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TOOLS > STATISTICS > AUTOCORRELATION > CATEGORICAL > RCT ANALYSIS


PURPOSE Perform randomization test of autocorrelation for a symmetric adjacency matrix which is partitioned into groups.

DESCRIPTION Relates a dyadic binary variable (an actor-by-actor adjacency matrix) to a monadic variable (a vector representing an attribute of each actor). For example, if the dyadic variable consists of who is friends with whom, and the categorical variable is gender, the procedure tests whether friendship is patterned by gender (e.g., do boys prefer boys and girls prefer girls?). The routine is similar to performing a standard chi squared test except instead of using the chi squared distribution the underlying distribution is constructed using a randomization procedure.

PARAMETERS 
Input Dataset
Name of file containing matrix to be analyzed. Data type: Graph

Attribute:
The name of an UCINET dataset that contains a partition of the actors into two groups. To partition the data matrix into groups specify a vector by giving the dataset name, a dimension (either row or column) and an integer value. For example, to use the second row of a dataset called ATTRIB, enter "ATTRIB ROW 2". The program will then read the second row of ATTRIB and use that information to define the groups. All actors with identical values on the criterion vector (i.e. the second row of attrib) will be placed in the same group.

No. of Permutations: (Default = 1000)
The number of random permutations required in the test.
 
Random number seed:
The random number seed sets off the random permutations.  UCINET generates a different random number as default each time it is run.  This number should be changed if the user wishes to repeat an analysis.  The range is 1 to 32000.

Output Dataset (Default= 'lltab')
Name of output dataset that contains the frequencies in the observed data corresponding to the partition.
 
LOG FILE The actor attributes are recoded to run from 1 and these are reported. 
A table which gives the cross classified frequencies, that is a contingency table corresponding to the attributes and the input dataset. 
A table which gives the expected values of the frequencies assuming that the ties are independent and randomly distributed throughout the groups.
The observed values in each cell of the first table divided by the corresponding cell in the second table are then reported. This is followed by the observed chi square value, ie the square of the observed minus the expected divided by the expected value.
The average permutation frequency table gives the mean values of the entries from all the permutation tests. Each of the generated entries have their  value compared with the observed value and the significance is the relative frequency of the number of times the generated value is larger than the observed.

TIMING O(N^2)

COMMENTS None

REFERENCES Cliff, A D and Ord, J K  1973 Spatial Autocorrelation. Pion, London.