Session 2: Modelling Social Segregation

1
Modelling Segregation Using Multilevel Models
FSM in England 2001-6
Session 2 Modelling Social Segregation Monday
30th June 2008
2
Outline

• Motivation the importance of segregation
• Research questions
• Data FSM obtained from PLASC
• Traditional index approaches
• Problems with an index approach
• Model-based approach
• Linking the model-based approach to indexes
• Applying the model-based approach
• Extensions of the model-based approach
• The Composition of Schools in England (June 2008)
  

3
Motivation are we become a segregated society?
EG in relation to schools
Virtuous and Vicious circles

• Following 1988 Education Reform Act with emphasis
  on choice, league tables, competition expectation
  of INCREASED segregation

Choice
increased polarization in terms of ability
increased polarization in terms of socio-economic
background poverty ethnicity etc
Choice
4
Research Questions

• FSM eligibility Only statutory available
  information on economic disadvantage
• Has school FSM segregation increased?
• Has LA segregation increased?
• Has segregation been differential between
  different types of LAs
• Which currently are the most segregated LAs in
  England?

5
FSM the data

• Source Pupil Level Annual School Census
• Outcome Proportion of intake Eligible for FSM
• Intake Year 7 of the national curriculum in
  2001-2006,

6
Greater than 25 departure from 6 year median
7
FSM Eligibility criteria
FSM Only statutory available information on
economic disadvantage

• The current eligibility criteria are that parents
  do not have to pay for school lunches if they
  receive any of the following
• Income Support
• Income-based Jobseeker's Allowance
• Support under Part VI of the Immigration and
  Asylum Act 1999
• Child Tax Credit, provided they are not entitled
  to Working Tax Credit and have an annual income
  (as assessed by HM Revenue Customs) that does
  not exceed 14,155
• the Guarantee element of State Pension Credit.
• Children who receive Income Support or
  income-based Job Seeker's Allowance in their own
  right

8
Measuring segregation traditional Index-based
approaches EG D index
Segregation or diversity indexes have a long
history (e.g. Wright 1937) and there are a lot of
them! Duncan and Duncans (1955) D ones of the
most popular
fsmi is number of pupils in school i eligible
for FSM and nonfsmi is number not eligible FSM is
the total number of pupils eligible in LEA
NONFSM is number not eligible D- 0, schools are
evenly mixed 0.3 30 of pupils move to get
evenness
NB based on OBSERVED proportions and little or
nothing is know about the sampling properties of
segregation measures (Reardon and Firebaugh,
2002, 100)
9
The need to go beyond an Index
Consider a pair of schools where we measure
proportion eligible for FSM and define
segregation as the absolute difference between
the pair Diff Index p1 p2
What values can we get for Index when there is no
real change, just stochastic fluctuations? Simula
te data and calculate Index when no real
change - 3000 pairs of schools, representing
two time points - true underlying proportion is
0.15 for both time points - no of pupils in
entry cohort in each school is 20 (n)
Mean of distribution is 0.079 Apparent
substantial change!
10
Expected value of the Difference Index(if just
stochastic fluctuations)
where is underlying proportion, N is number
of pupils in each school.
Diff of 3 even when n 200
The same thing applies to other Indices.
11

• E the expected value for D if there was NO
  segregation
• Structured higher D when small schools and more
  extreme proportion

12
Model-based approaches

• Traditional index construction uses definitions
  based upon observed proportions.
• By contrast, a statistical model-based approach
  allows us to make inferences about underlying
  processes by allowing random fluctuations that
  are unconnected with the difference of interest
• Extract parameters (signal) from the
  stochastic noise
• Either use parameters as natural measure of
  segregation OR simulate from parameter and use
  indices after taking account of random
  fluctuations
• Moreover Multilevel model .

13
Benefits of multilevel approach

• Explicit and separate modelling of trends and
  segregation fixed part of model gives general
  trend variance between schools gives segregation
• Simultaneous modelling of segregation at any
  level eg decreasing at LA (local economy?), but
  increasing School (admission policies?)
• Segregation for different types of areas not
  just variances, but variances as a function of
  variables
• Explicit modelling of binomial fluctuations
• Confidence intervals
• BUT the approach is retrograde, and of no clear
  practical value (Gorard, 2004)

14
(No Transcript)
15
Results from simple model
Logit -1.84 when transformed median of 0.137
(95 CIs 0,133 and 0.142) and mean of 0.182
(0.177 and 0.187)
Significant between school segregation Equivale
nt to a D of 0.374 (see next slide)
Distributional assumptions for school differences
16
Linking models to indexes

• Using model parameters we can derive expected
  values of any function of underlying school
  probabilities
• Consequently, derive index by simulation from
  model parameters.

