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Stephen Fisher, Jane Key, Nicky Best, Sylvia Richardson Department of Sociology, University of Oxford and Department of

Ethnic dealignment? Combining individual and aggregate data to improve estimates of ethnic voting in Britain in 2001 and 2005. Stephen Fisher, Jane Key, Nicky Best, Sylvia Richardson Department of Sociology, University of Oxford and Department of Epidemiology and Public Health

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Stephen Fisher, Jane Key, Nicky Best, Sylvia Richardson Department of Sociology, University of Oxford and Department of

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  1. Ethnic dealignment? Combining individual and aggregate data to improve estimates of ethnic voting in Britain in 2001 and 2005 Stephen Fisher, Jane Key,Nicky Best, Sylvia Richardson Department of Sociology, University of Oxford and Department of Epidemiology and Public Health Imperial College, London http://www.bias-project.org.uk

  2. Outline • Introduction and substantive issues • Methods and Results • Standard multilevel model • Results • Ecological and Hierarchical Related Regression • Results • Discussion and further work

  3. Introduction and substantive issues

  4. NCRM BIAS project: Overall goals • To develop a set of statistical frameworks for combining data from multiple sources • To improve our capacity to handle limitations inherent in observational data. • Key statistical tools: Bayesian hierarchical models and ideas from graphical models form the basic building blocks for these developments

  5. A decline in ethnic minority support for Labour? • Ethnic minority vote consistently around 80% from 1974 to 2001 • Between 2001 and 2005 there were • Islamic terrorist attacks • US and UK led invasions of Afghanistan and Iraq • Heightened security and suspicion of non-whites • Unlawful detention of foreign terror suspects • Convictions of British soldiers for Iraqi prisoner abuse • These and other events are thought to have undermined support for Labour among ethnic minorities. • On the other hand, harsh stance on immigration in Conservative 2005 election campaign may have alienated ethnic voters • This paper seeks to test whether the gap in Labour vote between whites and non-whites narrowed between 2001 and 2005.

  6. Data • Problem: • Not enough high quality survey data on ethnic minorities • So combine individual and aggregate data using new class of multilevel models developed by BIAS • Individual-level: • British Election Study post-election surveys. • 97 registered ethnic minorities in 2001, and 137 in 2005 • Constituency-level: • 2001 and 2005 election results • 2001 Census data on % who are non-white • Population: • Focus on Labour voting as proportion of registered pop. since census might be reasonable proxy for this, but not voting pop.

  7. Methods and Results

  8. Data sources: individual data

  9. Multilevel model for individual BES data b a s2 qi xij yij person j area i

  10. Multilevel model for individual BES data yij = voted Labour (1) / other (0) xij = non-white (1) / white (0) b a s2 qi xij yij person j area i

  11. Multilevel model for individual BES data yij = voted Labour (1) / other (0) xij = non-white (1) / white (0) yij ~ Bernoulli(pij), person j, area i b a s2 logit pij = a+ b xij + qi qi xij yij person j area i

  12. Multilevel model for individual BES data yij = voted Labour (1) / other (0) xij = non-white (1) / white (0) yij ~ Bernoulli(pij), person j, area i b a s2 logit pij = a+ b xij + qi qi qi ~ Normal(0, s2) xij yij person j area i

  13. Multilevel model for individual BES data yij = voted Labour (1) / other (0) xij = non-white (1) / white (0) yij ~ Bernoulli(pij), person j, area i b a s2 logit pij = a+ b xij + qi qi qi ~ Normal(0, s2) xij yij b = individual-level effect of ethnicity on vote choice qi = “unexplained” area effects person j area i

  14. Results: Share of the vote for whites and non-whites based on BES survey data A. As a proportion of voters

  15. Results: Share of the vote for whites and non-whites based on BES survey data A. As a proportion of voters

  16. Results: Share of the vote for whites and non-whites based on BES survey data B. As a proportion of electorate

  17. Results: Share of the vote for whites and non-whites based on BES survey data B. As a proportion of electorate

  18. Results from regression analysis of BES electorate data

  19. Comments • Between 2001 and 2005, non-white vote drops from • 72% to 51% (voters) • 55% to 37% (electorate) • Small sample size →large SE and CI for the proportion of non-whites voting Labour • Gap in Labour vote between whites and non-whites narrows from • 29 points in 2001 to 15 points in 2005 (voters) • 22 points in 2001 to 10 points in 2005 (electorate) • But, change is not statistically significant (multilevel analysis) • Is this just because sample size is too small? • What can we learn from aggregate data?

  20. Data sources: individual and aggregate data

  21. Xi Standard ecological regression model a b t2 ci Yi Ni area i

  22. Xi Standard ecological regression model Yi = number voting Labour Ni = registered electorate Xi = proportion non-white a b t2 ci Yi Ni area i

  23. Xi Standard ecological regression model Yi = number voting Labour Ni = registered electorate Xi = proportion non-white a b t2 Yi ~ Binomial(qi,Ni), area i ci logit qi = a + bXi + ci Yi ci ~ Normal(0, t2) Ni area i

  24. Xi Standard ecological regression model Yi = number voting Labour Ni = registered electorate Xi = proportion non-white a b t2 Yi ~ Binomial(qi,Ni), area i ci logit qi = a + bXi + ci Yi ci ~ Normal(0, t2) b = effect of area ethnicity on probability of voting Labour b ≠ b→ ecological bias Ni area i

  25. Ecological bias Bias in ecological studies can be caused by: • Confounding • confounders can be area-level (between-area) or individual-level (within-area). → include control variables and/or random effects in model • Non-linear covariate-outcome relationship, combined with within-area variability of covariate • No bias if covariate is constant in area (contextual effect) • Bias increases as within-area variability increases • …unless models are refined to account for this hidden variability

