶

Name	Kind	Description
`SimulationInferenceState`	class	Simulation inference results for post-fit or power analysis simulations

structs.specs¶

Name	Kind	Description
`Distribution`	class	Protocol for distribution objects that can generate random samples
`FAMILIES`	attribute	Supported distribution families
`FAMILY_DEFAULT_LINKS`	attribute	Default link functions per family
`LINKS`	attribute	Supported link functions
`METHODS`	attribute	Supported estimation methods
`ModelSpec`	class	Immutable model configuration
`SimulationSpec`	class	Specification for data generation in simulation-first workflows
`VaryingSpec`	class	Specification for random effect grouping in simulation

schemas¶

Name	Kind	Description
`AugmentedDataCols`	attribute
`Col`	class	Namespace for all column name constants used across DataFrame outputs
`ComparisonAic`	attribute
`ComparisonBic`	attribute
`ComparisonCv`	attribute
`ComparisonDevianceChi2`	attribute
`ComparisonDevianceF`	attribute
`ComparisonFTest`	attribute
`ComparisonLrt`	attribute
`DiagnosticsCvCols`	attribute
`DiagnosticsGaussian`	attribute
`DiagnosticsGlm`	attribute
`DiagnosticsLmer`	attribute
`DiagnosticsPredCvCols`	attribute
`EffectsAsympCols`	attribute
`EffectsBaseCols`	attribute
`EffectsBootCols`	attribute
`EffectsPermCols`	attribute
`MetadataBase`	attribute
`MetadataMixed`	attribute
`ParamsAsymp`	attribute
`ParamsBase`	attribute
`ParamsBoot`	attribute
`ParamsCv`	attribute
`ParamsPerm`	attribute
`PowerSummaryCols`	attribute
`PredictionsAsymp`	attribute
`PredictionsBase`	attribute
`PredictionsCv`	attribute
`ResamplesRawSchema`	attribute
`SimulationsInferCols`	attribute
`VaryingCorrSchema`	attribute
`VaryingOffsetsBaseCols`	attribute
`VaryingOffsetsInferSuffix`	attribute
`VaryingParamsBaseCols`	attribute
`VaryingSpreadBase`	attribute
`VaryingSpreadInfer`	attribute
`VifSchema`	attribute

validators¶

Name	Kind	Description
`convert_corr_to_dict`	function	Convert correlation specification to dictionary format
`is_choice_str`	function	Build a validator for a string constrained to a fixed set of choices
`is_conf_level`	function	Validate that a value is a normalized confidence level in (0, 1)
`is_ndarray`	function	Validate that a value is a numpy ndarray
`is_nonnegative_int`	function	Validate that a value is a non-negative integer
`is_optional_conf_level`	function	Validate that a value is a normalized confidence level or None
`is_optional_int`	function	Validate that a value is an int or None
`is_optional_ndarray`	function	Validate that a value is a numpy ndarray or None
`is_optional_positive_int`	function	Validate that a value is a positive integer or None
`is_optional_sparse_csc`	function	Validate that a value is a scipy.sparse.csc_matrix or None
`is_optional_str`	function	Validate that a value is a string or None
`is_optional_str_key_dict`	function	Validate that a value is a dict with string keys or None
`is_optional_tuple_of_str`	function	Validate that a value is a tuple of strings or None
`is_positive_int`	function	Validate that a value is a positive integer
`is_tuple_of_str`	function	Validate that a value is a tuple of strings
`normalize_conf_level`	function	Normalize conf_level to a float in (0, 1)
`normalize_optional_conf_level`	function	Normalize an optional confidence level
`to_factor_dict`	function	Convert factor dict values from lists to tuples
`to_frozen_dict`	function	Ensure dict values are tuples where applicable
`to_optional_tuple`	function	Convert an optional list of strings to a tuple
`to_tuple`	function	Convert list to tuple for immutability
`to_tuple_of_tuples`	function	Convert dict values to tuples for immutability
`validate_correlations`	function	Validate correlation values are in [-1, 1]
`validate_sigma`	function	Validate sigma is non-negative
`validate_slope_sds`	function	Validate slope SDs are non-negative

