Create New Territory Column
The Creating New Territory Column allows the user to include latitude and longitude data in an analysis. MultiRate will group the data points into territories, attempting to assign a roughly equal amount of exposure to each territory (more information about this process can be found below). This will allow data from each territory to be credibility weighted with data from nearby territories, using Variable Gradient Geospatial Smoothing.
In order to create a territory column, first use the Data and Analysis Control Panel to select the Server/Database and ultimately the Training Data table that contains latitude and longitude columns.
Next the points must be assigned to territories. The software will do this by adding a territory column to the Training Table and storing information about the territories in Custom Geographic Tables. To begin this process, select Tools -> Custom Geographic -> Create New Territory Column from the menu bar.
When the window below appears, select the columns containing the latitude, longitude, and exposure data. Latitude and Longitude must be in decimal degrees format. Also, enter the desired number of territories to be created. As a result of the grouping algorithm, there will likely be a few more territories created than is entered (more information about this process can be found below).
*Note: If no exposure is selected in the "Select Latitude and Longitude" window, all points will be treated as if they have an exposure of 1, resulting in a roughly equal number of points in each territory.
Next the user will be prompted to enter a name for the column to be created. This name will be used for the column created in the Training Table, as well as the three Custom Geographic Tables created to store the territory information.
To use this newly created field in an analysis, select the new territory column in the Column Selection window, using Custom Geographic as the data type:
Territory Grouping Process:
The first step for grouping the records into territories is to map each latitude and longitude point onto an XY grid to allow for calculations to be performed. This process sets the center of all of the latitude and longitude points as (0, 0) and then maps each point relative to that origin, with meters as the unit. This is the basis for the XY points that appear in the Custom Geographic tables. While this mapping is very useful for doing calculations concerning the relative position of the points, it is important to note that since the origin will be different for every unique dataset, these XY points are not useful for comparing points from different Training Files; use latitude and longitude for that purpose.
Next the "Northwestness" of each point is calculated by taking each point's Y-coordinate and subtracting its X-coordinate. (The green lines on the graph below represent sets of points with the same "Northwestness", with "Northwestness" increasing in the direction of the arrow.) The most northwest point is selected, and larger and larger squares are drawn around it (keeping the selected point in the center) until it contains of the exposure (i.e. 1/1000 of the total exposure if the default of 1000 territories was selected). Once this exposure threshold has been reached, all of the points in the box are placed in territory 1.
This process is repeated over and over, each time throwing out the points that have already been assigned to a territory and decreasing the number of territories in the denominator of the threshold by 1. So after creating territory 1, the most northwest point not in territory 1 will be selected, and larger and larger squares are drawn around it until it contains of the remaining exposure (i.e. 1/999 of the total exposure not in territory 1 if the default of 1000 territories was selected). The process continues until all points have been assigned a territory.
*Note: This method should result in relatively equal amounts of exposure in each territory. However, this cannot always be achieved when there are a few points with very high exposures or when a territory must be divided (this is discussed in the next paragraph). This can result in territories with significantly more or less exposure than the threshold.
It is important to note that even though the square is drawn all the way around the selected point, there will never be any points located northwest of the point itself, since it was selected precisely because it was the most northwest. The majority of the territory will generally be southeast of the selected point, but there will often be points either north or west (but never both north and west) of the selected point included. For example, see box 4 in the diagram below where point A is the selected point.
As a result of the way that the territories are being drawn, there is the potential for some of the territories to be shaped like a backwards "L", usually with high exposure areas in the ends of the "L". These territories are identified and then divided into two territories by drawing a line through the exposure weighted centroid, running 45° from northwest to southeast. The southwestern portion of the divided territory is assigned the same territory number as the original combined territory, and the northeastern portion is assigned the territory number of the original territory plus the number of desired territories. For example, in the diagram above territory 9 was divided into two territories (9 & 9 + 1000 = 1009, assuming the default of 1000 territories was selected) by drawing a 45° line through point B, the exposure weighted centroid.
After all of the records have been assigned to a territory, a column is added to the Training Data containing each record's territory number. Also, three Custom Geographic Tables are created in SQL, containing information about each territory, mapping information, and parameters used in the calculations.