Lecture 5

LECTURE 5. DIFFUSION NETWORKS

Models of diffusion across networks used for:- Diffusion of risk behaviours: smoking, obesity, alcohol consumption, drug use- Adoption of innovations: new medicine, a new laptop, etc (marketing studies)- Spread of diseased: needle exchange, STD

EG: whole network of peer influence and smoking behaviours in classrooms.Perception of peers’ behavioursPerception of social normsLongitudinal studies that untangle homophily from influence

Studying of branding positions

Studying of epidemiology and sexual activities

Christakis N. A., Fowler J. H., 2007, The Spread of Obesity in a Large Social Network over 32 Years, The New England Journal of medicine, 357, 4: 370-379.

MethodsWe evaluated a densely interconnected social network of 12,067 people assessedrepeatedly from 1971 to 2003 as part of the Framingham Heart Study. The bodymassindex was available for all subjects. We used longitudinal statistical models toexamine whether weight gain in one person was associated with weight gain in hisor her friends, siblings, spouse, and neighbors. NB: WRONG METHOD!

ResultsDiscernible clusters of obese persons were present in the network at all time points, and the clusters extended to three degrees of separation. These clusters did not appear to be solely attributable to the selective formation of social ties among obese persons. A person’s chances of becoming obese increased by 57% if he or she had a friend who became obese in a given interval. Among pairs of adult siblings, if one sibling became obese, the chance that the other would become obese increased by 40%. If one spouse became obese, the likelihood that the other spouse would become obese increased by 37% . These effects were not seen among neighbors in the immediate geographic location.

Christakis N. A., Fowler J. H., 2008, The Collective Dynamics of Smoking in a Large Social Network, The New England Journal of medicine, 358, 21: 2249-2258.

Same study but analysis of smoking behaviours

RESULTSDiscernible clusters of smokers and nonsmokers were present in the network, andthe clusters extended to three degrees of separation. Despite the decrease in smokingin the overall population, the size of the clusters of smokers remained the sameacross time, suggesting that whole groups of people were quitting in concert. Smokerswere also progressively found in the periphery of the social network. Smokingcessation by a spouse decreased a person’s chances of smoking by 67% (95% confidenceinterval [CI], 59 to 73). Smoking cessation by a sibling decreased the chancesby 25% (95% CI, 14 to 35). Smoking cessation by a friend decreased the chancesby 36% (95% CI, 12 to 55 ). Among persons working in small firms, smoking cessationby a coworker decreased the chances by 34% (95% CI, 5 to 56). Friends withmore education influenced one another more than those with less education. Theseeffects were not seen among neighbors in the immediate geographic area.

Interest in the processes through which customs, practices, attitudes, or messages spread.

Study of physicians in four citiesData collected 15 months after a new drug with wide potential use, here called "gammanym," had been placed on the market

Each doctor interviewed was asked three sociometric questions: • To whom did he most often turn for advice and information? • With whom did he most often discuss his cases in the course of an ordinary week? • Who were the friends, among his colleagues, whom he saw most often socially? It was decided to include in the sample, as nearly as possible, all the local doctors in whose specialties the new drug was of major potential significance. This assured that the "others" named by each doctor in answer to the sociometric questions were included in the sample

Accordingly, 125 general practitioners, internists, and pediatricians were interviewed; they constituted 85 per cent of the doctors practicing in these fields in four Midwestern citie

The Diffusion of an Innovation Among PhysiciansJames Coleman, Elihu Katz and Herbert MenzelSociometry, Vol. 20, No. 4 (Dec., 1957), pp. 253-270

The dependent variable is the month during which each doctor first used the drug.

This information was obtained through a search of the prescription records of the local pharmacies for three-day sampling periods at approximately monthly intervals over the 15 months following the release date of gammanym.

Three kinds of data: • the month of each doctor's first prescription for the new drug, obtained through a

search of pharmacists' files; • data about the informal social structure of the medical community, derived from

doctors' replies to sociometric questions in an interview; • and many individual attributes of each doctor, likewise obtained by interview

The date on which a doctor first prescribed the new drug was related to a large number of his individual attributes, e.g., • his age• the number of medical journals he subscribed to• his attachments to medical institutions outside his community• certain attitudinal characteristics.