builders¶

Name	Kind	Description
`append_inference_columns`	function	Append standard inference columns to a DataFrame if available
`build_cv_state`	function	Build a CVState from cross-validation computation
`build_effects_dataframe`	function	Build the `.effects` DataFrame from marginal effects state
`build_fit_state`	function	Build a FitState instance with validation
`build_inference_state`	function	Build an InferenceState from computed inference values
`build_joint_test_dataframe`	function	Build an ANOVA-style DataFrame from joint test results
`build_joint_test_state`	function	Build a JointTestState from computed joint test values
`build_mee_resamples`	function	Build ResamplesState from MEE inference if samples are available
`build_mee_state`	function	Build a MeeState from marginal effects computation
`build_model_spec`	function	Build a ModelSpec from raw inputs
`build_model_spec_from_formula`	function	Build ModelSpec from a pre-parsed formula structure and resolve defaults
`build_params_dataframe`	function	Build the `.params` DataFrame from fit state
`build_params_resamples`	function	Build ResamplesState from params inference if samples are available
`build_prediction_state`	function	Build a PredictionState from prediction computation
`build_predictions_dataframe`	function	Build the `.predictions` DataFrame from prediction state
`build_resamples_dataframe`	function	Build a long-format DataFrame of raw resampled values
`build_resamples_state`	function	Build a ResamplesState from resampling results
`build_simulation_inference_state`	function	Build a SimulationInferenceState from computed values
`build_simulation_spec`	function	Build a SimulationSpec for data generation
`build_simulation_spec_from_formula`	function	Build SimulationSpec from formula with defaults for unspecified variables
`build_simulations_dataframe`	function	Build the `.simulations` DataFrame with optional inference columns
`build_varying_corr_dataframe`	function	Build the `.varying_corr` DataFrame from random effect correlations
`build_varying_offsets_dataframe`	function	Build the `.varying_offsets` DataFrame from varying state
`build_varying_params_dataframe`	function	Build the `.varying_params` DataFrame (population + offsets)
`build_varying_spec`	function	Build a VaryingSpec for random effect structure
`build_varying_spread_dataframe`	function	Build the `.varying_spread` DataFrame from variance components
`build_varying_spread_state`	function	Build a VaryingSpreadState from variance component estimates
`build_varying_state`	function	Build a VaryingState from computed BLUPs
`extract_mee_names`	function	Extract human-readable names from a MeeState
`get_varying_random_terms`	function	Get all random terms (Intercept + slope terms) for a VaryingSpec

domain¶

compare¶

Name	Kind	Description
`compare`	module	Model comparison utilities for nested model testing
`compare_aic`	function	Compare models by AIC with delta-AIC and Akaike weights
`compare_bic`	function	Compare models by BIC with delta-BIC and Schwarz weights
`lrt`	module	Likelihood ratio test for comparing nested mixed models

design¶

Name	Kind	Description
`DesignColumnInfo`	class	Parsed design matrix column metadata
`RandomEffectsInfo`	class	Complete random effects specification for lmer/glmer
`array_to_coding_matrix`	function	Convert user-specified contrasts to a coding matrix for design matrices
`build_random_effects`	function	Build complete random effects specification
`build_reference_design_matrix`	function	Build design matrix for reference grid points
`build_reference_row`	function	Build a single row of the reference design matrix
`build_slope_reference_matrix`	function	Build reference matrices for computing marginal slopes
`build_z_crossed`	function	Build Z matrix for crossed random effects
`build_z_nested`	function	Build Z matrix for nested random effects
`build_z_simple`	function	Build Z matrix for single grouping factor
`convert_coding_to_hypothesis`	function	Convert a coding matrix back to interpretable hypothesis contrasts
`extract_base_term`	function	Extract base term name from column name
`extract_categorical_variables`	function	Find all categorical base variable names from design matrix columns
`extract_level_from_column`	function	Extract level value for a specific focal variable from column name
`helmert_coding`	function	Build Helmert contrast matrix
`helmert_coding_labels`	function	Get column labels for Helmert contrast
`identify_column_type`	function	Identify column type from name (simplified version)
`parse_design_column_name`	function	Parse design matrix column name into components
`poly_coding`	function	Build orthogonal polynomial contrast matrix
`poly_coding_labels`	function	Get column labels for polynomial contrast
`sequential_coding`	function	Build sequential (successive differences) contrast matrix
`sequential_coding_labels`	function	Get column labels for sequential contrast
`sum_coding`	function	Build sum (effects) contrast matrix
`sum_coding_labels`	function	Get column labels for sum contrast
`treatment_coding`	function	Build treatment (dummy) contrast matrix
`treatment_coding_labels`	function	Get column labels for treatment contrast

