/**
 * Item Response Theory (IRT)
 *
 * Implements the 1PL (Rasch), 2PL, and 3PL IRT models for:
 * - Calculating probability of correct response
 * - Estimating learner ability (theta)
 * - Calculating item information
 * - Adaptive item selection
 *
 * @see Lord, F.M. (1980). Applications of item response theory to practical testing problems.
 *
 * @packageDocumentation
 */
import type { IRTParameters, IRTAbilityEstimate, IRTConfig, QuestionId } from '../types/index.js';
/**
 * Default IRT configuration
 */
export declare const IRT_CONFIG_DEFAULTS: Required<IRTConfig>;
/**
 * IRT response data for estimation
 */
export interface IRTResponse {
    /** Question ID */
    questionId: QuestionId;
    /** Item parameters */
    params: IRTParameters;
    /** Whether response was correct */
    correct: boolean;
}
/**
 * Calculate probability of correct response using IRT model
 *
 * 1PL (Rasch): P(θ) = 1 / (1 + exp(-(θ - b)))
 * 2PL: P(θ) = 1 / (1 + exp(-a(θ - b)))
 * 3PL: P(θ) = c + (1 - c) / (1 + exp(-a(θ - b)))
 *
 * @param theta - Ability parameter
 * @param params - Item parameters
 * @returns Probability of correct response (0-1)
 */
export declare function calculateProbability(theta: number, params: IRTParameters): number;
/**
 * Calculate the first derivative of P with respect to theta
 * Used in ability estimation
 */
export declare function calculateProbabilityDerivative(theta: number, params: IRTParameters): number;
/**
 * Calculate Fisher Information for an item at a given ability
 *
 * Information represents how precisely the item measures ability at theta.
 * Higher information = more useful for measuring that ability level.
 *
 * I(θ) = [P'(θ)]² / [P(θ)(1-P(θ))]
 */
export declare function calculateInformation(theta: number, params: IRTParameters): number;
/**
 * Calculate test information (sum of item information)
 */
export declare function calculateTestInformation(theta: number, items: IRTParameters[]): number;
/**
 * Calculate standard error of ability estimate
 * SE(θ) = 1 / √I(θ)
 */
export declare function calculateStandardError(theta: number, items: IRTParameters[]): number;
/**
 * IRT Ability Estimator
 *
 * Estimates learner ability (theta) from response patterns using
 * Maximum Likelihood Estimation (MLE) or Expected A Posteriori (EAP).
 */
export declare class IRTEstimator {
    private readonly config;
    constructor(config?: IRTConfig);
    /**
     * Estimate ability using Maximum Likelihood Estimation (MLE)
     *
     * Uses Newton-Raphson iteration to find the theta that maximizes
     * the likelihood of the observed response pattern.
     */
    estimateMLE(responses: IRTResponse[]): IRTAbilityEstimate;
    /**
     * Estimate ability using Expected A Posteriori (EAP)
     *
     * Uses numerical integration with a prior distribution.
     * More stable than MLE, especially with few responses.
     */
    estimateEAP(responses: IRTResponse[]): IRTAbilityEstimate;
    /**
     * Estimate ability using Maximum A Posteriori (MAP)
     *
     * Like MLE but includes prior distribution.
     */
    estimateMAP(responses: IRTResponse[]): IRTAbilityEstimate;
    /**
     * Auto-select best estimation method based on response count
     */
    estimate(responses: IRTResponse[]): IRTAbilityEstimate;
    /**
     * Calculate log-likelihood derivatives for Newton-Raphson
     */
    private calculateDerivatives;
    /**
     * Calculate likelihood of response pattern
     */
    private calculateLikelihood;
    /**
     * Normal PDF for prior
     */
    private normalPDF;
    /**
     * Build ability estimate result
     */
    private buildEstimate;
    /**
     * Default estimate when no responses
     */
    private defaultEstimate;
    /**
     * Handle extreme response patterns
     */
    private extremeEstimate;
}
/**
 * Select next item for adaptive testing using Maximum Fisher Information
 *
 * Selects the item that provides the most information at the current ability estimate.
 */
export declare function selectNextItemMFI(currentTheta: number, availableItems: {
    id: QuestionId;
    params: IRTParameters;
}[], administeredIds: Set<QuestionId>): {
    id: QuestionId;
    params: IRTParameters;
    information: number;
} | null;
/**
 * Convert ability (theta) to percentile
 *
 * Assumes standard normal distribution of ability.
 */
export declare function abilityToPercentile(theta: number): number;
/**
 * Convert ability to grade-level equivalent (rough approximation)
 *
 * Maps theta to approximate grade level (K-12 scale).
 */
export declare function abilityToGradeLevel(theta: number): number;
/**
 * Create an IRT estimator
 */
export declare function createIRTEstimator(config?: IRTConfig): IRTEstimator;
/**
 * Quick ability estimation using EAP
 */
export declare function estimateAbility(responses: {
    params: IRTParameters;
    correct: boolean;
}[], config?: IRTConfig): number;
//# sourceMappingURL=irt.d.ts.map