|SAS/SPECTRAVIEW Software User's Guide|
This chapter provides information that explains how SAS/SPECTRAVIEW loads data and how you can affect the results, and the chapter provides instructions on how to load data into SAS/SPECTRAVIEW .
|Understanding the Volume Grid|
When data is loaded into SAS/SPECTRAVIEW , the software creates a three-dimensional volume grid by plotting the values for the axis variables along the X, Y, and Z axes. Each intersection of an x,y,z coordinate is a data point in three-dimensional space. The shape and size of the volume grid is determined by the number of unique X, Y, and Z values.
The resulting total number of data points can be calculated by
multiplying the number of unique X values * unique Y values * unique Z values.
For example, if you have 10 X-axis values, 5 Y-axis values, and 2 Z-axis values,
the result is 100 data points (10x5x2). If you have 10 values on each axis,
the result is 1,000 data points (10x10x10).
Data that represents a complete grid contains at least one set of x,y,z coordinates for each possible X, Y, Z variable combination. That is, when loading data, each time SAS/SPECTRAVIEW finds a unique axis value, the software creates a new grid intersection. For the grid to be complete, the data set must contain corresponding X, Y, and Z values for each possible intersection. The resulting number of data points would be the same as the number of observations in the data set, with the data points uniformly distributed in the volume grid, unless there are duplicate observations for a set of x,y,z coordinates. Note that SAS/SPECTRAVIEW works best with data that represents a complete grid.
Examples of data that would result in a complete grid is an air quality survey that includes a full grid of sample data from an entire area, scientific numerical models, medical images, or complete financial models like a mortgage table.
To have an idea of how much data is required for a complete grid, think of it like a three-dimensional spreadsheet where multiple sheets extend along the Z axis and where each cell on each sheet represents the values for one observation. Suppose the variables ROW represents X, COLUMN represents Y, and SHEET represents Z. The values ROW=2, COLUMN=2, and SHEET=1, which is one observation, would be located in the spreadsheet as shown in Three-Dimensional Spreadsheet.
For a complete column 2, you would need these observations:
ROW COLUMN SHEET 1 2 1 2 2 1 3 2 1 4 2 1 5 2 1
For a complete sheet 1, you would need observations for all five columns:
ROW COLUMN SHEET 1 1 1 2 1 1 3 1 1 4 1 1 5 1 1 1 2 1 2 2 1 3 2 1 4 2 1 5 2 1 1 3 1 2 3 1 3 3 1 4 3 1 5 3 1 1 4 1 2 4 1 3 4 1 4 4 1 5 4 1 1 5 1 2 5 1 3 5 1 4 5 1 5 5 1
Finally, to complete the entire grid, you would need
all those observations for sheet 2 and for sheet 3.
Data that represents less than a complete grid is data that does not have every possible combination but has at least one of the three values for X, Y, or Z. For example, data that represents an incomplete grid could be an air quality survey that consists of samples from random locations within a certain cubic area.
For an incomplete grid, when the software plots the actual axis values, any grid intersections without a data point are completed with software-generated filler points for the missing X, Y, or Z values to complete the grid.
For example, consider the following eight observations, which contain three unique values for each axis:
OBS X Y Z Response 1 1 1 1 111 2 2 1 1 211 3 3 1 3 313 4 3 2 1 321 5 3 3 1 331 6 2 2 1 221 7 2 2 2 222 8 2 3 2 232The software would generate and plot 27 data points (3x3x3) -- 8 actual data points representing the observations and 19 filler points as shown in 3x3x3 Volume Grid. The first volume grid shows the actual data points; the second volume grid shows the actual data points and the filler points.
3x3x3 Volume Grid
The larger the number of unique values for an axis, the larger the resulting number of data points. For example, consider the following eight observations, which contain 7 unique values for the X axis, and three unique values for the Y and Z axes.
OBS X Y Z Response 1 1 4 5 145 2 3 2 3 323 3 2 2 3 223 4 4 6 5 465 5 6 4 3 643 6 7 2 1 721 7 5 2 5 525 8 1 6 1 161The software would generate and plot 63 data points (7x3x3) - .8 actual data points representing the observations and 55 filler points as shown in 7x3x3 Volume Grid. The first volume grid shows the actual data points; the second volume grid shows the actual data points and the filler points.
7x3x3 Volume Grid
Data that does not contain at least one value for an x,y,z coordinate within the volume grid is referred to as sparse data. Generally, sparse data occurs when the unique values for an axis are widely distributed along the axis, for example, an air quality survey where an entire section of a test area was not sampled. And often, sparse data is not related spatially, for example, a data set where the X, Y, and Z values are height, weight, and age. Note that sparse data can also result from subsetting.
Unlike for locations having at least one value for x,y,z coordinate, the software does not replace non-existent x,y,z coordinates with filler points. Instead, the volume grid displays a visual gap indicating an area within the volume grid where no data is available. The actual data points appear to be non-uniformly distributed because of the gap in the data. Consider the following data, which contains three unique values for the axis variables:
OBS X Y Z Response 1 1 4 5 145 2 1 2 3 123 3 2 2 3 223 4 7 6 5 765 5 2 4 3 243 6 1 2 1 121 7 7 2 5 725 8 2 6 1 261When the actual data values are plotted and the volume grid is completed, the actual data points are not uniformly distributed, resulting in a volume grid that appears to have gaps. The software would generate and plot 27 data points (3x3x3) - 8 actual data points representing the observations and 19 filler points as shown in Sparse Data Volume Grid. The first volume grid shows the actual data points; the second volume grid shows the actual data points, the filler points, and visual gaps:
Sparse Data Volume Grid
Note that when loading character data, gaps will not occur. The software assigns sequential numerical values to the character values, resulting in uniformly distributed data points.
|Understanding Missing Values|
A missing value is a value in the SAS System indicating that no data is stored for the variable in the current observation. In SAS/SPECTRAVIEW , any grid intersections with missing X, Y, or Z values or any x,y,z coordinate without an associated response value are completed with software-generated filler points. Filler points are handled as missing values.
Missing values, by default, have no color. If you want missing values to display in an image, you must use the color palette to assign a color as explained in Assigning Color to Missing Values.
If your data represents an incomplete grid or sparse data, the software may create many filler points. However, if your data represents a complete grid, displaying missing values lets you see holes, which may indicate a possible failure of the measuring equipment.
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Copyright 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.