fit¶

Name	Kind	Description
`FitResult`	class	Immutable result of the fit lifecycle
`VALID_SOLVERS`	attribute
`augment_data_with_diagnostics`	function	Augment raw data with diagnostic columns after fit
`build_mixed_post_fit_state`	function	Compute BLUPs, variance components, and emit convergence warnings
`build_predict_grid`	function	Build a Cartesian-product prediction grid
`check_convergence`	function	Run convergence diagnostics on a fitted mixed model
`compute_diagnostics`	function	Compute model-level diagnostics as a single-row DataFrame
`compute_metadata`	function	Compute model metadata as a single-row DataFrame
`compute_optimizer_diagnostics`	function	Compute optimizer convergence diagnostics as a single-row DataFrame
`compute_predictions_from_formula`	function	Parse a predict formula, build the grid, compute predictions, and attach grid...
`compute_r_squared`	function	Compute R-squared and adjusted R-squared from raw arrays
`compute_varying_spread_state`	function	Compute VaryingSpreadState (variance components) from theta parameters
`compute_varying_state`	function	Compute VaryingState (BLUPs) from fitted random effects parameters
`execute_fit`	function	Execute the full fit lifecycle: bundle rebuild → fit → post-fit state → diagn...
`fit_glm_irls`	function	Fit generalized linear model using Iteratively Reweighted Least Squares
`fit_glmer_pirls`	function	Fit generalized linear mixed model using Penalized IRLS
`fit_lmer_pls`	function	Fit linear mixed-effects model using Penalized Least Squares
`fit_model`	function	Dispatch to appropriate fitter based on model specification
`fit_ols_qr`	function	Fit ordinary or weighted least squares using QR decomposition
`get_theta_lower_bounds`	function	Get lower bounds for theta parameters
`parse_fit_kwargs`	function	Validate and extract fitting parameters from `**kwargs`
`parse_predict_formula`	function	Parse an explore-style formula and build a prediction grid
`per_factor_re_info`	function	Split global RE metadata into per-factor structures and names
`resolve_condition_values`	function	Resolve a :class:`Condition` to concrete values or `None`
`resolve_solver`	function	Select the appropriate solver for a model configuration
`validate_fit_method`	function	Validate and apply a user-specified fitting method to a ModelSpec

formula¶

Name	Kind	Description
`DesignResult`	class	Output of build_design_matrices(). Separates arrays from metadata
`FormulaError`	class	Exception raised for formula parsing errors
`TermResult`	class	Result of evaluating one formula term
`build_design_matrices`	function	Build X and y matrices from a parsed formula spec
`build_random_effects_from_spec`	function	Build random effects design matrix from FormulaSpec
`evaluate_newdata`	module	Newdata evaluation — apply learned encoding to new observations
`expand_double_verts`	function	Expand \|\| syntax into separate uncorrelated random effects terms
`expand_nested_syntax`	function	Expand nested / syntax into separate crossed random effects terms
`parse_formula`	function	Parse formula and detect categoricals from data

infer¶

Name	Kind	Description
`InferResult`	class	Immutable result of inference dispatch
`augment_spread_with_profile_ci`	function	Augment variance components with profile likelihood confidence intervals
`build_emm_reference_grid`	function	Build reference grid X matrix for EMM computation
`compute_bootstrap_params`	function	Generate bootstrap distribution of coefficient estimates
`compute_bootstrap_pvalue`	function	Compute bootstrap p-values
`compute_cv_metrics`	function	Compute k-fold or leave-one-out cross-validation metrics
`compute_jackknife_coefs`	function	Compute leave-one-out jackknife coefficient estimates
`compute_mee_bootstrap`	function	Compute bootstrap inference for marginal effects
`compute_mee_permutation`	function	Compute permutation-based inference for marginal effects
`compute_params_asymptotic`	function	Compute asymptotic (Wald) inference for model parameters
`compute_params_bootstrap`	function	Compute bootstrap inference for parameters
`compute_params_bootstrap_mixed`	function	Compute bootstrap inference for mixed model parameters
`compute_params_cv_inference`	function	Compute CV-based parameter importance via ablation
`compute_params_permutation`	function	Compute permutation-based inference for model parameters
`compute_prediction_asymptotic`	function	Compute asymptotic inference for predictions via delta method
`compute_prediction_bootstrap`	function	Compute bootstrap inference for predictions
`compute_profile_inference`	function	Compute profile likelihood CIs for variance components
`compute_satterthwaite_emm_df`	function	Compute Satterthwaite denominator df for EMM contrast rows
`compute_simulation_inference`	function	Compute inference for simulations
`dispatch_infer`	function	Dispatch inference to the correct backend based on method and last operation
`dispatch_mee_inference`	function	Dispatch marginal effects inference to the appropriate method
`dispatch_params_inference`	function	Dispatch parameter inference to the appropriate method
`dispatch_prediction_inference`	function	Dispatch prediction inference to the appropriate method
`generate_group_kfold_splits`	function	Generate group-aware k-fold cross-validation indices
`generate_kfold_splits`	function	Generate k-fold cross-validation train/test indices

