Download Session 3 Multi-level Modelling – Andrew Bell

Multilevel Modelling
Dr Andrew Bell,
Lecturer in Quantitative Social Sciences
A basic linear regression model
Y = B0 + B1*X + e
Y
e
X
What’s the problem?
Assume that the residuals (e) are independent from each other.
Ie that the model has accounted for everything systematic
only white noise remains
This is often simply not realistic
Multilevel structures
“once you know hierarchies exist, you see them everywhere” (Kreft and
De Leeuw, 1998 p1)
Hairs on heads
Students nested in schools
Voters nested in electoral wards
Cows nested in farms
Occasions nested in individuals (panel data)
Occasions nested in students nested in schools
Multilevel structures
“once you know hierarchies exist, you see them everywhere” (Kreft and
De Leeuw, 1998 p1)
Non-hierarchical structures:
• Students in both schools and neighbourhoods
• Students in more than one classroom
• F1 race results nested in drivers and teams
A basic linear regression model
Y = B0 + B1*X + e
Y
e
X
A basic linear regression model
Y = B0 + B1*X + e
Y
e
X
A basic multilevel model
Y = B0 + B1*X + u + e
Y
u
e
X
What are we doing?
• Modelling complex structures
• Modelling heterogeneity
• Modelling dependency
• Modelling context
Why use MLMs? Toy example
Sometimes:
single level
models can be
seriously
misleading!
An example:
‘contextual value
added’ school
league tables
age16attainment = 0.002 + 0.563*age11attainment
Another example
•Reinhart and Rogoff – Growth in a time of debt (2010)
•“median growth rates for countries with public debt over
roughly 90 percent of GDP are several percent lower.”
•Conclusions used by Paul Ryan, David Cameron, etc, to justify
austerity policies
Another example
• Problems with it (1)
•Arbitrary exclusion of countries
•A weird weighting system
•An excel spreadsheet error that excluded a number of observations
alphabetically
• Herndon, Ash and Pollin (2013) Does high public debt consistently stifle
economic growth? A critique of Reinhart and Rogoff. Cambridge Journal of
Economics, online.
Another example
• Problems with it (2)
•Assumes a single consistent effect, rather than allowing
that effect to vary between countries.
• But why should the effect of debt on growth be the
same in USA and Britain?
• Instead, can use multilevel models to allow for differences
across countries
Country
Year
Bell, Jones and Johnston (2015) Stylised fact or situated messiness? The
diverse effects of increasing national debt on economic growth. Journal
of Economic Geography, 15(2), 449-472
8
Another example (and back to 2 levels)
6
New Zealand
Australia
Predicted Growth (%GDP)
4
UK
2
US
0
-2
Japan
-4
0
70
140
Debt:GDP ratio
210
Variance Functions
•Key aim of multilevel models: model heterogeneity – the variance can
vary!
•As well as estimating separate effects for higher level entities, we can
see how much variance varies
•Eg schools matter more (are more varied) for clever students
Final example: F1 racing
Team
Driver
Team-Year
Observation
Final example: F1 racing
Final example: F1 racing
Overall
• Why multilevel models are good:
•Technically sound: Make realistic assumptions about independent residuals;
explicitly model heterogeneity and dependency (rather than ‘correct’ for it)
•Substantively interesting: Answer questions you cannot answer with standard
modelling techniques
•Widely applicable: education, epidemiology, veterinary science,
political/electoral science, economics, biology, geography............
Useful resource
•CMM LEMMA training courses
•https://www.cmm.bris.ac.uk/lemma/
•Online courses from multilple regression (module 3), up to a
range of different MLM structures, outcomes, etc
•Practical exercises using MLwiN, Stata, R, SPSS
•Free, you just need to register
Shameless self promotion
• Bell, Andrew, and Kelvyn Jones. 2015. “Explaining Fixed Effects: Random
Effects Modelling of Time-Series Cross-Sectional and Panel Data.” Political
Science Research and Methods 3(1): 133–53.
• Comparison of MLM (or ‘Random Effects’) to Fixed effects modelling;
and argues for the benefits of the former
• Bell, Andrew, Ron Johnston, and Kelvyn Jones. 2015. “Stylised Fact or
Situated Messiness? The Diverse Effects of Increasing Debt on National
Economic Growth.” Journal of Economic Geography 15(2): 449–72.
• Bell, Andrew, James Smith, Clive Sabel, Kelvyn Jones. 2016. Formula for
success: Multilevel modelling of Formula One driver and constructor
performance, 1950-2014. Journal of Quantitative Analysis in Sports 12(2):
99-112
Email: [email protected]
Tweet @andrewjdbell