Methods for investigating zoning effects Mark Tranmer CCSR

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.

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.

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?

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

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.

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.

Zoning effects example Ward A1

Zoning effects example Ward B1

Zoning effects example Overlay wards A1 and B1

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

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.

Two level model(s)

Cross-classified model

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).

I assumed these zonings

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

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.