marginal¶

Name	Kind	Description
`Condition`	class	A conditioning specification in explore formula
`ExploreFormulaError`	class	Error in explore formula syntax
`ExploreFormulaSpec`	class	Parsed explore formula
`ResolvedConditions`	class	Typed buckets for resolved conditioning specifications
`apply_bracket_contrasts`	function	Apply bracket contrast expression to an EMM MeeState
`apply_bracket_contrasts_grouped`	function	Apply bracket contrasts within each condition group of a crossed MeeState
`apply_contrasts`	function	Apply contrast matrix to marginal means/effects
`apply_contrasts_grouped`	function	Apply contrasts within each condition group of a crossed MeeState
`apply_rhs_bracket_contrast`	function	Apply a bracket contrast on a RHS condition column
`build_all_pairwise_matrix`	function	Build all pairwise contrasts between EMM levels
`build_bracket_contrast_matrix`	function	Build contrast matrix and labels from bracket contrast expression
`build_contrast_matrix`	function	Build a contrast matrix based on contrast type
`build_helmert_matrix`	function	Build Helmert contrasts (each level vs mean of previous levels)
`build_pairwise_matrix`	function	Build (n-1) linearly independent pairwise contrasts
`build_poly_matrix`	function	Build orthogonal polynomial contrast matrix for EMMs
`build_reference_grid`	function	Construct reference grid for marginal effects evaluation
`build_sequential_matrix`	function	Build sequential (successive differences) contrasts
`build_sum_to_zero_matrix`	function	Build sum-to-zero contrasts (deviation coding)
`build_treatment_matrix`	function	Build treatment (Dunnett-style) contrasts against a reference level
`combine_resolved`	function	Merge two ResolvedConditions, with b taking precedence on conflicts
`compose_contrast_matrix`	function	Compose contrast matrix with prediction matrix
`compute_compound_bracket_contrasts`	function	Compute bracket contrasts for a compound focal variable
`compute_conditional_emm`	function	Compute per-group conditional EMMs incorporating intercept BLUPs
`compute_conditional_slopes`	function	Compute per-group conditional slopes incorporating BLUPs
`compute_contrasts`	function	Apply contrast matrix to EMMs
`compute_emm`	function	Compute estimated marginal means for a categorical focal variable
`compute_joint_test`	function	Compute joint hypothesis tests for model terms
`compute_mee_inference`	function	Compute delta method inference for marginal effects
`compute_mee_inference_fallback`	function	Compute inference for MEE without L_matrix (fallback path)
`compute_mee_se`	function	Compute standard errors for MEE estimates (means or slopes)
`compute_slopes`	function	Compute marginal slope for a continuous focal variable
`compute_slopes_crossed`	function	Compute crossed slopes over focal variable x condition grid
`compute_slopes_finite_diff`	function	Compute marginal slopes via centered finite differences
`dispatch_marginal_computation`	function	Route a parsed explore formula to the appropriate marginal computation
`get_contrast_labels`	function	Generate human-readable labels for contrasts
`parse_explore_formula`	function	Parse an explore formula string
`resolve_conditions`	function	Classify each Condition into the appropriate typed bucket

rendering¶

Name	Kind	Description
`build_equation`	function	Build a structural LaTeX equation from model containers
`dataframe_to_markdown`	function	Convert a Polars DataFrame to a pipe-delimited markdown table
`equation_to_markdown`	function	Wrap a LaTeX equation in display math delimiters for Quarto
`to_markdown`	function	Convert a Polars DataFrame to a markdown table, optionally saving to file
`write_text`	function	Write text content to a file, creating parent directories

simulation¶

Name	Kind	Description
`MonteCarloResult`	class	Results from a Monte Carlo simulation study
`SimulateResult`	class	Immutable result of the simulate lifecycle
`bias`	function	Compute bias: E[beta_hat] - beta_true
`compute_mc_iteration`	function	Execute a single Monte Carlo iteration
`compute_mu_with_new_re`	function	Compute conditional mean with newly sampled random effects
`compute_wilson_ci`	function	Wilson score confidence interval for a binomial proportion
`coverage`	function	Compute coverage probability
`empirical_se`	function	Compute empirical standard error (SD of estimates)
`execute_simulate`	function	Execute simulation: power analysis, post-fit sampling, or pre-fit generation
`expand_sweep_grid`	function	Full factorial grid from base DGP + power sweep overrides
`generate_data_from_spec`	function	Generate a synthetic dataset from a simulation specification
`generate_glm_data`	function	Generate GLM data with known parameters
`generate_glmer_data`	function	Generate GLMM data with known parameters
`generate_lm_data`	function	Generate linear model data with known parameters
`generate_lmer_data`	function	Generate linear mixed model data with known parameters
`mean_se`	function	Compute mean of standard errors across simulations
`rejection_rate`	function	Compute rejection rate (proportion of p-values < alpha)
`rmse`	function	Compute root mean squared error
`run_monte_carlo`	function	Run a Monte Carlo simulation study
`run_power_analysis`	function	Run simulation-based power analysis for a model formula
`run_power_study`	function	Run power analysis across a sweep grid
`simulate_responses_from_fit`	function	Simulate new responses from a fitted model

