Advanced & Applied Topics · Item Response Theory (IRT)

Item response theory: Fundamental assumptions and mathematical architecture of psychometrics

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction High Specialty Technical Treatise

Overview

Topics covered

  • Introduction
  • Fundamental Assumptions of Item Response Theory (IRT)
  • Theoretical Transition: from Classical Test Theory (TCT) to IRT
  • Unidimensionality: The One-Dimensional Latent Space
  • 2.1 Mathematical modeling of the latent space
  • Diagnosis of Unidimensionality I: Factorial Methods

Related concepts

Main connections

  • Conditional probability & independence
  • Variance & standard deviation
  • Maximum likelihood estimation
  • Linear algebra & matrices
  • Calculus & differentiation
  • Mathematical expectation & moments

Compatible notation

Mathematical sample in LaTeX

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

X=T+E
View LaTeX sourceX = T + E