Multilevel models : practical applications
Kelvyn Jones is Professor and Head of the Department of Geography at the
University of Portsmouth and Co-director of Health Information Research
Services. He has held a Nuffield Social Science Fellowship for investigating
multilevel modelling. He teaches research design, quantitative techniques,
and the geography of health. His publications include Health, Disease and
Society (Routledge) and articles in Social Science and Medicine, British
Medical Journal, British Journal of Political Science, Environment and
Planning. He has taught multilevel workshops in Scotland, Canada, the
Netherlands, Belgium. and at the Essex summer school throughout the 1990's
Populations commonly exhibit complex structure with many levels, so that
workers (at level 1) work in particular orgaizational environments (at level
2); while individuals (1) may 'learn' their health-related behaviour in the
context of households (2) and local cultures (3). Similar data structures
result from multi-stage sample surveys so that respondents (1) are nested
within households (2), in postcode sectors (3), in districts (4), and in
regions (5). In many cases, the survey design reflects the population
structure, so in a survey of voting intentions the respondents (1) are
clustered by constituencies (2). Multilevel models are currently being
applied in a growing number of social science research areas including
educational and organisational research, epidemiology, voting behaviour,
sociology, and geography.
These levels in data are often seen as a convenience in the design which has
become 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.
In substantive terms, by working simultaneously at the individual and
contextual levels, these analytic models begin to reflect the realities of
social organisation. 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 course begins by building on standard single-level models, and we
develop the two-level model with continuous predictors and response.
Examples of analysis will include house prices varying over districts, and
pupil progress varying by school. These models are subsequently extended to
cover complex variation, both within and between levels, three-level models,
and models with categorical predictors and response (the multilevel logit
model). A common pattern of delivery is used throughout the course:
graphical examples, verbal equations, algebraic formulation, class-based
model interpretation, and practical modelling using the software package Mln/
Mlwin
On completion of the course, participants should be able to recognise 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-type data, multivariate
responses, or survival data, although the course does provide the groundwork
for these extensions. This course is appropriate if you are analysing 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 organisation.
Bibliography
Remedial Reading
Weisberg, S. 1980. Applied Linear Regression. Wiley. chs. 1 and 2.
Main references (used during the workshop)
- Paterson, L. and Goldstein, H. 1992. 'New statistical models for analysing
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.
In terms of web-based resources, have a look at
Multilevel models project (IOE London)
and
Multilevel searchable mailbase list
Prerequisites
Participants taking this course should have some familiarity with regression
modelling and inferential statistics. The aim is not to cover mathematical
derivations and statistical theory, but to provide a conceptual framework and
hands-on experience with the interactive package MLwin. Students should
understand regression intercepts and slopes, standard errors, t-ratios,
residuals, and concepts of variances and covariances. In terms of software,
previous exposure to Dos and Windows environments is all that is required.
Multilevel models cannot currently be fitted using standard packages such as
SPSS. Consequently full training will be given in Mlwin.