---
title: "IRT (GMMSGE01): Parametric IRT (dichotomous data)"
author: "Jorge N. Tendeiro"
date: "2017-12-13T20:53:55Z"
link: "https://bookdown.org/jorgetendeiro/ParametricIRT/"
length_weight: "3.2%"
pinned: false
---

IRT (GMMSGE01): Parametric IRT (dichotomous data) [...] Parametric item response theory (IRT) provides a theoretical framework that allows modeling the relationship \[\text{item} \longleftrightarrow \text{person}\] by means of a mathematical function: \[P(X_i = c|\theta_n) = f(\theta_n)\] \(X_i\) is the random variable denoting the answer to item \(i\), with discrete response categories; \(\theta_n=\) \(n^\text{th}\) person’s trait parameter. This is the item response function (IRF). The IRF is therefore a function relating the latent trait to the probability of answering the item correctly. ...
