RPAD637 Week 13 Reading Summary: Models for Studying Network Effects & Diffusion Jackson and Nampoothiri

Size: px

Start display at page:

Download "RPAD637 Week 13 Reading Summary: Models for Studying Network Effects & Diffusion Jackson and Nampoothiri"

Wilfrid Hancock
6 years ago
Views:

1 Both the following articles are cited often by contemporary network scholars and important to the discussion of social network analysis. Watts (1999) was published in tandem with publication of his book Small Worlds: The Dynamics of Networks Between Order and Randomness, while the work of Provan & Milward (1995) was an important precursor to works published later by themselves as well as other academics. Provan, K.G. & Milward, H.B. (1995). A preliminary theory of interorganizational network effectiveness: A comparative study of four community mental health systems. Administrative Science Quarterly, 40, [Abstract, p. 1] Background Despite little empirical evidence before publication of this article, there was a lot of anecdotal work describing the perceived benefits of mental health patient service provision through networks of providers. The prevailing view among many service professionals, policy makers, and researchers is that by intergrating services through a network of provider agencies linked through referrals, case management, and joint programs, clients will gain the benefits of reduced fragmentation and greater coordination of services, leading to a more effective system (Warren, Rose and Bergunder, 1974; Rogers and Whetten, 1982; Department of Health and Human Services, 1991; Goldman et al., 1992; Alter and Hage, 1993) (pp. 2-3).

2 In the public and not-for-profit sectors, where a public interest motive is involved, network outcomes are especially salient, and the rationale for organizations cooperating to accomplish system goals rather than organizational ends is often stronger than in the private sector, even when specific incentives to integrate and cooperate are weak (p. 3). Unfortunately, although the rationale for network involvement may be strong, there is almost no empirical evidence to support the presumed relationship between integration and network effectiveness or to indicate what network characteristics are associated with effective outcomes (p. 4). Research Question Consistent with the ideas discussed above, our study was organized around a single fundamental research question: What, if any, is the relationship between the structure and context of mental health networks and their effectiveness (p. 4)? [T]he basic question underlying our research is whether network structure, particularly integration and related issues of coordination, is related to network effectiveness (p. 10). Research Sites and Population Four sites were selected to represent metropolitan areas large enough to have multiple mental health service providers, but small enough to make data collection manageable: Tucson, Arizona; Albuquerque, New Mexico; Providence, Rhode Island; and Akron, Ohio. Provan and Milward focused on a subset of mental health clients, those categorized as severely mentally ill (SMI). SMI clients were defined as adults (over 18) whose emotional or behavioral functioning is severely and persistently impaired in a way that interferes with their capacity to remain in the community without supportive treatment (p. 7). Data Collection Extensive data collection procedures are described in detail pp Important here is their use of questionnaires, interviews and follow-up phone calls to remedy any inconsistencies in the data, improving validity. Provan and Milward interviewed SMI clients, and also members of their family to get impressions from both the mental health client and the family. The total population studied included 265 individuals across the four sites, and took over a year to collect. 2

Client (QofL/satisfaction): Items related to client quality of life Client (psychiatric/medical status): Items related to the psychopathology and physiological status Family: Repsonses by family

3 Client (QofL/satisfaction): Items related to client quality of life Client (psychiatric/medical status): Items related to the psychopathology and physiological status Family: Repsonses by family members of clients Case management/therapist: Responses by client case managers and/or therapists Service Links: [C]onfirmed scores for each of the five types of linkages for all agencies in each system [divided] by the total number of agencies in that system (p. 11). Organizational Links: [T]he mean number of agency links of any of the five types that occurred in each system (p.11). 3

4 4

5 Based on the results in the tables (above), and the rich qualitative data explored for each site (pp ), Provan and Milward propose a model of network effectiveness (below). Conclusion 5

Watts, D.J. (1999). Networks, dynamics, and the small-world phenomenon. American Journal of Sociology, 105(2), 493-527. What Is the Small-World Phenomenon?

6 Watts, D.J. (1999). Networks, dynamics, and the small-world phenomenon. American Journal of Sociology, 105(2), What Is the Small-World Phenomenon? We ve all experienced the small world phenomenon. You meet someone at an office or a restaurant. You start a seemingly trivial conversation where you grew up, where you work, and the like. Then a connection is made to a person you both know, and your relationship with this former stranger is cemented. How does that happen in a city with so many people? What are the chances? Basically, Watts explores a mathematical explanation of the small world phenomenon. Minute Changes in Local Network Structure Matter One of my favorite takeaways from the work of Watts is the immense significance of even seemingly small changes at the local level on the larger global network structure. This is a basic tenet in complex science. To wit: equally significant changes in global structure can result from changes in local structure that is so minute as to be effectively undetectable at the local level (p. 498). This is the idea of a butterfly that flaps its wings in Canada causes tornados in Kansas. Initial Notation L: Characteristic Path Length C: Clustering Coefficient v: Vertex k: Number of Connections n: Number of Actors in the Sample N: Total Actors in the World 6

Properties of Random-Clustered Networks Formalization of the Small-World Phenomenon Bearing in mind these conditions, the following questions present themselves:

What graph has the lowest possible characteristic path length, and what is its clustering coefficient> 3.