  26. Alleviating ecological bias • Alleviate bias associated with within-area covariate variability • Obtain information on within-area distribution fi(x)of covariates, e.g. from individual-level data • Use this to form well-specified model for ecological data by integrating (averaging) the underlying individual-level model Yi ~ Binomial(qi , Ni);qi = pij(x) fi(x) dx qi is average group-level probability (of voting Labour) pij(x) is individual-level probability given covariates x fi(x) is distribution of covariate x within area i

  27. Integrated group-level model Xi = proportion non-white in area i (mean of xij) qi = average probability (proportion) voting Labour area i = ∑j pij /Ni = ea (1-Xi) + ea+b Xi Alleviating ecological bias • Consider single binary covariate x, e.g. white/non-white • f(xi)→ proportion of individuals with x=1 in each area • Individual-level model pij = probability of voting Labour log pij = a + b xij(log link assumed for simplicity) → pij = ea if person j is white (xij=0) pij = ea+b if person j is non-white (xij=1)

  28. Xi Standard ecological regression model a b Yi ~ Binomial(qi,Ni), area i t2 ci logit qi = a + bXi + ci ci ~ Normal(0, t2) Yi Ni area i

  29. Xi Integrated ecological regression model a b Yi ~ Binomial(qi,Ni), area i s2 qi =  pij(xiji,a,b,qi)fi(x)dx qi qi ~ Normal(0, s2) Yi Ni area i

  30. Xi Integrated ecological regression model a b Yi ~ Binomial(qi,Ni), area i s2 qi =  pij(xiji,a,b,qi)fi(x)dx qi qi ~ Normal(0, s2) Yi b can be interpreted as individual-level effect of ethnicity on probability of voting Labour Ni area i

  31. Xi Combining individual and aggregate data Multilevel model for individual data Integrated ecological model b a s2 a b s2 qi qi xij yij Yi person j Ni area i area i

  32. Xi Combining individual and aggregate data a s2 b Hierarchical Related Regression (HRR) model Joint likelihood for yij and Yi depending on shared parameters a, b, qi and s2 qi xij yij Yi person j Ni area i

  33. Xi Combining individual and aggregate data a s2 b Estimation carried out using R software (maximum likelihood) or WinBUGS (Bayesian) qi xij yij Yi person j Ni area i

  34. Comparison of results from individual and HRR analysis

  35. Comparison of results from individual and HRR analysis

  36. Discussion and further work

  37. Conclusions • BES survey estimates halving of gap in Labour voting between whites and non-whites of from 29 to 15 points • Due to small-N for ethnic minorities, not statistically significant • Combined aggregate and individual level HRR analysis suggests a significant decline in the ethnic voting gap • But if constituency level random effects are allowed for the change is again statistically insignificant → considerable heterogeneity between constituencies → suggests other important individual or area predictors • Lack of statistical significance • may reflect data problems (see below) • may be ‘real’ – BES mayover-estimate change in Labour share of ethnic vote (quota sample reported 66% ethnic minorities questioned voted Labour in 2005, compared with 51% in BES)

  38. Substantive Data Limitations • Norm is to consider share of the vote, so unfortunate that this can’t be done using HRR model • But Labour voting as a share of the electorate still a valid issue, substantive conclusions likely to be similar. • Ethnic minorities aren’t all the same • Previous research suggests Blacks more Labour than S Asians • Unfortunately not enough data or variance (at both levels) to explore differences between minority groups. • Other sources of ecological bias are likely due to absence of controls for other relevant variables, eg. socio-economic factors • HRR models can be extended to include additional variables • Requires constituency-level data on joint distribution of ethnicity and other relevant variables

  39. Strengths of HRR approach…… • Aims to provide individual-level inference using aggregate data by: • Fitting integrated individual-level model to alleviate one source of ecological bias • Including samples of individual data to help identify effects • Uses data from all constituencies, not just those in BES survey • Improves precision of parameter estimates

  40. …..and limitations of HRR approach • Integrated individual-level model relies on large contrasts in the predictor proportion across areas • Limited variation in % non-white across constituencies: (median 2.7%, 95th percentile 33%; only 9 constituencies in 2005 had non-white majority) • Our estimates may not be completely free from ecological bias (Jackson et al, 2006) • Estimation of ethnicity effect strongly confounded with area random effects

  41. Further Work • Further analysis will consider fuller model specifications with ethnic contextual effects and individual and aggregate level control variables • Also intend to investigate inclusion of other sources of individual-leveldata, such as opinion polls, in HRR models

  42. References Fisher S, Key J, Best N, Richardson S. Ethnic dealignment? Combining individual and aggregate data to improve estimates of ethnic voting in Britain in 2001 and 2005. Paper in preparation. Jackson C, Best N and Richardson S. (2008) Studying place effects on health by synthesising individual and area-level outcomes. Social Science and Medicine, 67:1995-2006 Jackson C, Best N and Richardson S. (2008) Hierarchical related regression for combining aggregate and individual data in studies of socio-economic disease risk factors. J Royal Statistical Society Series A: Statistics in Society 171(1):159-178 Jackson C, Best N and Richardson S. (2006) Improving ecological inference using individual-level data Statistics in Medicine, 25(12):2136-2159 Papers available from www.bias-project.org.uk

  43. Validated turnout based on BES data

  44. True Effect % exposed: 0-25% (100 areas) Individual data Area data Area data + sample of 10 individuals % exposed: 0-50% (100 areas) % exposed: 0-100% (100 areas) % exposed: 0-25% (25 areas) Log RR of IHD for smokers Simulation Study Estimated effect of exposure on outcome whites

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