Structural Holes

Purpose. This program is designed to familiarize you with constructing Burt's structural hole measures and how to extract local-network information from a global network (such as from the Add Health data). This assignment builds on previous programming, so a bit less detail is given for each of the steps than in earlier assignments.

1) Calculate Burt's measures (effective size, Efficiency, Constraint, and Hierarchy) on the example below. If you have UCINET, you can use that or you can write an IML program based on the formulas given in class. An example based on a different network can be found on the class homework page. The formulas for the measures can be found in Burt, or from the day's web page.

2) Construct ego-networks from one of the Add Health full-network data. Substantively, we are simply identifying each person, the people they nominate (or nominate them, depending on how you specify the program) and then comparing ego's attributes to alter's attributes.

a) download hs_egonet.sas from the homework page. This is the program that will calculate the measures. READ THE PROGRAM and the COMMENTS. Again, you may find it useful to re-type the program, to help you understand it better. b) download the data (fakeschl) from the resource page. c) download the SPAN files from the course directory and extract them from the winzip file. (you may have already done this for an earlier homework) d) Open SAS and load the program. Make some initial modifications as you read the program: 1) Change directory statements . These are macro assignments, so you should only have to do it at the top of the program 2) Calculate the sex and grade composition of each person's local network. We do this using the %ego_xmat macro from SPAN, which calculates the peer composition variables. This subroutine produces new variables (in this case named ENFEMAL and ENGRADE) that are the mean values of "female" and "grade" for each person’s network. The key “SOR” option asks for the network of Sent or Received ties. If you wanted only Sent ties, you would specify S instead, or R for only received, or SNR for reciprocated. 3) NOTE THAT WHEN YOU RUN THE PROGRAM, it will ask you for a password for the data. The password was given in class (hint: the name of a musician).

Turn in: a) The program currently writes out the PAJEK file for the school network, read that network into PAJEK and plot it, using the grade partition. b) Calculate and report: (1) descriptive statistics for average grade of each person's local network and the proportion female in each person's networks. (2) the average size of each persons local network and (3) the average density. c) Repeat (b) but give the statistics by gender.

3) Modify the GSS ego-network program (gss_egonet.sas) to calculate Burt’s effective size measure for people in the GSS sample. Do the measures differ by ego’s gender and ego’s race? You will do this by modifying the programs you used in the earlier homeworks.

a) Download gss_egonet.sas (this is also the solution to homework 2) b) download gss85.xpt c) download gssformat.sas d) Open Gss_egonet.sas and: 1) change all directories to point to where you saved the files 2) Recall that effective size is the actual size, minus the redundancy in the network. So first we need to calculate redundancy. Redundancy is the average number of people in the network every other person knows, and is equal to 2t/n, where t is the number of ties in the network and n is the number of alters. i. Recode close variables from 1, .5 and 0 to 1, 1, 0). ii. Get t by summing the close12, close13, etc. variables. iii. Recode the numgiven variable, because the range is higher than the matrix values (i.e. max numgiven is 6, max in the network we collect data on is 5). Code numgiven = 5 if numgiven > 5.) iv. Effective size is then calculated as: (number ego nominates) – (redundancy).

4) summarize effective size by ego’s race and gender. Do you think this would differ by Kin status? How would you find out?