jones

Kelvyn Jones is Professor of Geography at the School of Geographical Sciences, University of Bristol. He teaches research design, quantitative techniques, and the geography of health. He was the inaugural Director of Learning Environment for Multilevel Methodology and Applications, an ESRC National Centre for Research Methods. His publications include Health, Disease and Society (Routledge), and articles in Social Science and Medicine, British Medical Journal, Area, British Journal of Political Science, Environment and Planning. He has taught multilevel workshops in Scotland, Canada, the Netherlands, Belgium, Switzerland and the USA. He is in the top 20 most highly cited human geographers over the last fifty years. He is an Academician of the Social Sciences. In 2016 he received the UK’s highest accolade for social scientists, being elected a Fellow of the British Academy for the quality of his research in quantitative social science. Further details from http://www.bristol.ac.uk/geography/people/kelvyn-jones/

Overview: this course is an applied introduction to multilevel modelling that aims to give you deep understanding of the standard model. It does not presume any prior knowledge in multilevel modelling but does require you to be very familiar with multiple regression analysis.

Course Content: 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 health-related behaviour in the context of households (2) and local 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). 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 the first week of the 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. In the second week, these models are 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 (operationalized through iterative generalized least squares) and a full Bayesian approach (operationalized through Monte-Carlo Markov Chain) Throughout the course, we shall use graphical examples, verbal equations, algebraic formulation, class-based model interpretation, and practical modeling using the software package MLwiN. We use this package because of its flexibility, graphics capability and the possibilities of estimating model via maximum likelihood and MCMC methods.

Course Objectives: On completion of the course, participants will be able to recognize a multilevel structure, specify a multilevel model with complex variation at a number of levels, and fit and interpret a range of multilevel models. The course does not cover multilevel analysis of panel data, multivariate responses, or survival data, although the course does provide the essential groundwork for these extensions. This course is appropriate if you are analyzing a survey with complex structure, are interested in the importance of contextual questions, or if you need to undertake a quantitative performance review of an organization. A distinctive feature of the course is the focus on variance functions estimated simultaneously as several levels.

Course Prerequisites: This is not an introductory course to statistical modelling, as participants require familiarity with regression modeling and inferential statistics, especially regression intercepts and slopes, standard errors, t-ratios, 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 with MLwiN. It does not require prior knowledge of multilevel modelling.

Remedial Reading:
Weisberg, S. 1980. Applied Linear Regression. Wiley. Chs. 1 and 2. Or equivalently, participants are strongly encouraged to undertake the Lemma course on regression modelling before coming to Essex; modules 1 to 3 of http://www.cmm.bristol.ac.uk/learning-training/course.shtml

Background Reading:
Paterson, L., and Goldstein, H. 1992. ‘New statistical models for analyzing social structures: An introduction to multilevel models’, British Education Research Journal, 20:190-9.
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.
Jones, K Multilevel models for geographical research; freely downloadable from https://www.researchgate.net/profile/Kelvyn_Jones

Overview:

This course is an applied introduction to multilevel modelling that aims to give you deep understanding of the standard model. It does not presume any prior knowledge in multilevel modelling but does require you to be very familiar with multiple regression analysis.

What are multilevel models?

Populations commonly exhibit complex structure with many levels, so that patients (at level 1) are assigned to clinics (at level 2); pupils (1) attend schools (2), while individuals (1) may ‘learn’ their health-related behaviour in the context of households nested within households (2), in postcode sectors (3) in districts (4) in regions (5). In many cases the survey design reflects the structure of the population so that in a survey of voting intentions, the respondents (1) are clustered by constituencies (2).

Longitudinal designs also give rise to multilevel structures so that there could be annual, repeated measures of income (level 1) on individuals (2) in different sectors of the economy (3). Another type of repeated-measures design is when the repetition occurs at the higher level. Thus schools (level 3) could be repeatedly monitored every year (2) for the performance of their students (1). Another possibility is a ‘multivariate’ structure where a number of different but related measurements are made on individuals. For example, there may be measurements of smoking, drinking and eating (all at level 1) for individuals (2) in communities (3). Yet another possibility arises in meta-analysis where an attempt is made to summarise quantitatively the results for subjects (level 1) nested within several studies (2). All these examples have so far been strictly hierarchical so that each lower unit nests exactly into one, and only one, higher-level unit. It is also possible to have cross-classified structures such as pupils (level 1) nested in neighbourhoods (2) and schools (also level 2), or respondents (1) in a survey nested within areas (2) and interviewers (2).

In traditional analysis these levels in the data are often seen as a convenience in the design which has become a nuisance in the analysis. In contrast, by using multilevel models we are able to model simultaneously at several levels, gaining the potential for improved estimation, valid inference, and a better substantive understanding. In substantive terms, by working simultaneously at the individual and contextual levels, these analytic models begin to reflect the social organisation of life. By providing estimates of both the average effect of a variable over a number of settings, and the extent to which that effect varies over settings, these models provide a means of ‘thick’ quantitative description. The complexity of the real-world of people and places, both with a history, is not ignored in the pursuit of a single universal equation.

Daily Topic

1 Hierarchies and levels; introducing multilevel structures; unit and classification diagrams, fixed and random classifications, what alternatives from of analysis are available, and why they are inferior to random coefficient modelling?

2 Contextuality and varying relationships

3 From graphs to equations; random intercepts; a worked example; houses within neighbours; context and composition

4 Random-slope models; exemplification with analysis of school performance

5 Modelling population heterogeneity: between-group variability, understanding dependency and autocorrelation

6 Models with complex heterogeneity at level 1; between-individual variability; significance testing

7 Models with categorical predictors; complex heterogeneity at level 1 and level 2

8 Variables at higher-levels; modelling the effects of environmental quality on house prices

9 Estimation, properties of shrinkage estimates, full information maximum likelihood and REML, a practical introduction to Bayesian modelling using MCMC estimation, DIC

10 Going further – models with categorical response; longitudinal analysis, spatial models; review and conclusions.

A common pattern is generally adopted throughout the course:

• Introduction of concept, usually through graphs with a specific example
• Turning the graphs into multilevel equations
• Specifying the equations in the MLwiN software
• Interpreting the results
• Hands-on experience of fitting and interpreting the results using MLwiN

An extensive training manual is provided which additionally covers models for counts (Poisson and NBD models) and three-level models. Participants apply the procedures illustrated in the training manual to other provided data sets. MLwiN is used because of the variety of models that can be specified and estimated and because of the excellent facilities for post-estimation interpretation and display. MLwiN can be called from Stata and from R.