Eikosstatistics & data science

Advanced & Applied Topics · Item Response Theory (IRT)

Item response theory: Scale equating and linking

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction Advanced Psychometrics · Latent Variable Modeling

Overview

Topics covered

  • Introduction
  • Item Response Theory: Equation and Connection
  • Fundamentals of metrics in IRT and the problem of indeterminacy
  • Data collection designs for connecting scales
  • 1. Design of Equivalent Groups (Single Group / Equivalent Groups Design)
  • 2. Common-Item Nonequivalent Groups Design (CINGD)

Related concepts

Main connections

  • Mean & expected value
  • Maximum likelihood estimation
  • Bayes' theorem & priors
  • Calculus & differentiation
  • Variance & standard deviation
  • Outliers & influence diagnostics

Compatible notation

Mathematical sample in LaTeX

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

Pj(θ)=cj+1−cj1+exp(−Daj(θ−bj)),
View LaTeX sourceP_j(\theta) = c_j + \frac{1 - c_j}{1 + \exp\left( -D a_j (\theta - b_j) \right)},