# Estimate populations for a set of zones based on pycnophylactic interpolation

### Description

Given a `SpatialGridDataFrame`

of population estimates and a set of polygons,
compute a population estimate based on Tobler's pycnophylactic interpolation
algorithm for each zone. The result is a vector.

### Usage

1 | ```
estimate.pycno(sgdf, spdf)
``` |

### Arguments

`sgdf` |
A |

`spdf` |
A |

### Details

Takes the estimate of population density for each pixel, checks which polygon each pixel is in, and aggregates them. Accuracy depends on the scale of pixels in the initial interpolation.

### Value

A vector in which each each pixel set at the estimated population aggregation to each zone in `spdf`

.

### Note

Pycnophylatic interpolation has the property that the sum of the estimated values associated with all of the pixels in any polygon equals the supplied population for that polygon. A further property is that all pixel values are greater than or equal to zero. The method is generally used to obtain pixel-based population estimates when total populations for a set of irregular polygons (eg. counties) are known.

### Author(s)

Chris Brunsdon

### References

Tobler, W.R. (1979) *Smooth Pycnophylactic Interpolation for Geographical Regions*. Journal of the American Statistical Association, v74(367) pp. 519-530.

### See Also

`pycno`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
# Read in data for North Carolina as a SpatialPolygonsDataFrame
nc.sids <- readShapeSpatial(system.file("shapes/sids.shp", package="maptools")[1],
IDvar="FIPSNO", proj4string=CRS("+proj=longlat +ellps=clrk66"))
# Compute the pycnophylactic surface for 1974 births as a SpatialGridDataFrame
# Note probably shouldn't really base grid cells on Lat/Long coordinates
# This example just serves to illustrate the use of the functions
births74 <- pycno(nc.sids,nc.sids$BIR74,0.05,converge=1)
# Create a new 'blocky' set of zones
blocks <- gUnionCascaded(nc.sids,1*(coordinates(nc.sids)[,2] > 36) +
2*(coordinates(nc.sids)[,1] > -80))
# Plot the bloocky zones
plot(blocks)
# Aggregate data to them
estimates <- estimate.pycno(births74,blocks)
# Write the estimates on to the map
text(coordinates(blocks),as.character(estimates))
``` |