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TOOLS > STATISTICS > AUTOCORRELATION > CATEGORICAL > ANOVA / DENSITY

PURPOSE Perform randomization test of autocorrelation for a categorical variable.

DESCRIPTION Relates a dyadic variable (an actor-by-actor 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 test is based upon the densities within each block and is similar to performing an analysis of variance. Three different models which have different patterns of density are possible.

PARAMETERS
Network or Proximity Matrix
Name of file containing matrix to be analyzed. Data type: Matrix.

Actor Attribute:
Name of file containing actor attributes, given as a vector of shared attributes so that (1,2,3,1,2,2) means that actors 1 and 4 share the same attribute actors 2,5,and 6 share the same attribute and actor 3 has a different attribute from all the others.

Model (Default = Structural Blockmodel)
Choices are:

Constant Homophily. Tests hypothesis that actors prefer to interact with members of their own kind (as defined by the actor attribute), and assumes that all groups have equal inbreeding tendencies.

Variable Homophily Similar to the constant homophily model, except that it assumes that each group or class of actors has a different homophilic tendency (different inbreeding parameter).

Structural Blockmodel. Most general model. Just asks whether the different classes have significantly different interaction patterns. For example, girls might prefer girls (inbreeding), while boys also prefer girls (outbreeding).

Number of random perms: (Default=1000)
Number of autocorrelations to compute between the data matrix and the randomly permuted structure matrix.  The larger the number of permutations, the better the estimates of standard error and "significance", but the longer the computation time.

Treat diagonals as valid? (Default = No)
If Yes, the values along the main diagonals of each matrix are included in the computations.  Otherwise, they are treated as missing.

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= 'AUTOSIM')

LOG FILE The actor attributes are recoded so they run from 1 to n, these are reported.
The between group and in-group means are reported if either of the homophily models were chosen. For constant homophily the in-group mean is the overall mean of all within group interactions. For variable homophily each separate within group mean is reported. For the structural blockmodels option the total sum, the average value and the number of cells within each block are reported. In all cases this is followed by the value of the autocorrelation together with the r-squared value, the root mean square and the sum of squares. Below this is the autocorrelation averaged over all the permutations together with the standard error. Finally the proportion of random values which are as large as the actual autocorrelation is reported. This gives the significance of the calculated value, so for example if this were below 0.05 we would conclude at the 5% level that the dyadic variable is related to the categorical attribute.

TIMING O(N^2)