Presentation on theme: "Methods for investigating zoning effects Mark Tranmer CCSR."— Presentation transcript:
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 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.
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).
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
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.