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Methods for investigating zoning effects Mark Tranmer CCSR

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Allowing for area effects Suppose we have some area level information Such as: aggregate information for a particular set of areal units e.g. wards; EDs; Output Areas; Districts Or individual level data with area indicators.

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Allowing for these effects in our analyses Then we might say great! Ill fit a multilevel model – especially if we have individual level data with area indicators. Or we might calculate correlations etc at the area level from aggregate area level data.

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But … If we calculate area level correlations because we want to make inferences about individuals that live in those areas but we only have area level data… problem: ecological fallacy So lets suppose we can actually do an analysis using individual level data with area indicators … e.g. a multilevel model. Hence simultaneously allowing for individual and area level effects. Does that solve the problem?

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No, because … What do we mean by an area? Modifiable Areal Unit Problem (MAUP) Analyses that involve areas are affected by The average population size of those areas: scale effects

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No, because … Once we choose a particular scale, they are also affected by the way in which those areas are defined. I.e. the choice of boundaries: Zoning effects. Also: Scope effects? What is the overall region of study? This will have implications for the extent of variation.

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Zoning effects example Suppose we have a region that contains a 9 areal units of equal population, and we want to make a ward from three of these contiguous units.

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Zoning effects example Ward A1

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Zoning effects example Ward B1

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Zoning effects example Overlay wards A1 and B1

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Zoning effects example We can also do the same thing for the other wards: e.g.

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Im interested in developing a statistical framework to investigate these effects I think a cross-classified multilevel model might be the way to tackle the problem What I hope to do is to find a way to assess the nature and extent of zoning effects at a particular scale.

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Two level model(s)

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Cross-classified model

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How to test this idea Simulated data: I set up a simulation study I generated some simulated data for a normally distributed variable. Each of the 9 cells in the grid has a different (but known) mean and within each of the 9 cells I set the variance to be equal (25). So I aimed to simulate complex between-cell variation (whilst knowing the procedure I had applied to induce that variation).

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I assumed these zonings

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Results Two level models * Variance component estimates WardIndiv A, person 427366 B, person 176616 Cell,person 642150 Cross-classified models Estimated parameter: Var(A)Var(B)Var(A*B)Var(Indiv) A,B,cell,person3334309150

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Conclusion I think we have a framework for investigating the causes of zoning effects It seems to work for simulated data, though I have yet to fully work out what these results mean Can anyone suggest to me some real data that investigate using this methodology.

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