| ability_gradient | Gradient of ML ability scores with respect to item parameters |
| ability_gradient_1pl | Gradient of ML ability scores w.r.t. 1PL item parameters |
| ability_risk | Propagated ability risk from item-parameter uncertainty |
| ability_risk_1pl | Propagated ability risk for a 1PL fit |
| diagnose_lambda_grid | Diagnose lambda values over a grid |
| fit_1pl | Fit a 1PL (one-parameter logistic) model |
| fit_2pl | Fit a unidimensional 2PL IRT model |
| fit_mixed_subjects | Fit a mixed-subjects 2PL calibration |
| fit_mixed_subjects_1pl | Fit a mixed-subjects 1PL calibration (frozen expected-count) |
| fit_mixed_subjects_from_quadrature | Fit from precomputed quadrature summaries |
| fit_mixed_subjects_iterative | Fit a mixed-subjects 2PL calibration with iterative EM |
| fit_mixed_subjects_mml | Fit a mixed-subjects 2PL calibration via marginal maximum likelihood |
| fit_mixed_subjects_mml_1pl | Fit a mixed-subjects 1PL calibration via marginal maximum likelihood |
| fit_mixed_subjects_split | Fit a split-sample mixed-subjects 2PL calibration |
| link_item_parameters | Link item parameters onto a target scale |
| make_quadrature | Create a standard-normal Gauss-Hermite quadrature grid |
| mixed_subjects_loss | Mixed-subjects objective function |
| mixed_subjects_quadrature | Convert responses to quadrature form |
| posterior_weights_2pl | Compute posterior quadrature weights for a 2PL model |
| score_theta | Estimate ability scores from a 2PL calibration |
| simulate_2pl | Simulate 2PL item responses |
| summarize_expected_counts | Summarize response data as expected quadrature counts |
| tune_lambda_ability_risk | Tune lambda by downstream ability-score risk |
| tune_lambda_ability_risk_1pl | Tune lambda by downstream ability-score risk for a 1PL model |
| tune_lambda_ability_risk_crossfit | Cross-fit ability-score-risk lambda tuning |
| tune_lambda_ability_risk_item | Per-item ability-risk lambda tuning via coordinate descent |
| tune_lambda_ppi_score | Plug-in PPI++ optimal tuning parameter |
| tune_lambda_ppi_score_1pl | Plug-in PPI++ optimal tuning parameter for a 1PL model |
| tune_lambda_ppi_score_item | Per-item PPI++ optimal tuning parameters |
| vcov_mixed_subjects | Sandwich covariance for a mixed-subjects fit |
| vcov_mixed_subjects_1pl | Sandwich covariance for a 1PL mixed-subjects fit |
| vcov_mixed_subjects_mml | Marginal-MML sandwich covariance for a mixed-subjects fit |