7 Properties of Random-Clustered Networks Formalization of the Small-World Phenomenon Bearing in mind these conditions, the following questions present themselves: 1. What is the most clustered graph possible, and what is its characteristic path length? 2. What graph has the lowest possible characteristic path length, and what is its clustering coefficient> 3. What do these results imply about the relationship between the clustering coefficient and characteristic path length of a sparse graph? (pp ) Watts then introduces the concept of the caveman, and a caveman graph. This convention is used throughout the remainder of the article. 7

8 The Theory of Length Contraction in Sparse Networks 8

$Watts then uses the following rules to create a graphic representation of the propensity of strangers to meet, given the fraction of the$

9 Watts then uses the following rules to create a graphic representation of the propensity of strangers to meet, given the fraction of the friends that they currently share. The resulting equation, equation #5 remains an important actor throughout the remainder of his argument. 9

This α-model suffers from a distinct problem, namely that for small α, the resulting graphs tend overwhelmingly to consist of small, isolated, and

Watts proposes a remedy by adding the following additional constraints to his model: [W]e will see that the results generated by the corresponding model

10 This α-model suffers from a distinct problem, namely that for small α, the resulting graphs tend overwhelmingly to consist of small, isolated, and densely internally connected components (p. 505). Watts proposes a remedy by adding the following additional constraints to his model: [W]e will see that the results generated by the corresponding model exhibit sufficiently generic features in the intermediate regime that quite general conditions can be specified under which small-world networks should arise (p. 506). Figure 5 compares the resultant path lengths and clustering coefficients on a normalized scale. 10

11 Watts furthers his arguments, adding important restrictions to the model that produces these graphs. There is so much information presented here, at some point it is just easier to tell you to read the article is these ideas sound interesting. He then applies his findings to real world networks, but not all of them are social networks ; rather they are a mix of social networks and other networks probed by the hard sciences as applied to social network theory. Thus is a convincing attempt to generalize his findings to real world scenarios. Watts looks at three networks movie actors appearing in the same movies, the United States power grid system, and the C. eglans neural network to test his small-world phenomenon findings. When plotted against his small-world and caveman hypotheses, two key graphs emerge (figures 9 and 10) that tell a stunning story. 11

Conclusion Again, if as interested as I am in the concept of small-world networks, and their application to a multitude of real world networks (albeit not all social in nature), I think you d get a

12 Conclusion Again, if as interested as I am in the concept of small-world networks, and their application to a multitude of real world networks (albeit not all social in nature), I think you d get a kick out of this article, and the work that has followed. Otherwise, I think this (below) is a good summary of the concepts discussed throughout the article, so I have copied the entire first paragraph of the two paragraph conclusion (p. 524): 12

13 Definitions Discussed by Watts (1999) 13

14 Ibarra, Herminia and Steven B. Andrews. (1993). Power, Social Influence, and Sense-Making: Effects of Network Centrality and Proximity on Employee Perceptions. Administrative Science Quarterly, 38(2), The paper explores the idea that network interaction patterns affect employee perceptions. This is carried out through two mechanisms: localized social influence based on network proximity (processes that produce attitude convergence among socially proximate pairs of individuals) systemic power based on network centrality (power effect by which individuals locations in the network shapes their access to and control over resources, and thus affects their evaluation of workplace features) The authors present three hypotheses H1: Network interaction affects individuals perceptions through two mechanisms: localized social influence based on network proximity and systemic power based on network centrality. H2a: Expressive network proximity will be a stronger predictor of work-related perceptions than instrumental network proximity. H2b: Instrumental network centrality will be a stronger predictor of work-related perceptions than expressive network centrality. H2a and H2b are based on the different types of network relationship. Expressive ties tend to be stronger, more intimate links, tend to connect people who are similar on a variety of personal characteristics, and involve more frequent interaction. On the other hand, instrumental links tend to be weaker ties linking people who differ in personal characteristics and/or in their positions, in the vertical and horizontal division of labor or in access to scarce resources. H3: The rank order of independent variables, from the least to the most effect on workrelated perceptions will be as follows: individual attributes (i.e., education, gender, tenure, and past experience), formal positions (i.e., rank and subunit membership), and centrality & proximity. The research The research was conducted in a New England advertising and public relations agency (N=79). In the first phase, included unstructured interviews with representatives from various groups to define boundary and construct dependent variables. Second phase included structured interviews to get actual data. The independent variables used were: Network centrality (friendship centrality and advice centrality) Network proximity Tenure Prestigious past work experience 14

