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The Choice Between Fixed and Random Effects Models: Some Considerations For Educational Research. Clarke, Crawford, Steele and Vignoles and funding from ESRC ALSPAC Large Grant. Motivation.

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the choice between fixed and random effects models some considerations for educational research

The Choice Between Fixed and Random Effects Models: Some Considerations For Educational Research

Clarke, Crawford, Steele and Vignoles

and funding from ESRC ALSPAC Large Grant

motivation
Motivation
  • Need evidence from different disciplines to answer the research question : how can we improve pupil achievement?
  • Contribute to multi-disciplinary understanding by comparing common alternative models used by different disciplines
introduction
Introduction
  • Pupils clustered within schools → hierarchical models
  • Two popular choices: fixed and random effects
  • Choice of model:
    • Often driven by discipline tradition – economists use fixed effects for example
    • May depend on whether primary interest is pupil or school characteristics
illustrations
Illustrations
  • What is the impact of SEN status on pupil achievement?
  • What is the impact of FSM status on pupil achievement?
why adjust for school effects
Why adjust for school effects?
  • Want to estimate causal effect of SEN on pupil attainment no matter what school they attend
  • Need to adjust for school differences in SEN labelling
    • e.g. children with moderate difficulties more likely to be labelled SEN in a high achieving school than in a low achieving school (Keslair et al, 2008; Ofsted, 2004)
    • May also be differences due to unobserved factors
  • Hierarchical models can account for such differences
    • Fixed or random school effects?
basic model
Basic model
  • FE: us is school dummy variable coefficient
  • RE: us is school level residual
    • Additional assumption required: E [us|Xis] = 0
      • That is, no correlation between unobserved school characteristics and observed pupil characteristics
  • Both: both models assume: E [eis|Xis] = 0
    • That is, no correlation between unobserved pupil characteristics and observed pupil characteristics
how to choose between fe and re
How to choose between FE and RE
  • Very important to consider sources of bias:
    • Is RE assumption (i.e. E [us|Xis] = 0) likely to hold?
  • Other issues:
    • Number of clusters
    • Sample size within clusters
    • Rich vs. sparse covariates
    • Whether variation is within or between clusters
  • What is the real world consequence of choosing the wrong model?
sen sources of selection
SEN: Sources of selection
  • Probability of being SEN may depend on:
    • Observed school characteristics
      • e.g. ability distribution, FSM distribution
    • Unobserved school characteristics
      • e.g. values/motivation of SEN coordinator
    • Observed pupil characteristics
      • e.g. prior ability, FSM status
    • Unobserved pupil characteristics
      • e.g. education values and/or motivation of parents
intuition i
Intuition I
  • If probability of being labelled SEN depends ONLY on observed school characteristics:
    • e.g. schools with high FSM/low achieving intake are more or less likely to label a child SEN
  • Random effects appropriate as RE assumption holds (i.e. unobserved school effects are not correlated with probability of being SEN)
intuition 2
Intuition 2
  • If probability of being labelled SEN also depends on unobserved school characteristics:
    • e.g. SEN coordinator tries to label as many kids SEN as possible, because they attract additional resources
  • Random effects inappropriate as RE assumption fails (i.e. unobserved school effects are correlated with probability of being SEN)
  • FE accounts for these unobserved school characteristics, so is more appropriate
    • Identifies impact of SEN on attainment within schools rather than between schools
intuition 3
Intuition 3
  • If probability of being labelled SEN depends on unobserved pupil/parent characteristics:
    • e.g. some parents may push harder for the label and accompanying additional resources;
    • alternatively, some parents may not countenance the idea of their kid being labelled SEN
  • Neither FE nor RE will address the endogeneity problem:
    • Need to resort to other methods, e.g. IV
slide13
Data
  • Avon Longitudinal Study of Parents and Children (ALSPAC)
    • Children born in Avon between April 1991 and December 1992
    • Rich data
      • Family background (including education, income, etc)
      • Medical and genetic information
      • Clinic testing of cognitive and non-cognitive skills
      • Linked to National Pupil Database
slide14
SEN
  • One in four pupils in England have SEN age 10
  • Just under 4% have statement
  • In 2003-04, the period relevant to our data, approximately £1.3billion spent on primary school SEN (excluding special schools)
    • £1,600 per pupil with SEN
slide15
SEN
  • Substantial variation in %SEN across schools
  • Quarter of schools have fewer than 15% SEN
  • Quarter with more than 24% SEN
  • Key question is whether the factors driving differences in % SEN between schools are correlated with unmeasured school-level influences on academic progress
results from this analysis
Results from this analysis
  • SEN negatively correlated with progress between KS1 and KS2
  • Choice of model does not seem to matter here
    • OLS, FE and RE give qualitatively similar results
    • Correlation between being SEN and unobserved school characteristics not important
  • Regression and random effects assumptions are likely to hold in this example - prefer the random effects model
conclusions
Conclusions
  • Often fixed effects approach is used because RE assumption is a strong one
  • Efficiency advantages to the RE approach
  • Failure of the regression assumption is major issue
  • Approach each problem with agnostic view on model/ may not make a difference
    • Should be determined by theory and data, not tradition