EG Converting logit Variance to D (simulate 500k
Logits with a given underlying mean and variance
convert to proportions, and calculate Index)
Variance of 0.7 equals D-Index of 0.30
17
Behaviour of the indexesUsing simulation

18
Gorard G index

Note how a change can be either due to changing
dispersion or mean
19
Back to Results from simple model
Logit -1.84 when transformed median of 0.137
(95 CIs 0,133 and 0.142) and mean of 0.182
(0.177 and 0.187)
Significant between school segregation Equivale
nt to a D of 0.374
Distributional assumptions for school differences
20
Results for simple model repeated for each entry
cohort 2001-2006
Segregation changes smaller than uncertainty
Median small improvement
21
Three-level model partitioning between LA, and
between school variance

• 3 Changes
• Pupils (i) in schools (j) In LAs (3)
• Average LA difference School difference
• Between LA difference
• Within LA, between school
• Modelling at two scales simultaneously

22
Results for 3 level model

• 3 level model applied to each cohort separately
• compared with Goldstein and Noden (earlier and
  overall school and not entry cohort)

• Greater segregation between schools than between
  LAs
• LAs trendless fluctuations
• Continued increasing between-school segregation

23
Area characteristics 1

• Are LAs that are selective (Grammar/Secondary)
  more segregated than totally Comprehensive
  systems?
• 3 level model, with a different variance for
  schools within different LA characteristics

• Average FSM
• - for English pupils living in a non-
  selecting LA
• - for English pupils living in a selecting
  LA
• Between LA variance
• Within LA
• - between school variance for schools located in
  a non-selecting LA
• - between school variance for schools located in
  a selecting LA

24
Results for Non and Selecting LAs

• Schools in Selecting areas are more segregated
• Slight evidence of an increase

• Pupils going to school in Selecting
• LAs are less likely to be in poverty
• Slight decline in poverty in both types of area

25
Area characteristics 2

• Is there more segregation in areas that are
  selective and where less schools are under LA
  control in terms of admission policies?
• Variance function for Selective/Non-selective,
  structured by the proportion of pupils in an LA
  who go to Community or Voluntary Controlled
  schools (contra Voluntary Aided,Foundation,
  CTCs, Academies)

• FSM over the period 2001-6
• Average FSM in selecting and non- selecting
  LAs and how this changes with degree of LA
  control
• Between LA variance
• Within LA between schools
• - variance function for non-selecting LA
• - variance function for selecting LA

26
Results for Non and Selecting LAs

• Schools in Selecting areas are more segregated
• Segregation decreases with greater LA control for
  both types of LA

• Pupils going to school in Non-Selecting LAs with
  low LA control are more likely to be in poverty

27
Area characteristics 3

• Which of Englands LAs have the most segregated
  school system?
• Model with 144 averages and 144 variances, one
  for each LA!

28
(No Transcript)
29
LAs with highest segregation (not including
estimates lees than 2 SE)
30
Extensions of the model-base approach

• multi- categorical responses eg ethnic group
  segregation.
• Multiple and crossed (non-nested levels) eg
  schools and neighbourhoods simultaneously
• Multiple responses in a multivariate model eg.
  model jointly the variation in the proportion FSM
  proportion entering with high levels of
  achievement
• Modelling spatial segregation with MM models

31
The Composition of Schools in England

• What they did
• Calculate D for LAs in 1999 and 2007 (ignoring
  sampling variability)
• Regress D for LAs on variables EG prop of LA in
  Grammar schools prop of faith schools, prop with
  FSM compare R2s
• What they found
• The level of FSM segregation increased for most
  LAs, but the average increase was relatively
  small.
• Levels of FSM primary segregation more
  associated with the prop of FSM than any other LA
  characteristics.
• Levels of FSM secondary segregation more
  associated with the proportion in grammar schools
  than any other LA characteristics.
• Some difficulties
• Sampling variability and n
• ignores the nature of the Index that a more
  extreme proportion will produce higher D (eg
  Poole highest increase in segregation but also
  highest drop in FSM 1999-2007) scale artefact
• - school size differs by type, and D index
  related to size of school
• Levels no recognition of within and between
• - eg does not address is there more segregation
  among schools within LAs for faith schools
• Regression models
• -Focus on R2s, but variation in D that cannot
  be explained, again not taken account of size

32
References

• Allen, R. and Vignoles, A. (2006). What should an
  index of school segregation measure? London,
  Institute of Education.
• Duncan, O. and B. Duncan (1955). A methodological
  analysis of segregation indexes American
  Sociological Review 20 210-217.
• Hutchens, R. (2004). One measure of segregation.
  International Economic Review 45 555-578.
• Goldstein, H. and Noden, P. (2003). Modelling
  social segregation. Oxford Review of Education
  29 225-237
• Gorard, S. (2000). Education and Social Justice.
  Cardiff, University of Wales Press.
• Gorard (2004) Comments on 'Modelling social
  segregation' by Goldstein and Noden, Oxford
  review of Education, 30(3), 435-440
• Reardon, S and Firebaugh, G (2002) Response
  segregation and social distance- a generalised
  approach to segregation measurement Sociological
  Methodology, 32, 85-101.