Multilevel Modeling

Lecturer: Andrew Bell.

Week 1 (16 - 20 August 2021).

Workshop contents and objectives

Populations commonly exhibit complex structure with many levels, so that patients (level 1) are assigned to clinics (level 2); while individuals (1) may ‘learn’ their behaviour in the context of households (2) and neighbourhood cultures (3). In many cases, the survey design reflects the population structure, so in a survey of voting intentions respondents (1) are clustered by constituencies (2), or in a study of school attainment, pupils (1) are clustered in schools (2). Multilevel models are currently being applied to a growing number of social science research areas, including educational and organisational research, epidemiology, voting behaviour, sociology, and geography. Data at different levels are often seen as a convenience in the design which is a nuisance in the analysis. However, by using multilevel models we can model simultaneously at several levels, gaining the potential for improved estimation, valid inference, and a better substantive understanding of the realities of social organisation.

In this course, and building on standard single-level models, we develop the two-level model with continuous predictors and response. Examples include house-prices varying over districts, and pupil progress varying by school. These models will then be extended to cover complex variation, both within and between levels, three-level models, and models with categorical predictors and response (the multilevel logit model). We end with a consideration of estimators including maximum likelihood and Bayesian MCMC estimators. Throughout the course, we shall use graphical examples, verbal equations, algebraic formulation, class-based model interpretation, and practical exercises that will be completed using either R or MLwiN, depending on students’ preferences and experience.

Prerequisites

Participants should be familiar with regression modelling and inferential statistics, especially regression intercepts and slopes, standard errors, residuals, and the concepts of variance and co-variance. Even so, the aim is not to cover mathematical derivations and statistical theory, but to provide a conceptual framework and ‘hands-on’ experience. It does not require prior knowledge of multilevel modelling. In terms of software, some past experience is required if you wish to use R in the practical exercises, but no experience is required if you wish to use MLwiN.

Software

Students will use either MLwiN or R, depending on their choice, software availability and past experience. Non-windows users will need to use R (due to MLwiN’s incompatability with non-windows operating systems). On occasions, R users will use the package R2MLwiN, which calls MLwiN and its functionality from within R.

The course has the option to use the MLwiN software because of its ability to fit a very broad range of multilevel models in both maximum likelihood and MCMC estimation. It can handle large datasets and has very efficient algorithms for estimation and many tools for post model estimation, thereby providing an ideal learning environment. A free time-delimited 30 day version is available from http://www.bristol.ac.uk/cmm/software/mlwin/download/.

Bibliography

Basic texts/overview (Representative text used during the course)

• Jones, K. and Duncan, C. 1998. 'Modelling context and heterogeneity: Applying multilevel models.' In E. Scarbrough and E. Tanenbaum (eds.), Research Strategies in the Social Sciences. Oxford University Press.
• A large provided course pack will include all necessary reading and transcripts of MLwiN sessions.

In terms of web-based resources, have a look at Centre for Multilevel Modelling.

Remedial Reading

• You must have a good working knowledge of single-level regression modelling including the handling of categorical predictors by dummy variables. If you do not have this knowledge/ experience, do not come on the course. All will benefit from taking the first 3 modules of the free online training provided by Lemma, especially Module 3 as it has been specifically designed to provide the necessary background and links to the software we are going to use.
• Jones, K Multilevel models for geographical research (freely downloadable here).