Analysing dichotomous and polytomous responses to items related to xenophobia using item response theory

Abstract

Item response theory (IRT), have many research applications, particularly in psychology. The idea behind IRT is that the probability of a response to an item is a mathematical function of person and item parameters. The person parameter is a single latent trait which cannot be measured directly, including personality trait such as attitude, ability, perception and behaviour. The item parameters include the difficulty of the item (known as the ‘location’, which represents its location on the difficulty scale) and the discrimination of the item (known as the ‘slope’, which represents how steeply individuals’ responses to an item vary with their latent personality trait). There are different types of IRT models including dichotomous and multichotomous IRT models. The former are appropriate when the response to an item has two possible categories. These include the 1-parameter (1-PL) and 2-parameter (2-PL) logistic models, known as Rasch models. The latter are appropriate when the response to an item has an ordinal categorical (Likert) scale. These include the Partial Credit model (PCM) and the Rating Scale model (RSM). A number of local and foreign participants will be asked to respond to a number of items related to xenophobia, including other demographic and psychographic details. All the above models will be fitted to this dataset using the facilities of GLLAMM, which is a subroutine of STATA®.