Latent Variable Models for Ordinal Data

**Speaker**: Damien McParland

**Time**: 1:00PM**Date**: Fri 1st April 2011

**Location**: Statistics Seminar Room- L550 Library building

**Abstract**

Ordinal data arise in many contexts and item response modelling is a long established method for analysing this type of data.

The ordinal response for individual i on item j is denoted Yij, where i=1,…,N and j=1,…,J. Corresponding to each ordinal data point Yij is a latent Gaussian variable Zij. The value of Yij is observed to be level k if the latent Gaussian variable Zij lies within a specified interval. In addition, another latent Gaussian variable θi, often called a latent trait, is used to model the underlying attributes of individual i. The mean of Zij depends on θi, i.e.

Zij∼N(ajθi−bj,1)

In the item response literature, aj and bj are typically known as discrimination and difficulty parameters respectively.

The extension to a mixture of two parameter item response models, which provides clustering capabilities in the context of ordinal data is also explored. In this context the mean of Zij also depends on which group individual i belongs to, i.e.

Zij∼N(agjθi−bgj,1)

where agj and bgj are group specific discrimination and difficulty parameters.

Estimation of both of these models within the Bayesian paradigm is achieved using a Metropolis-within-Gibbs sampler.

(This talk is part of the Working Group on Statistical Learning series.)

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