The SPP Procedure

Example 105.1 Exploration of a Multitype Point Pattern

This example demonstrates how you can use PROC SPP to explore a multitype point pattern. Consider the following data set, which consists of locations of retinal amacrine cells in a rabbit’s eye. The data set contains three variables: X and Y are the coordinates of the cell locations, and Type is the type of each cell (which is based on whether it turns on or off when exposed to light). The data were originally analyzed by Diggle, Eglen, and Troy (2006) and  Hughes (1985).

data amacrine;
   input X Y Type $ @@;
   label Type='Cell Type'; 
0.0224   0.0243   on 
0.0243   0.1028   on 
0.1626   0.1477   on 
0.1215   0.0729   on 
0.2411   0.0486   on 
0.0766   0.1776   on 
0.1047   0.2579   on 

   ... more lines ...   

1.5729   0.729    off
1.457    0.6822   off
1.4168   0.7374   off

Accounting for mark types enables you to study possible interaction across types. You can study such interactions by using the cross-type variants of distance functions. The following statements compute the cross-K-function between the types of amacrine cells:

proc spp data=amacrine edgecorr=on seed=1
         plots(equate)= (observations(attr=mark) K);
   process cells= (X,Y / area=(0,0,1.6,1) mark=Type)
                  / K cross=types('on' 'off');

Output 105.1.1 shows two types of cells that are characterized by their state as on (in red) and off (in blue).

Output 105.1.1: Amacrine Cell Types

 Amacrine Cell Types

Output 105.1.2 lists exploratory information for the amacrine point pattern, and identifies it as a marked point pattern.

Output 105.1.2: Exploratory Information for the Amacrine Marked Point Pattern

Summary of Point Pattern
Data Type Marked Point Pattern
Pattern Name cells
Region Type User Defined Window
Region X Range [0,1.6] Units
Region Y Range [0,1] Units
Region X Size 1.6 Units
Region Y Size 1 Unit
Region Area 1.6 Square Units
Observations in Window 294
Average Intensity 183.75
Grid Nodes in X 50
Grid Nodes in Y 50
Grid Nodes in Window 2500
Mark Type
Mark Type Multitype

Output 105.1.3 shows the information for each mark type, including the frequency, percentage in the data set, and the first-order intensity, which measures the number of events of that particular mark type per unit of area that is contained in the marked point pattern.

Output 105.1.3: Mark Information for the Amacrine Marked Point Pattern

Level Information for Type
Value Frequency Percentage Intensity
off 142 48.30% 88.7500
on 152 51.70% 95.0000

Output 105.1.4 shows the cross-K-function test to detect a clustering of points for which Type=off around points for which Type=on and vice versa. It is very clear from the plots in the top left corner and top right corner that there is no significant difference between the computed cross-K function and the theoretical cross-K function. This clearly indicates that there is no significant clustering of on amacrine cells around off amacrine cells.

Output 105.1.4: Cross-K Function Panel

 Cross-K Function Panel