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Developing multilevel models for REAListically COMplex social science data

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The ESRC has rated this project as outstanding. The outstanding grade indicates that a project has fully met its objectives and has provided an exceptional research contribution well above average or very high in relation to the level of award. Go to ESRC award details.

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The project developed new methodology and associated training materials in the following areas of multilevel modelling: structural equation models, measurement errors and multivariate mixed response types at more than one level of the data hierarchy.

The methodology builds upon that already implemented in MLwiN version 2.02 which is described in the MLwiN manuals. The training materials are written in MATLAB. and are available as free-standing programs. They are designed to interface with MLwiN in terms of data transfer but have their own graphical user interfaces for setting up models and displaying results. There is a set of training materials which provides an introduction to the methodology and a guide to using the software.

Applications are to a variety of problems, including flexible prediction models, multiple imputation for missing data in multilevel models, and misclassification errors in social status data.

Three repeated 1-day workshops were held in Bristol, London and Birmingham, June/July 2007.

Papers

Modelling measurement errors and category misclassifications in multilevel models

Harvey Goldstein, Daphne Kounali and Anthony Robinson: Statistical Modelling 2008; 8 (3): 243-261

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Models are developed to adjust for measurement errors in normally distributed predictor and response variables and categorical predictors with misclassification errors. The models allow for a hierarchical data structure and for correlations among the errors and misclassifications. Markov Chain Monte Carlo (MCMC) estimation is used.

The models with examples are also described in the REALCOM training manual and users can fit these in the REALCOM software.

Multilevel Structural Equation Models for the Analysis of Comparative Data on Educational Performance

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Harvey Goldstein, Gérard Bonnet, Thierry Rocher Ministère de l’Education Nationale, de l’Enseignement Supérieur et de la Recherche, Direction de l’Évaluation et de la Prospective, Paris

The Programme for International Student Assessment comparative study of reading performance among 15-year-olds is reanalyzed using statistical procedures that allow the full complexity of the data structures to be explored. The article extends existing multilevel factor analysis and structural equation models and shows how this can extract richer information from the data and provide better fits to the data. It shows how these models can be used fully to explore the dimensionality of the data and to provide efficient, single-stage models that avoid the need for multiple imputation procedures. Markov Chain Monte Carlo methodology for parameter estimation is described.

Multilevel Models with multivariate mixed response types

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Harvey Goldstein, James Carpenter, Michael G Kenward, Kate A Levin

We build upon the existing literature to formulate a class of models for multivariate mixtures of Gaussian, ordered or unordered categorical responses and continuous distributions that are not Gaussian, each of which can be defined at any level of a multilevel data hierarchy. We describe a MCMC algorithm for fitting such models. We show how this unifies a number of disparate problems, including partially observed data and missing data in generalised linear modelling. The 2-level model is considered in detail with worked examples of applications to a prediction problem and to multiple imputation for missing data. We conclude with a discussion outlining possible extensions and connections in the literature. Software for estimating the models is freely available.

This paper is based upon the REALCOM research project.

The Realcom team

Harvey Goldstein, (Project Director), Jon Rasbash, Fiona Steele (Co-Directors), Christopher Charlton (Research Officer), Hilary Browne (Web Developer), Sophie Pollard (Project Assistant)

This three-year ESRC-funded research project developed multilevel modelling techniques, software and training materials in three areas: models with responses at several levels of a data hierarchy, multilevel structural equation models, and measurement error modelling.  The models developed under the project were estimated using Markov Chain Monte Carlo (MCMC) estimation.

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