Multilevel Modelling Using Stata I: Two-level models for continuous responses

Application deadline: TBC

This course is only open to social science PhD students from the Bristol, Bath, Exeter, Plymouth or UWE arms of the South West Doctoral Training Partnership (SWDTP).

To apply for a place, please email and give your name, department and institution. Please only apply for a place if you satisfy the course prerequisites and if you can attend both days.

Instructor: Dr George Leckie

Date: 17-18 May 2017

Time: 10:00 - 17:00

Location: Small Computer Room 1.4n, School of Geographical Sciences, University Road, Bristol, BS8 1SS.

How to get to the University: MapDirections

Description: This course provides an introduction to multilevel modelling for continuous responses (continuous dependent or outcome variables) when the data are clustered or hierarchical. We focus on two-level models for cross-sectional data (individuals nested within groups) and longitudinal data (repeated measures nested within individuals).

On Day 1 we start with a general non-technical overview of multilevel modelling where we introduce the notion of clustering and multilevel data structures. We describe problems with various traditional approaches to dealing with clustered data. We then introduce the simplest multilevel model, the two-level variance components model for measuring the degree of clustering in a continuous response. We then extend this by adding covariates (explanatory or predictor variables) at level-1 and level-2 to explain the within- and between-cluster variability. These models can be viewed as linear regression models where the intercept is allowed to vary across clusters. This allows one to study cluster effects on individual outcomes. Popular applications include using these models to study school effects on student learning, hospital effects on patient outocmes, or country effects on individual attitudes and opinions.

On Day 2, we start by discussing confounding in multilevel models. We explain how regression coefficients can differ within-clusters and between-clusters. We then extend the two-level model to include not just random-intercepts, but random-slopes. This allows the regression coefficients to vary across clusters enabling us to study how the relationships between the response and the covariates can differ across contexts. A particuarlly attractive application is to repeated measurse data, where we can use these models to study variation in individuals' developmental trajectories and the factors which predict differences in growth rates. However, these models can equally be applied to many other social science settings.



10:00 - 12:00 Session 1 - Overview of multilevel modelling - multilevel data structures, typical multilevel research questions, problems with standard analyses, ...
12:00 - 12:45 Lunch
12:45 - 14:45 Session 2 - Variance components models - testing for group effects, variance partition coefficient (VPC) and intraclass correlation (ICC), predicting group effects, shrinkage, …
14:45 - 15:00 Break
15:00 - 17:00 Session 3 - Random-intercept models with covariates - contextual effects, consequence of ignoring clustering, ...


10:00 - 12:00 Session 4 - Between and within-effects of level-1 covariates - pooled OLS models, random-effects models, between-effects models, within-effects models (fixed-effects models), hybrid-effects models, contextual-effects models (Mundlak formulation), Hausman endogeneity test, ...
12:00 - 12:45 Lunch
12:45 - 14:45 Session 5 - Random-coefficient models - cross-level interactions, variance functions (heteroskedasticity), …
14:45 - 15:00 Break
15:00 - 17:00 Session 6 - Growth-curve models - quadratic growth-curve model, including level-2 covariates, including multiple random coefficients, complex level-1 variation (heteroskedasticity), autocorrelated residuals, recentring time

The course will also describe popular multilevel modelling resources which participants can use to support their learning after the course (useful web sites, online course, software, discussion boards, email lists, books, ...).

Each new methodological development will be illustrated with applications to social science data sets. The course will consist of an approximately 2:1 mix of lectures and computer practicals using the Stata statistical software package (especially the -mixed- command). On completion of this course, participants should be able to apply multilevel models to their own data using Stata. 

Prerequisites: Participants must be familiar with estimating and interpreting multiple regression models to the level of knowledge obtained by completing Module 3 of the LEMMA online course (including the writing and interpretation of model equations, hypothesis testing and model selection, and the use and interpretation of dummy variables and interaction terms). No previous knowledge of Stata is assumed. However, participants are encouraged to familiarise themselves with Stata before the course by reading and, ideally, working through the Stata practical which accompanies Module 3 of the LEMMA online course.

Optional background reading: Duncan et al. (1998) provide a non-technical introduction (no equations) to multilevel modelling. Chapter 2 of Hox (2011) provides a more technical introduction.

Other details: Participants are expected to attend both days of the course. Please bring a memory stick so that you can take the course electronic materials away with you. While there is no dedicated time to analysing your own data, you are welcome to apply what you have learnt on the course to your own data during the lunch and coffee breaks should you wish to do so. The instructor will be around for some of this time and is happy to discuss your research with you and in particular to answer questions relating to carrying out multilevel modelling in your own research.

Refreshments: As this is a free course, lunch and coffee are not provided. However, there are various cafes close to the computer lab where you can purchase refreshments.

Contact: Please email George Leckie ( if you have any queries about the course.

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