A two mode personal network method for creating categories of knowing Christopher McCarty H. Russell Bernard University of Florida Dimitri Fazito Universidade Federal de Minas Gerais Sunbelt XXXI, St. Pete Beach, FL February

NSUM The network scale-up method (NSUM) is based on a four part equation. m/c=e/t t is the total size of a population e is the size of a sub-population in E that we want to estimate m is the average number of people in e that each member of our sample knows c is the average personal network size. Each person’s network (c) reflects, with some deviations the distribution of various populations, e’s, in the total population t, and the deviations average out if we study a large, representative sample of people.

Testing NSUM We tested NSUM in the U.S. in seven surveys, using two methods to estimate c: – 1. The known population method: Asking people how many people they know in 29 populations of known size and estimating c using a maximum-likelihood method. (See Killworth et al. 1998) – 2. The summation method: Asking people how many people they know in each of 17 relation categories – people in their immediate family, people who are co- workers, etc. – and summing to find c. (See McCarty et al.) Both methods produced an average network size of 290 (sd 232, median 231) P. D. Killworth, C. McCarty, H. R. Bernard, G. A. Shelley, and E. C. Johnsen. Estimation of Seroprevalence, Rape and Homelessness in the U.S. Using a Social Network Approach. Evaluation Review 22:289–308. McCarty, C., P. D. Killworth, H. R. Bernard, E. Johnsen, and G. A. Shelley. Comparing Two Methods for Estimating Network Size. Human Organization 60:38–39 H Russell Bernard, Tim Hallett, Alexandrina Iovita, Eugene C Johnsen, Rob Lyerla, Christopher McCarty, Mary Mahy, Matthew J Salganik, Tetiana Saliuk, Otilia Scutelniciuc, Gene A Shelley, Petchsri Sirinirund, Sharon Weir, Donna F Stroup (2010) “Counting hard-to-count populations: the network scale-up method for public health” Sexually Transmitted Infections, : ii11-ii15.

Applications of NSUM NSUM was developed to understand who people know and how they know each other. – It is used today to estimate the size of hard-to-count populations, like populations at risk for HIV/AIDS and illegal migrants. – Where good, trackable statistics are available for many populations of known size, the known population method is preferred. – In countries where good statistics on populations of known size are lacking we rely on the summation method for estimating c.

Finding relation categories In the U.S., the categories for the summation method were derived from ethnography and from experiments we did on how people know one another. The result was the reliable estimate reported above of 290 for c, across seven surveys.

The Challenge NSUM is of most interest to public health officials in countries with non- Indo-European languages. How do we insure that the summation categories are mutually exclusive (alters are not double- counted) and exhaustive (everyone in the network is included)?

The Solution We need a method that can discover categories of knowing that are mutually exclusive and exhaustive. The method must be able to discover categories in the language of the respondent without pre- conceived categories as cues. We apply two methods developed in cognitive science: free listing and frame substitution. Frake, C. O Notes on queries in anthropology. In Transcultural studies in cognition, A. K. Romney and R. G. D’Andrade, eds. American Anthropologist 66, Part II. Rosch, Elizabeth Cognitive representations of semantic categories. Journal of Experimental Psychology 104:192–233.)

One-Mode Personal Network Typically, we use name generators to elicit the names of alters. Respondents provide information on their alters, including the ties between them. The result is a one-mode network of ties between actors.

Two-Mode Personal Network In contrast, two mode networks represent ties between actors and situations. For a personal two-mode network we elicit alter names from respondents using a name generator. Respondents then answer whether each alter corresponds to some event.

Reasonable and unreasonable two- mode event questions Some questions would not be reasonable as we would not expect respondents to be accurate in reporting about all of their alters: – Attendance at meetings – Places they shop Respondents can report accurately on the way they perceive their alters – How you know them

Method – Step 1 Twenty one participants at an NSUM workshop in Thailand free-listed the words in Thai that describe how people know each other. The Thai terms were ordered by frequency. We cut off the terms at those that were mentioned at least three times resulting in 26 categories.

Method – Step 2 From each of the 21 respondents we elicited a network of 30 alters using the following name generator “You know them and they know you by sight or by name, you have had some contact in the past two years and you could contact them now.” For each alter the respondent then evaluated if each of the 26 categories applied to them or not.

Method – Step 3 We created 21 category by category matrices and summed these one- mode matrices into a single one mode matrix. The numbers in the cells indicate the number of times the two terms were used for the same alter. High numbers indicate high overlap between terms; low numbers indicate low overlap.

Results - Objective Ultimately we want a set of categories that are culturally salient in the language of the respondent (in this case, Thai). Categories that have high overlap can then be collapsed. This will produce a set of mutually exclusive and – we hope – culturally salient categories.

Results – Unconstrained graph We treat the affiliation matrix as a network and use the spring embedder program in NetDraw (available in UCINET) to visualize the connections in the matrix This visualization shows the overlap between categories. A line exists if even one alter is a member of the two categories There is one large component and four isolates These isolates are candidates for mutually exclusive categories We need to identify which categories are functionally overlapping so they can be consolidated

Unconstrained

Greater than 1

Greater than 2

Greater than 3

Greater than 4

Greater than 5

Greater than 6

Greater than 7

Greater than 8

Greater than 9

Greater than 10

Greater than 96

Distribution of ties between categories Mode – 0 Median – 0 Mean – 2.38 How much overlap should we tolerate? Look at gaps between overlap values

Gaps between overlap values This graph shows the distribution of the gap between overlap values. A Very large number of overlaps do not occur until values 67 and 96. Smaller but noticeable increases occur at number 17 and number 31.

Visual using constrained tie definitions Tie for overlap >= 17Tie for overlap>=41

To avoid duplicate alter nominations with the summation method we would look for categories (or sets) to collapse Tie for overlap >= 17Tie for overlap>=41

Future Directions Develop other quantitative methods to decide where the tolerance for overlap should be. For example: present 20 native speakers of Thai with a pack of 26 cards, each with the name of one category. Free pile sort these cards and run consensus analysis (using the informal model) to see if there is agreement about the way the categories should be sorted. – If there is agreement, we ask the same or other native speakers to name the piles.