15 Gender Rank Departments in the firm (one responsible for client relationships, one responsible for core work of firm such as creative department, and one providing support services) The dependent variables: Encouragement of risk taking Information access Individual acceptance Job autonomy Inter-departmental conflict Results Table 1 provides the means and standard deviations. Table 2 reports the inter-correlations. All non-network variables were significantly correlated with at least one of the five dependent variables. Advice centrality showed higher correlations with dependent variables than friendship centrality. It was also highly correlated with rank thus suggesting more likelihood of duplicating the effects of formal position. 15

16 Table 3 showed that the individual attributes were insignificant, which is consistent with H3. The columns 2 and 3 showed that friendship centrality was insignificant, and that advice centrality was significant on three dependent variables (i.e., risk taking, acceptance, and information access). Thus, the H 2b was supported. Table 3 16

17 The effects of rank disappeared when advice centrality was added to the risk-taking, acceptance, and information access models. This finding suggested that the portion of variance accounted for by formal rank in the models in column 1 was captured by advice centrality, which was consistent with H3. Table 4 was the result of the network-effects models in advice network. Table 4 showed that proximity (the rho effect) was insignificant in advice network. By contrast, advice centrality is significant in risk taking, acceptance, and information access as the OLS model showed. Table 5 was the result of the network-effects models in friendship network. The result showed that friendship network proximity was not a very good predictor of employees perception. But, consistent with H2a, interaction in the friend network affected perceptions of interdepartmental conflicts. In conclusion, network factors shape job-related perceptions more than the effects of individual attributes and formal positions. And, both advice network centrality and friendship network proximity were significant effect on employees perception although advice network centrality had a stronger effect. 17

18 Marsden, Peter V. and Noah E. Friedkin. (1994). Network Studies of Social Influence. Pp in Wasserman and Galaskiewicz (eds.) Advances in Social Network Analysis. Hypothesis The proximity of two actors in social networks is associated with the occurrence of interpersonal influence between the actors. Two perspectives of social influences are compared and contrasted Structural Cohesion: emphasizes network connectivity among actors Equivalence: describes the similarity of actors in terms of their profiles of interpersonal relations. Substantive Bases of Social Influence Attitude similarity based on social comparison to reference group attitudes are confirmed and reinforced when they are shared with the comparison group but altered when they are discrepant. How reference groups are determined possession of information about attitude or behavior of another actor is necessary for influences Influence based on solidary relations such as friendship or hierarchical ones such as authority Effects of local environments (geographic proximity, roles) Approach 1: Structural Cohesion Structural cohesion defines social proximity in terms of the number, length, and strength of paths o Simple adjacency (direct tie) implies intense ties Short connections via intermediaries is a variation o Emphasis of structural features indicate retain the idea that actors are proximate to the extent that they are jointly located in structurally cohesive regions of networks Approach 2: Equivalence Equivalence defines social proximity in terms of similarity of actor s profiles of network relations o Structural equivalence identical relations o Automorphic equivalence o Regular Equivalence equivalent network environment Problems of both approaches Cohesive and Equivalent cluster membership intersect in most networks Underlying social processes is therefore likely to overlap Therefore, suitable statistical controls are needed to assess the relative contribution of social processes 18

Statistical Model The authors suggest that a Network Effects Model is the best to study social influence The model is more appropriately estimated using : maximum likelihood (ML) and Instrumental/two

19 Statistical Model The authors suggest that a Network Effects Model is the best to study social influence The model is more appropriately estimated using : maximum likelihood (ML) and Instrumental/two stage LS (IV/2SLS) Many variations of this model have been employed by various researchers. The following points must be considered while developing a statistical model: How to determine and specify lagged time for influence process Use least-squares dummy-variable regression (as applied by Mizruchi, 1989) to study homogeneity of network elements If measuring effect on single dependent variable, network effect model is preferable If measuring effect on multiple dependent variables, dyadic approach is more advantageous. Empirical Applications by researchers over the years Less attention on experiments and more use of the network effects model (e.g. Davies and Kandel, 1981) Several studies focus on dyads (e.g. Duncan et al. 1971) that assume a simple influence structure Several network effect studies focused on territorial units (e.g. Gould, 1991) Number of organizational studies examine one or both of the theoretical perspectives on influence (e.g. Mizruchi, 1989, 1990) Problems and open issues in network studies of social influences Claims about effects are mostly derived from non-experimental and cross-sectional studies Analyst infer from homogeneity & network pattern Structural cohesiveness and Equivalence can become flawed if network measure miss some important resources Conformity pressure (majority effects) affect influence model 19

WORKPLACE FRIENDSHIPS: ORIGINS AND CONSEQUENCES FOR MANAGERIAL EFFECTIVENESS

WORKPLACE FRIENDSHIPS: ORIGINS AND CONSEQUENCES FOR MANAGERIAL EFFECTIVENESS HILLA DOTAN Recanati Graduate School of Business Administration Tel-Aviv University Ramat Aviv, Tel-Aviv 69978, Israel ABSTRACT