maths¶

backend¶

Name	Kind	Description
`ArrayOps`	class	Protocol for array operations across backends
`BackendName`	attribute
`backend`	function	Context manager for temporary backend switching
`clear_ops_cache`	function	Clear the backend operations cache
`get_backend`	function	Get the current backend name
`get_ops`	function	Get array operations for the current backend
`lock_backend`	function	Lock the backend to prevent switching after model fitting
`reset_backend`	function	Reset backend state (for testing only)
`set_backend`	function	Set the backend to use for computations

batching¶

Name	Kind	Description
`compute_batch_size`	function	Compute optimal batch size for jax.lax.map
`get_available_memory_gb`	function	Query available system memory in GB

config¶

Name	Kind	Description
`get_display_digits`	function	Get the number of significant figures for DataFrame display output
`get_singular_tolerance`	function	Get the current singular tolerance for mixed models
`is_singular`	function	Check whether a mixed model fit is singular
`set_display_digits`	function	Set the number of significant figures for DataFrame display output
`set_singular_tolerance`	function	Set the global singular tolerance for mixed models

convergence¶

Name	Kind	Description
`ConvergenceMessage`	class	A convergence diagnostic message with technical and user-friendly parts
`diagnose_convergence`	function	Analyze model convergence state and generate diagnostic messages
`format_convergence_warnings`	function	Format convergence messages for display as warning text

differentiation¶

Name	Kind	Description
`compute_gradient_richardson`	function	Compute gradient using Richardson extrapolation
`compute_hessian_numerical`	function	Compute Hessian using central finite differences
`compute_hessian_richardson`	function	Compute Hessian using Richardson extrapolation with genD method
`compute_jacobian_numerical`	function	Compute Jacobian using central finite differences
`compute_jacobian_richardson`	function	Compute Jacobian using Richardson extrapolation

distributions¶

Name	Kind	Description
`ConvolvedDistribution`	class	Distribution representing the sum of two independent random variables
`Distribution`	class	Wrapper for scipy.stats distributions with visualization
`FoldedDistribution`	class	Distribution of \|X\| - the absolute value of X
`Probability`	class	Rich probability result from distribution queries
`TransformedDistribution`	class	Distribution resulting from an affine transformation: Y = scale*X + shift
`TruncatedDistribution`	class	Distribution truncated to an interval [low, high]
`beta`	function	Beta distribution
`binomial`	function	Binomial distribution
`chi2`	function	Chi-squared distribution
`exponential`	function	Exponential distribution (rate parameterization)
`f_dist`	function	F distribution
`figure_to_html`	function	Convert matplotlib figure to base64-encoded HTML img tag
`gamma`	function	Gamma distribution
`normal`	function	Normal (Gaussian) distribution
`poisson`	function	Poisson distribution
`t`	function	Student’s t distribution (location-scale parameterization)
`t_dist`	function	Student’s t distribution
`uniform`	function	Uniform distribution

