Clustering Network Data
Anuska Ferligoj, Tamas Rudas

Bojan Korenini - Zenel Batagelj
Segmenting the market according to consumer's benefits and value orientations - the application of structurally determined laddering method

As marketing practice accepted the viewpoint that company does best when directing its activities according to the needs and desires of customers in chosen target markets, the necessity for the research methods that would increase the depth of understanding of the consumers emerged.

The laddering research method counts as one of new approaches that are trying to fulfill this request. Although there are different approaches to laddering, the method originates in the field of qualitative methodology. Theoretically it draws from means-end theory that treats objects as means to achieving certain valued states, or ends. By using a series of directed probes, typified by the question "Why is this important to you" it identifies the specific linkages between product attributes, consumer benefits and consumer's value orientations. The data create a hierarchical value map. Such map is treated as a directed graph, which shows a unique way in which a product is linked to consumer's personality.

There are a lot of different quantitative and qualitative research methods that are aimed at exploring the relationship between the product and consumer's value orientations. In the case of quantitative research methods, there is a lack of information, how specifically different characteristics of a product fit into the consumer's life. On the other hand qualitative methods are better at revealing such information, but because of unstructured nature of such methods they are usually conducted on smaller samples. This fact qualifies them to explore just the respondents under examination rather then to be representative for the whole population of consumers.

Laddering overcomes such problems. The method provides information about specific individual-based linkages between consumer product characteristics and consumer's value orientations. Because of structured gathering of the data, method can be conducted on larger samples.
There are different approaches to laddering: soft laddering, hard laddering and structurally determined laddering method. The later was developed by the authors of this paper. Although one of the advantages of soft laddering method is that it can be conducted on larger samples, in practice sample size usually doesn't exceed 50 or 100 respondents, because soft laddering interviews are difficult and require specially trained interviewers. Besides identification of common structures in complex qualitative data is very laborious.

Most frequently the type of marketing decisions where laddering method proves supportive require statistically grounded conclusions. The new approach - structurally determined laddering can be conducted on several hundred or more respondents (it can be also conducted over the phone). In this way conclusions of the laddering research are no longer limited to the sample of respondents under the scope. Beside that structurally determined laddering opens a lot of new possibilities, in the sense of analysis and practical application of research results, which depart significantly from the possibilities that soft laddering could offer.

Authors of the paper wish to discuss different approaches to laddering method in the context of quantitative and qualitative research methods, statistical analyses of such network data and benefits that follow from the application in marketing, mainly in the field of market segmentation.

Simona Korenjak- erne - Vladimir Batagelj - University of Ljubljana
Clustering Personal Networks as Symbolic Objects

Personal or ego-centered networks are frequently encountered in the social science research. A unit of the analysis is a respondent (ego) with his/her personal network (alters). Each unit is described by selected variables, which are usually measured in different scales.
Several (other) variables are also measured on alters, that describe relationship among ego and alters and properties of alters. Personal networks can be very large.

In the paper we focus on two problems:
- Presentation or description of a personal network.
- Reduction of a personal network's size.
For the descriptions of personal networks symbolic objects are used.
Using variable's distributions (instead of the value of an appropriate statistics - e.g. mean value used in the "standard" approach), the symbolic objects provide a more detailed description of personal networks. Based on this descriptions the adapted version of the leaders method was developed, which is a variant of the dynamic clustering method.

The results of the proposed approach will be presented on the social support networks in Ljubljana 2000 data set, collected at the Faculty of social sciences of University of Ljubljana.

Mark Sh. Levin - Ben-Gurion University of Negev
Towards Multilayer Network and Combinatorial Models

We examine multilayer network, multilayer cellular automata, and their combinations. Applications are oriented to complex composite systems (social networks, organizational systems, sociotechnical
systems, etc.).

Multilayer network consists of the following: (1) basic elements for each layer: a set of elements (persons/individuals, tasks, groups/teams, rules, rights, rooms, goods, etc.) and some structures on them (binary relations, hierarchy, etc. as horizontal correspondence); (2) binary relations between structures of different layers (vertical correspondence). k-layer cellular automata is the following: (a) a set of elements at each layer; (b) each element has several types of basic states and four kinds of influences (logical or probabilistic functions, optimization models) as follows: selfinfluence, neighbor influence, influence of the higher layer, and influence of the lower layer; (c) layers can be composite ones. The following combinatorial problems are considered: (i) assignment/allocation; (ii) clustering (e.g., grouping, skeleton clustering); (iii) routing; (iv) approximation / covering; and (v) multiple matching.

A list of applied examples involves the following: (a) allocation of personnel; (b) allocation of information access and / or decision making functions into a set of specialists; etc.

Andrej Mrvar(1) - Vladimir Batagelj(2) - (1)Faculty of Social Sciences, University of Ljubljana Slovenia - (2) Faculty of Mathematics and Physiscs, University of Ljubljana Slovenia
Visualization of Social Networks using SVG

SVG (Scalable Vector Graphics) is a language for describing two-dimensional vector graphics based on XML (eXtensible Markup Language). Three different types of graphic objects are supported:
paths consisting of straight lines and curves, images and text. SVG provides all transformations which are usual in standard vector graphics packages. Additionally, animation can be applied to SVG pictures. Pictures in SVG can be examined using Web browsers using a special plug-in. Objects in SVG DOM (Document Object Model) can be accessed using JavaScript language and in this way parts of the picture can be manipulated dynamically from the Web browser.

In the paper some approaches to visualization of social networks implemented in Pajek as options for exporting layouts to SVG will be discussed and illustrated by some typical examples.

Wolfgang Sodeur - University of Essen
Patterns of Institutional Affiliations of Household Members and Children's Social Contacts

The aim of this paper is to analyse the impact of properties of the local household environment on structural aspects of children's social relations.

The structure of social relations of children is described by some aspects like the relative amount of social relations at different locations (home, street, school, sport clubs), multiplexity of contacts (same persons at different locations), more or less restricted size of social circles (number of persons met simultaneously), and so on which seem to be important for socialisation processes under a theoretical perspective. On this basis children are clustered into a few classes. Afterwards these classes are partly reconstructed by means of patterns of relations of other (mainly older) members of the households.

The empirical data were generated in 40 systematically selected small areas ("extreme cases") with 3000 to 15000 inhabitants each. Within each regional unit, a random sample of about 25 children age 8-9 and 13-14 was drawn. The children and one parent were interviewed, mainly about their personal relations and the institutions they were affiliated with.

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