Post on 16-Jan-2016
Workshop 1
• Specify a multilevel structure for EITHER a response variable of your choice OR for a model to explain house prices OR voting behaviour
Template for answer• what is the response (must always be measured at
level 1)?• What are the levels: 1, 2 , etc?• What are the predictor variables, and at what level are
they measured (1,2 etc)?
Varying relationships
“There are NO general laws in social science that are constant over time and independent of the context
in which they are embedded”
Rein (quoted in King, 1976)
VARYING RELATIONS• Multilevel modelling can handle
- multiple outcomes- categorical & continuous predictors- categorical and continuous responses
• But KISS………
• Single response: house price• Single predictor
- size of house, number of rooms
• Two level hierarchy- houses at level 1 nested within- neighbourhoods at level 2 are the contextsSet of characteristic plots………………
3210-1-2-3-4
87654321Rooms
Example of varying relations (BJPS 1992)• Stucture: 3 levels strict hierarchy
individuals within constituencies within regions
• Response: Voting for labour in 1987
• Predictors
1 age, class, tenure, employment status
2 %unemployed, employment change, % in mining in 1981
• Expectation: coal mining areas vote for the left
• Allow: mining parameters for mining effect(2) to vary over region(3) in a 3-level logistic model
Varying relations for Labour voting and % mining
Type of questions tackled by multilevel
modelling I • 2-level model: current attainment given prior attainment of pupils(1)
in schools(2)• NB assuming a random sample of pupils from a random samples of
schools
• Do Boys make greater progress than Girls (F)
• Are boys more or less variable in their progress than girls?(R)
• What is the between-school variation in progress? (R)
• Is School X different from other schools in the sample in its effect?
(F)
• continued…….
Type of questions tackled by multilevel
modelling II • Are schools more variable in their progress for pupils with low
prior attainment? (R)
• Does the gender gap vary across schools? (R)
• Do pupils make more progress in denominational schools?(F)
• Are pupils in denominational schools less variable in their
progress? (R)
• Do girls make greater progress in denominational schools?
(F) (cross-level interaction)
Workshop 2
• Draw a diagram relating a response (fat consumption) to a continuous predictor (age) centred around its national mean with the following characteristics
no national relationship; substantial differences between seven 6 places in terms of the elderly, but less marked for middle-ages and least for young
Workshop 3
• Draw three separate graphs showing the following relations between response of house prices and a 3-category predictor (detached, semi-detached, terrace)
• a) differences between 3 categories of housing but no differences between places
• b) differences between 3 categories of housing and same differences between places (random intercepts model)
• c) differences between 3 categories of housing and different differences between places (random intercepts & slopes)
• HINT: use different colours or line styles to show different places
Higher-level variables• So far all predictors have been level 1 (Math3,
boy/girl); (size,type of property)
• Now higher level predictors (contextual,ecological)
- global occurs only at the higher level;
-aggregate based on summarising a level 1 attribute
• Example: pupils in classes
progress affected by previous score (L1); class average
score (A:L2); class homogeneity (SD, A:L2); teaching style
(G:L2)
• NOW: trying to account for between school differences
Systematic Social Observation
Policy variables
Environmental, Physical attributes of an area
Measure attributes of groups, organizations, or areas.
Occurs uniquely at the higher level.
Individual analogue cannot be measured, thus, irreducible.
Integral, Global
Proportion smokers
Suicide rate
Infectious disease prevalence
Aggregate of the individual-level outcome, rather than predictor, that in turn predicts the individual name-sake of the same variable.
Individual analogue is the outcome.
Contagion, Peer
Mean/Median income
Proportion reporting mistrust
Gini coefficient for inequality
Aggregate of attributes measured at the individual (or lower) level.
Expressed as a measure of central tendency (e.g. mean, median), or measures of variation of individual-level variables (e.g. standard deviation), but caution when sample-based.
Individual analogue can often be measured.
Derived, Aggregate,Collective
Examples DescriptionTypology
Main and cross-level relationships:a graphical typology
The individual and the ecological - 1
% Working class
Pro
pen
sity
for
left
vot
e
High SES
Low SES
The individual and the ecological - 2
% Working class
Pro
pen
sity
for
left
vot
e
High SES
Low SES
The individual and the ecological - 3 consensual
% Working class
Pro
pen
sity
for
left
vot
e
High SES
Low SES
A graphical typology of cross-level interactions (Jones & Duncan 1993)
Consensual
Individual Ecological
Reactive
Reactive for W; Consensual for M
Non-linear cross-level interactions
• STRUCTURE: 2275 voters in 218 constituencies, 1992• RESPONSE: vote Labour not Conservative• PREDICTORS: Level- individual: age, sex, education, tenure, income 1
: 8-fold classification of class- constituency:% Local authority renters 2
% Employers and managers;100 - % Unemployed
• MODEL: cross-level interactions between INDIVIDUAL&CONSTITUENCY characteristics
Fixed part main effects: 8 fold division of classRandom part at level 2: 2 fold division of classWorking class: unskilled and skilled manual, foremanNon-working class:public and private-sector salariat, routine non-
manual, petty-bourgeoisie, ‘unstated’
Cross-level interactions
Conclusions3 Substantive advantages
1 Modelling contextuality and heterogeneity
2 Micro AND macro models analysed simultaneously
-avoids ecological fallacy and atomistic fallacy
3 Social contexts maintained in the analysis; permits intensive, qualitative research on ‘interesting’ cases
“The complexity of the world is not ignored in the pursuit of a single universal equation, but the specific of people and places are retained in a model which still has a
capacity for generalisation”
Fat
Age-46
District level price-type relationship