family¶

Name	Kind	Description
`CANONICAL_LINKS`	attribute
`ESTIMATED_DISPERSION_FAMILIES`	attribute
`Family`	class	Family configuration for GLM fitting
`LINK_FUNCTIONS`	attribute
`apply_link`	function	Apply link function by name: η = g(μ)
`apply_link_deriv`	function	Apply link function derivative by name: dη/dμ
`apply_link_inverse`	function	Apply inverse link function by name: μ = g⁻¹(η)
`binomial`	module	Binomial family functions for GLM fitting
`binomial_deviance`	function	Binomial unit deviance: d(y, μ) = 2[y log(y/μ) + (1-y) log((1-y)/(1-μ))]
`binomial_dispersion`	function	Dispersion parameter for binomial family
`binomial_initialize`	function	Initialize μ for binomial family
`binomial_loglik`	function	Binomial conditional log-likelihood (per observation)
`binomial_variance`	function	Binomial variance function: V(μ) = μ(1-μ)
`build_family`	function	Create a Family object from family and link names
`cloglog_link`	function	Complementary log-log link function: η = log(-log(1-μ))
`cloglog_link_deriv`	function	Cloglog link derivative: dη/dμ = 1/((1-μ) * (-log(1-μ)))
`cloglog_link_inverse`	function	Cloglog inverse link: μ = 1 - exp(-exp(η))
`gamma`	module	Gamma family functions for GLM fitting
`gamma_deviance`	function	Gamma unit deviance: d(y, μ) = 2[-log(y/μ) + (y - μ)/μ]
`gamma_dispersion`	function	Estimate dispersion parameter for Gamma family
`gamma_initialize`	function	Initialize μ for Gamma family
`gamma_loglik`	function	Gamma conditional log-likelihood (per observation)
`gamma_variance`	function	Gamma variance function: V(μ) = μ²
`gaussian`	module	Gaussian family functions for GLM fitting
`gaussian_deviance`	function	Gaussian unit deviance: d(y, μ) = (y - μ)²
`gaussian_dispersion`	function	Estimate dispersion parameter for Gaussian family
`gaussian_initialize`	function	Initialize μ for Gaussian family
`gaussian_loglik`	function	Gaussian conditional log-likelihood (per observation)
`gaussian_variance`	function	Gaussian variance function: V(μ) = 1
`identity_link`	function	Identity link function: η = μ
`identity_link_deriv`	function	Identity link derivative: dη/dμ = 1
`identity_link_inverse`	function	Identity inverse link: μ = η
`inverse_link`	function	Inverse link function: η = 1/μ
`inverse_link_deriv`	function	Inverse link derivative: dη/dμ = -1/μ²
`inverse_link_inverse`	function	Inverse link inverse: μ = 1/η
`log_link`	function	Log link function: η = log(μ)
`log_link_deriv`	function	Log link derivative: dη/dμ = 1/μ
`log_link_inverse`	function	Log inverse link: μ = exp(η)
`logit_link`	function	Logit link function: η = log(μ/(1-μ))
`logit_link_deriv`	function	Logit link derivative: dη/dμ = 1/(μ(1-μ))
`logit_link_inverse`	function	Logit inverse link: μ = 1/(1 + exp(-η))
`poisson`	module	Poisson family functions for GLM fitting
`poisson_deviance`	function	Poisson unit deviance: d(y, μ) = 2[y log(y/μ) - (y - μ)]
`poisson_dispersion`	function	Dispersion parameter for Poisson family
`poisson_initialize`	function	Initialize μ for Poisson family
`poisson_loglik`	function	Poisson conditional log-likelihood (per observation)
`poisson_variance`	function	Poisson variance function: V(μ) = μ
`probit_link`	function	Probit link function: η = Φ⁻¹(μ)
`probit_link_deriv`	function	Probit link derivative: dη/dμ = 1/φ(Φ⁻¹(μ))
`probit_link_inverse`	function	Probit inverse link: μ = Φ(η)
`resolve_sigma`	function	Resolve optional sigma to a concrete float
`sample_response`	function	Sample response values from a GLM family distribution
`tdist`	module	Student-t family functions for robust GLM fitting
`tdist_deviance`	function	Placeholder - use tdist(df=...) factory to get proper function
`tdist_dispersion`	function	Estimate dispersion (scale) parameter for Student-t family
`tdist_initialize`	function	Initialize μ for Student-t family
`tdist_loglik`	function	Placeholder - use tdist(df=...) factory to get proper function
`tdist_robust_weights`	function	Placeholder - use tdist(df=...) factory to get proper function
`tdist_variance`	function	Student-t variance function: V(μ) = 1

