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NETWORK > EGO NETWORKS > HOMOPHILY

PURPOSE Provide various measures of each ego's homophily with its alters based on a specified attribute.

DESCRIPTION Homophily refers to correlation between ego attributes and alter attributes. For example, we might measure the extent to which egos tend to have ties with alters of the same gender as themselves. In categorical data, such as gender, similarity is measured by being in the same category (e.g., female).  This routine accepts a network dataset and an attribute dataset and measures how often ego's alters are in the same category for that attribute, computed across a variety of measures.

Homophily is always relative to the ego's categorization on an attribute.

PARAMETERS Input Network Dataset
This parameter specifies the network dataset indicating the presence and absence of ties.  Datatype: directed graph. 

Input Attribute Dataset
This parameter specifies the dataset containing attribute data for the network specified above.  Once the filename is entered, UCINET will read the labels.  You can specify that the attributes appear on the column (the default) or the row Dimension, and then select the attribute's label from the drop down list under Value.

Output Measures Dataset
Specifies the name of the dataset created to store the resulting measures.  By default it is the same as the input dataset name with "-EgoHomophily" appended.

Definition of Ego Network
Allows you to specify which nodes connected to ego are included in the ego network calculations.

Attribute Data Type 
Not yet implemented, but will allow specification of categorical or continuous variable types.  UCINET will calculate the appropriate measures based on the data type.  Presently, only categorical data are included.

LOG FILE The output includes a table with various measures of homophily for each ego in the network specified by the input file.  Each measure is described below.

PctHomoph.  Number of ties between ego and an alter in the same attribute category divided by ego's total number of ties.

EI Index.  Calculates the E-I Index for each ego in the network.  (See E-I Index for more information).
 
Matches.  A measure of homophily that accounts for both the presence of homophilous ties and the absence of heterophilous ties divided by the total number of possible ties (n-1, where n is the number of nodes in the network specified by the input dataset).

Yules Q.  A measure of similarity which ranges from -1 for perfect heterophily to +1 for perfect homophily.  A value of 0 means no pattern of homophily.

Log Odds.  This is the log of the odds of homophilous behavior over heteropholous behavior.  Cannot be calculated for perfect heterophily (Yules Q of -1) or perfect homophily (Yules Q of +1).  Approaches (negative) infinity for perfect homophily (heterophily).  

Cohen Kappa.  The measure of categorical agreement on the specified attribute for the ego with each alter.  A value of 1 means complete agreement.  A value of 0 means no more agreement than expected by chance.

Correlation.  This calculates the correlation between the presence or absence a tie between ego and each alter in the network and a vector indicating ego and alter's similarity on the selected attribute.  As a correlation, a value of 1 indicates perfect correlation (i.e., perfect homophily) and 1 a value of -1 indicates a perfect negative correlation (i.e., perfect heterophily).

TIMING O(N^3)