Eikosstatistics & data science

Advanced & Applied Topics · Item Response Theory (IRT)

Item response theory: Introduction to advanced models and formal developments

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction Advanced Mathematical Psychometrics · Spatial Modeling of Latent Traits

Overview

Topics covered

  • Introduction
  • Item Response Theory
  • Epistemology and Theoretical Foundations of IRT
  • One-Dimensional Models for Dichotomous Items
  • 2.1 · One Parameter Model (1PL) and Rasch Model
  • 2.2 · Two Parameter Model (2PL)

Related concepts

Main connections

  • Maximum likelihood estimation
  • Bayes' theorem & priors
  • Conditional probability & independence
  • Calculus & differentiation
  • Variance & standard deviation
  • Markov chain Monte Carlo (MCMC)

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

P(Y1=y1,Y2=y2,…,YJ=yJ∣θ)=∏j=1JP(Yj=yj∣θ)
View LaTeX sourceP(Y_1 = y_1, Y_2 = y_2, \dots, Y_J = y_J \mid \theta) = \prod_{j=1}^J P(Y_j = y_j \mid \theta)