inference¶

Name	Kind	Description
`CellInfo`	class	Information about factor cells for Welch-style inference
`Chi2TestResult`	class	Result container for chi-square test
`FTestResult`	class	Result container for F-test
`InferenceResult`	class	Results from coefficient inference computation
`MixedModelProtocol`	class	Protocol for mixed-effects models compatible with profile likelihood
`TTestResult`	class	Result container for t-test
`adjust_pvalues`	function	Adjust p-values for multiple comparisons
`build_cholesky_with_derivs`	function	Build Cholesky factor L and its derivatives w.r.t. theta
`compute_aic`	function	Compute Akaike Information Criterion
`compute_akaike_weights`	function	Compute Akaike weights from information criterion values
`compute_bic`	function	Compute Bayesian Information Criterion
`compute_cell_info`	function	Compute cell-based variance information for Welch inference
`compute_chi2_test`	function	Compute Wald chi-square test for L @ β = 0
`compute_ci`	function	Compute confidence interval bounds
`compute_coefficient_inference`	function	Compute inference statistics for regression coefficients
`compute_contrast_variance`	function	Compute variance-covariance of linear contrasts L @ β
`compute_cooks_distance`	function	Compute Cook’s distance for influence
`compute_cr_vcov`	function	Compute cluster-robust covariance matrix for Gaussian mixed models
`compute_deviance`	function	Compute deviance from log-likelihood
`compute_f_pvalue`	function	Compute p-value from F-statistic
`compute_f_test`	function	Compute F-test for linear hypothesis L @ β = 0
`compute_glm_cr_vcov`	function	Compute cluster-robust covariance matrix for non-Gaussian mixed models
`compute_glm_hc_vcov`	function	Compute heteroscedasticity-consistent covariance matrix for GLM
`compute_hc_vcov`	function	Compute heteroscedasticity-consistent covariance matrix
`compute_leverage`	function	Compute diagonal of hat matrix (leverage values)
`compute_mvt_critical`	function	Compute multivariate-t critical value for simultaneous inference
`compute_pvalue`	function	Compute p-values from test statistics
`compute_satterthwaite_df`	function	Compute Satterthwaite degrees of freedom for each fixed effect
`compute_satterthwaite_summary_table`	function	Compute full coefficient table with Satterthwaite df and p-values
`compute_satterthwaite_t_test`	function	Compute t-statistics, p-values, and confidence intervals
`compute_sd_jacobian`	function	Compute SDs and Jacobian of SDs w.r.t. varpar = [theta, sigma]
`compute_se_from_vcov`	function	Compute standard errors from variance-covariance matrix
`compute_sigma_se_wald`	function	Compute Wald standard error for sigma
`compute_studentized_residuals`	function	Compute internally studentized (standardized) residuals
`compute_t_critical`	function	Compute t-distribution critical value for confidence interval
`compute_t_test`	function	Compute t-test for a single contrast L @ β = 0
`compute_tukey_critical`	function	Compute Tukey HSD critical value for pairwise comparisons
`compute_vif`	function	Compute variance inflation factors
`compute_wald_ci_varying`	function	Compute Wald CIs for variance components on SD scale
`compute_wald_statistic`	function	Compute Wald statistic for testing L @ β = 0
`compute_welch_satterthwaite_df_per_coef`	function	Compute per-coefficient Welch-Satterthwaite degrees of freedom
`compute_z_critical`	function	Compute z-distribution critical value for confidence interval
`convert_theta_ci_to_sd`	function	Convert theta-scale CIs to SD-scale CIs
`delta_method_se`	function	Compute standard errors for predictions via delta method
`extract_ci_bound`	function	Extract CI bound by finding where spline equals target zeta
`extract_factors_from_formula`	function	Extract factor (categorical) column names from a model formula
`format_pvalue_with_stars`	function	Format p-value with R-style significance codes
`parse_conf_int`	function	Parse flexible confidence interval input to float
`profile_likelihood`	function	Compute profile likelihood confidence intervals for variance components
`profile_theta_parameter`	function	Profile a single theta parameter bidirectionally from its MLE
`satterthwaite_df_for_contrasts`	function	Compute Satterthwaite degrees of freedom for arbitrary contrasts

linalg¶

Name	Kind	Description
`CHOLMODFactorization`	class	Wrapper around CHOLMOD sparse Cholesky factorization
`QRSolveResult`	class	Result container for QR solve
`SPLUFactorization`	class	Wrapper around scipy.sparse.linalg.splu factorization
`SVDSolveResult`	class	Result container for SVD solve
`SparseFactorization`	class	Abstract base class for sparse matrix factorization
`compute_sparse_cholesky`	function	Factor a sparse symmetric positive definite matrix
`compute_vcov_schur_sparse`	function	Compute variance-covariance matrix of fixed effects via Schur complement
`detect_rank_deficiency`	function	Detect rank deficiency in a design matrix via pivoted QR
`qr_solve`	function	Solve least squares via pivoted QR decomposition
`qr_solve_jax`	function	Solve least squares via pivoted QR decomposition (returns backend arrays)
`svd_solve`	function	Solve least squares via SVD (handles rank deficiency)
`svd_solve_jax`	function	Solve least squares via SVD (returns backend arrays)

predict¶

Name	Kind	Description
`fill_valid`	function	Fill valid positions in result array with computed values
`get_valid_rows`	function	Identify valid (non-NA) rows in a design matrix
`init_na_array`	function	Create an array of NaN values

rng¶

Name	Kind	Description
`RNG`	class	Unified RNG wrapper for JAX and NumPy backends
`build_rng`	function	Create RNG from seed (convenience function)

rounding¶

Name	Kind	Description
`round_float_columns`	function	Round all Float64 columns to digits significant figures
`round_sigfigs`	function	Round array values to n significant figures

