Andrew Bell is Lecturer in Quantitative Social Sciences at the Sheffield Methods Institute at the University of Sheffield. Before moving to Sheffield, Andy was a lecturer at the University of Bristol, where he also completed his undergraduate degree (in Geography) and PhD (in Advanced Quantitative Methods). His current substantive research focuses on mental health from a life course perspective, but also spans a diverse range of other subject areas, including geography, political science, social epidemiology and economics. Methodologically, Andy’s interests are in the development and application of multilevel models, with work focusing on age-period-cohort analysis and fixed and random effects models.

Course content
This course is an introduction to some more advanced extensions to the multilevel models introduced in the course “Multilevel analysis: concepts and applications” taught by Kelvyn Jones (24th July – 4th August). It is thus suitable for those familiar with the material covered in that course, who want to extend those concepts to models with non-continuous outcomes, more than 2 levels, non-hierarchical data structures, and data with a temporal dimension. The course will be taught primarily in MLwiN, but with some sections taught in Stata or R. In particular we will cover non-continuous Y variables with multilevel models, non-nested structures, different estimation methods (both Bayesian and Frequentist), and both longitudinal and cross-sectional data. We will also cover simulation studies: what they are for, what they show, and how to perform them.

Objectives
This module emphasises the practical use of multilevel models of various types. You will learn how to specify, run and interpret models for a range of different structures, for different data types (continuous, count, and categorical Y varaibles) for cross-sectional and longitudinal data. You will also learn how to conduct simulation studies to understand and assess the performance of the models that you are using.

Prerequisites
Students will need to be familiar with the content of Kelvyn Jones’ course “Multilevel analysis: concepts and applications”. They would thus either need to have attended that course, or have been through module 5 of the LEMMA online course and feel comfortable applying those methods to their own datasets, using MLwiN.

An extensive training manual is provided We will use MLwiN throughout the course. At times we will use runmlwin and r2mlwin, which is a Stata/R package that allows MLwiN to be called from within Stata/R. As such, some experience of these software packages would be beneficial.

Remedial Reading
The best preparation for the course would be to complete Module 5 of the Centre for Multilevel Modelling’s LEMMA course: http://www.cmm.bristol.ac.uk/learning-training/course.shtml. You should be comfortable undertaking the practical using the MLwiN software.

Representative Background reading
Bell, A and Jones, K (2013) The impossibility of separating age, period and cohort effects. Social Science & Medicine, 93, 163-165
Bell, A and Jones, K (2015) Explaining fixed effects: random effects modelling of time-series cross-sectional and panel data. Political Science Research & Methods, 3(1), 133-153
Bullen, N, Jones, K and Duncan, C (1997) Modelling complexity: analysing between-individual and between-place variation – a multilevel tutorial. Environment and Planning A, 29, 585-609.

Timetable

Day 1: Introduction; Recap of concepts behind 2-level multilevel modelling (including random itercepts, Bayesian shrinkage, cross-level interactions, etc

Day 2: Continued recap of 2-level models (random slopes, variance functions, etc) and extending that to three-level models

Day 3:
Estimation methods: shrinkage estimators; maximum likelihood, restricted maximum likelihood, Bayesian modelling and MCMC estimation

Day 4: Simulation studies 1: What are simulation studies, why do them, key concepts, using runmlwin and r2mlwin

Day 5: Simulation studies 2: Key quantities of interest, displaying results from simulations

Day 6: Multilevel Logit models: From continuous Y to GLM; conditional and marginal estimators

Day 7: Multilevel Poisson/Negative Binomial models

Day 6: Non-hierarchical structures: cross classified models and multiple membership models

Day 9: Longitudinal analysis 1: Fixed and Random effects models

Day 10: Longitudinal analysis 2: life-course models; age-period-cohort modelling