EAP Ability Estimation in base R

Expected A Posteriori (EAP) estimation scores examinees in computerised adaptive tests and stays stable where Maximum Likelihood fails, for example on all-correct or all-incorrect response patterns.

Each tutorial rebuilds the full adaptive-testing pipeline for one IRT model in plain base R and checks every function against the catR package: response probabilities, item information, next-item selection, EAP estimate and standard error.

Model	Items	Tutorial
4PL (includes 1PL, 2PL, 3PL)	Right/wrong	Dichotomous
Rating Scale Model	Ordered, shared thresholds	RSM
Partial Credit Model	Ordered, item-specific steps	PCM
Graded Response Model	Ordered, item-specific slopes	GRM
Modified Graded Response Model	Ordered, slopes + shared thresholds	Modified GRM
Nominal Response Model	Unordered categories	NRM

EAP Dichotomous Ability Estimation in base R

4PL model for right/wrong items: response probabilities, item information, EAP scoring and an adaptive test, validated against catR.

EAP RSM Ability Estimation in base R

Andrich’s Rating Scale Model: one shared set of thresholds for every Likert item.

EAP PCM Ability Estimation in base R

Masters’ Partial Credit Model: ordered categories with item-specific step parameters.

EAP GRM Ability Estimation in base R

Samejima’s Graded Response Model: ordered categories with item-specific discriminations.

EAP Modified GRM Ability Estimation in base R

Muraki’s modified graded response model (catR MGRM, mirt grsm): GRM slopes with shared category thresholds.

EAP NRM Ability Estimation in base R

Bock’s Nominal Response Model: unordered categories, each with its own slope and intercept.