solvers¶

Name	Kind	Description
`LambdaTemplate`	class	Template for efficient Lambda matrix updates during optimization
`PLSInvariants`	class	Pre-computed quantities that don’t change during theta optimization
`PatternTemplate`	class	Template for preserving sparsity patterns across theta evaluations
`apply_sqrt_weights`	function	Apply sqrt(weights) transformation to design matrices and response
`build_lambda_sparse`	function	Build sparse block-diagonal Lambda matrix from theta
`build_lambda_template`	function	Build a Lambda template for efficient repeated updates
`compute_agq_deviance`	function	Compute AGQ deviance for Stage 2 optimization
`compute_irls_quantities`	function	Compute IRLS working weights and working response
`compute_pls_invariants`	function	Pre-compute quantities that are constant during optimization
`fit_glm_irls`	function	Fit GLM using IRLS algorithm
`fit_glmm_pirls`	function	Fit GLMM using PIRLS with outer optimization over theta
`glmm_deviance`	function	Compute GLMM deviance via Laplace approximation
`glmm_deviance_objective`	function	Compute GLMM deviance for outer optimization
`lmm_deviance_sparse`	function	Compute LMM deviance for optimization
`optimize_theta`	function	Optimize theta using BOBYQA via NLOPT
`pirls_sparse`	module	Sparse PIRLS (Penalized Iteratively Reweighted Least Squares) core routines
`solve_pls_sparse`	function	Solve Penalized Least Squares system using Schur complement
`solve_weighted_pls_sparse`	function	Solve weighted Penalized Least Squares for GLMM
`theta_to_cholesky_block`	function	Convert theta vector to lower-triangular Cholesky block
`update_lambda_from_template`	function	Update Lambda matrix from template using new theta values

tolerances¶

Name	Kind	Description
`DEFAULT_SAFETY`	attribute
`EPS`	attribute
`MAX_COND`	attribute
`MAX_COND_INVERSE`	attribute
`algorithm_comparison_atol`	function	Absolute tolerance for comparing different algorithms
`algorithm_comparison_rtol`	function	Relative tolerance for comparing different algorithms
`decomposition_atol`	function	Absolute tolerance for decomposition properties
`fitted_atol`	function	Absolute tolerance for fitted value comparisons
`glm_score_atol`	function	Absolute tolerance for GLM score equation checks
`has_full_rank`	function	Check if matrix has full column rank
`hat_matrix_atol`	function	Absolute tolerance for hat matrix property checks
`inference_atol`	function	Absolute tolerance for inference result comparisons
`is_well_conditioned`	function	Check if matrix is well-conditioned for stable computation
`orthogonality_atol`	function	Absolute tolerance for orthogonality checks
`residual_atol`	function	Absolute tolerance for residual orthogonality checks
`solve_atol`	function	Absolute tolerance for linear solve operations
`solve_rtol`	function	Relative tolerance for linear solve operations

transforms¶

Name	Kind	Description
`Center`	class	Mean-centering transform: x - mean(x)
`Norm`	class	Normalization transform: x / std(x)
`Rank`	class	Average-method rank transform: rank(x)
`STATEFUL_TRANSFORMS`	attribute
`Scale`	class	Gelman scaling transform: (x - mean(x)) / (2 * std(x))
`SignedRank`	class	Signed-rank transform: sign(x) * rank(\|x\|)
`StatefulTransform`	class	Base class for stateful transforms
`TransformState`	class	Container for captured transform parameters
`Zscore`	class	Z-score transform: (x - mean(x)) / std(x)
`build_transform`	function	Create a stateful transform instance by name

variance¶

Name	Kind	Description
`theta_to_variance_components`	function	Convert theta parameters to named variance components

weights¶

Name	Kind	Description
`WeightInfo`	class	Metadata for weights derived from factor columns
`compute_inverse_variance_weights`	function	Compute inverse-variance weights from a factor column
`detect_weight_type`	function	Check if a column is categorical (should use inverse-variance weights)

viz¶

Name	Kind	Description
`BOSSANOVA_STYLE`	attribute
`compute_figsize`	function	Compute figure size based on number of items
`compute_grid_figsize`	function	Compute figure size for grid/subplot layouts
`extract_params`	function	Extract parameter estimates from a fitted model
`extract_residuals`	function	Extract residual diagnostics from a fitted model
`get_model_fitted`	function	Extract fitted values from model, supporting both APIs
`get_model_formula`	function	Extract formula string from model, supporting both old and new API
`get_model_params`	function	Extract parameter estimates from model, supporting both APIs
`get_model_residuals`	function	Extract residuals from model, supporting both APIs
`get_model_response`	function	Extract response variable name from model, supporting both APIs
`is_unified_model`	function	Check if model is the new unified model() class (or proxy)
`plot_compare`	function	Compare coefficients across multiple fitted models
`plot_design`	function	Plot design matrix as an annotated heatmap
`plot_explore`	function	Plot marginal estimated effects
`plot_params`	function	Plot fixed effect estimates as a forest plot
`plot_predict`	function	Plot marginal predictions across a predictor’s range
`plot_profile`	function	Plot profile likelihood curves
`plot_ranef`	function	Plot random effects as a caterpillar plot
`plot_relationships`	function	Plot pairwise relationships between response and predictors
`plot_resamples`	function	Plot distribution of resampled statistics
`plot_resid`	function	Plot residual diagnostics as a faceted grid
`plot_vif`	function	Plot VIF diagnostics as correlation heatmap