Scale Conversion/Interpolation (formerly Spatial Interpolation)

The Scale Conversion/Interpolation methods are used to assign values observed in one geography their analogous values in a second geography.  SpaceStat allows you to convert/interpolate:

-> data from a source polygon dataset to a polygon dataset with a different geography,

-> data from a source point dataset to a destination file with a polygon geography,

-> data from a source polygon dataset to destination file with a point geography, and

-> data from a source point dataset to a destination file with a different point geography.

You can also incorporate a weight dataset when you convert data, which is described below under weighted interpolation.  Typically, if you want to aggregate population data or any other type of count data, such as number of cases, you will not use a weight set, and you will not select the "normalize weights" option (see below).

Details on the methods for Scale Conversion/Interpolation

All of the scale conversion methods involve a series of steps in which SpaceStat manipulates both the temporal and spatial aspects of the data.  The general process for the conversion methods will be outlined first, followed by additional details for each type of conversion below.   When the method is run, SpaceStat first merges the time intervals for the source and destination geographies, and then successively merges time intervals for source and user-supplied weight sets, resulting in a set of time intervals that have constant geographies and data.   

Next, for each destination polygon or point, SpaceStat determines which of the points or polygons in the source dataset will be used to determine its value (based on overlap or proximity).  We refer to the relative importance of each source point or polygon that goes into determining the value of a destination as this source's "geographic weight".  This step also identifies missing values in source or destination geographies.  If you have an additional weighting factor (e.g., population size) that you would like to apply, this value will be multiplied by the geometric weights.  A last optional step is that the weights for each destination point or polygon can be normalized (sum of all weights will equal one).  

-> polygon to polygon: The contribution of each source polygon's value to the value of the destination polygon (i.e., it's geographic weight) depends on the percent overlap of the source polygon with the polygon in the destination geography.  Thus, the value for a polygon within the destination geography is a weighted average of source polygon data with weights derived from the relative coverage of each of the source polygons within a particular destination polygon.  

-> point to polygon:  To determine geographic weights, SpaceStat takes the average value for all points falling within the boundaries of a given polygon.  Thus, for each source point, the geographic weight is one divided by the number of source points per destination polygon.  If one or more source points in a destination polygon are located on the boundary between two or more polygons, the geographic weight calculation takes this into account as well, and equals 1 divided by the number of source points per destination polygon multiplied by the number of polygons each source point overlaps.  

-> polygon to point:  The value assigned to points in the destination geography is the value for the polygon in the source geography with which the point overlaps.  If the point overlaps more than one polygon (i.e., occurs on a boundary between two or more polygons), the geographic weight for each source polygon is the inverse of the number of polygons overlapping the point.  

-> point to point:  To interpolate from a point geography to a different point geography, you can choose between a distance- and a nearest neighbor-based method.  For the distance method, you select a radius around each point in the destination geography, and points from the source geography within that distance will be used to determine the destination point's value.  The weighting for each source point is set to 1/(the number of points within the specified distance, multiplied by the number of destination points the source point "belongs" to).   Alternatively, you can specify a number of nearest neighbors rather than a distance, and the geographic weight applied to each value from the source geography will be 1/(the number of nearest neighbors multiplied by the number of destination points for which the source is a nearest neighbor).  Inverse distance weighting is also available

Note that any of these source/destination geography combinations can also use a kriging method to interpolate values.  

Weighted interpolation

SpaceStat allows you to interpolate source data to a destination geography using a weighting scheme that is a function of BOTH the geographic weight (described above for each form of interpolation), and an additional weighting factor (e.g., population size) that is assigned to each of the source points or polygons.  The final weight used to compute the point or polygon value's contribution to the destination geography is the product of the geographic weight and the weight assigned by the user.  

For example, SpaceStat can create a new polygon dataset with a SEA (state economic area) geography from a source data set of county-level data on cancer rates for black females (RBF), using the size of the black female population at risk (PBF) in the counties as a weighting factor, and the normalize weights option.  As a result of this weighting scheme, if (for example) two counties encompass equal areas within an SEA, but county "A" has a population at risk that is twice as high as county "B", the cancer rate for the county "A" will be "double counted" relative to the county with the smaller population at risk ("B").  

Normalizing weights

When you use your own weight set in an interpolation procedure, you will have the option of normalizing the weights.  This means that each individual weight value (geographic multiplied by user-assigned weight) is divided by the sum of the weights assigned to all of the units being interpolated. Thus, the sum of all weights will equal one.  This option allows you to compute a population-weighted average when applied to rate data weighted by a population dataset, or by other types of count data.

New file creation

When you run the interpolation method, SpaceStat produces two new files that are added to the data view.  The first set is listed under the destination geography, and is given the default name of "poly to poly mean", "point to poly mean", etc., depending on which form of interpolation you performed.  You can verify that the file is the one you just created by right clicking on the name, and then selecting "properties" to view the history of the new dataset, and can use "rename" from the right-click options to give it a more descriptive name (highly recommended if you will be interpolating more than one dataset).  

The second file created by invoking the interpolation method is listed below the source dataset, and will be named "overlapped poly ids" or "overlapped point ids."  You can use choose "Table" from the "View" menu or click the table icon in the main toolbar to see the id of the destination polygon/point for each polygon/point in the source dataset.  

If the normalize weights option is set to "Yes" and you are not performing poly to point interpolation then a standard deviation dataset is also produced.

Hint: if you pull the information into a table but don't see any values in the id column, check the time slider on the table to make sure that the time shown is within the interval over which you interpolated data sets.

Missing values in interpolation procedures

If any of the values for points or polygons in the source dataset are missing, the points or polygons that would include information from those locations are coded as missing values in the output file.  Similarly, destination polygons or points for which no source data are available (e.g., a polygon that does not overlap any source points/polygons) are reported as missing values.  A "bad" destination polygon, for example one with self-intersecting boundaries, will also be coded as a missing value in output files.  If you are using a weight set, a destination point or polygon will be output as a missing value if any of the weights of its source points or polygons are missing.