Eg: attitudesHow would you rank the importance of these characteristics in recognizing a good doctor in a town like this? a. The respect in which he is held by his own patients b. His general standing in the communityc. The recognition given him by his local colleaguesd. The research and publications he has to his credit

The following rankings were classified as "profession-oriented": cdab, cadb, cbda, cabd; the following rankings were classified as "patient- oriented": abed, acbd, acdb, bacd.

Results 1Individual attributes

Stronger relations were found when we turned to social attributes-those characterizing a doctor's ties to his local colleagues. Doctors who were mentioned by many of their colleagues in answer to any of the three sociometric questions used the drug, on the average, earlier than those who were named by few or none of their colleagues

The degree of a doctor's integration among his local colleagues was strongly and positively related to the date of his first use of the new drug.

Results 2Social attributes

The constant difference between the profession-oriented and patient- oriented doctors suggests that they differ individually in their receptivity to new developments in medicine. On the other hand, the accelerating difference between the integrated and isolated doctors suggests a kind of "'snowball" or "chain-reaction' process for the integrated

The socially integrated doctors "pull away" from their isolated colleagues, while the doctors differing in some individual attribute simply maintain their intrinsically different receptivity as time goes on Individual process-the number of doctors introducing the new drug each month would remain a constant percentage of those who have not already adopted the drug.

Snowball process-the number of doctors introducing the new drug each month would increase in proportion to those who have already been converted

The highly integrated doctors seem to have learned from one another, while the less integrated ones, it seems, had each to learn afresh from the journals, the detail man (drug salesman), and other media of information

The proportion of pairs whose members had introduced gammanym during the same month, one month apart, two months apart, and so on, according to the chance model proved to be almost identical to the proportion of actual discussion pairs who had introduced gammanym simultaneously or with varying intervals.

This meant the rejection of our original hypothesis that pairs of doctors in contact would introduce the drug more nearly simultaneously than pairs of doctors assorted at random.

Whether the networks, though ineffective for the whole period studied, may have been effective for the early period, immediately after the drug was marketed. An inspection of Figure 5 suggests that this could easily be the case. If only the upper left-hand portion of the matrix, representing the first two, three, or four months, is considered, then there appears to be a tendency for both members of a pair to introduce the drug in the same month.

How closely did the drug introduction of each doctor follow upon the drug introductions of those of his associates who had introduced the drug before him? The answer is: very closely, for early introducers of the drug; not at all closely, for late introducers of the drug.

(avge. interval for random pairs) - (avge. interval for sociometric pairs) avge. interval for random pairs

This measure expresses the difference between the random and actual intervals as a fraction of the difference between the random interval and complete simultaneity (i.e., an interval of zero).

The measure thus has a maximum of 1, and is zero when pairs are no closer than chance

the networks of doctor-to-doctor contacts operated most powerfully during the first 5 months after the release of the new drug: such influence as any doctor's drug introduction had upon his immediate associates evidently occurred soon after the drug became available. • The discussion network and the advisor network showed most pair- simultaneity at the

very beginning and then progressively declined. • The friendship network shows initially less pair-simultaneity than the other two, but-

with some instability-appears to reach its maximum effective- ness later. • Finally, after the fifth or sixth month following the release of the new drug, none of the

networks any longer showed pair-simultaneity beyond chance.

The first networks to be operative as chains of influence appear to be those which connect the doctors in the professional relationships of advisors and discussion partners. Only then, it seems, does the friendship network become operative-among those doctors who are influenced in their decisions more by the colleagues they meet as friends than by those whom they look to as advisors or engage in discussion during working hours. Finally, for those doctors who have not yet introduced the drug by about 6 months after the drug's release these networks seem completely inoperative as chains of influence. The social structure seems to have exhausted its effect.

When more isolated doctors did introduce the drug early, it was not with the help of the social networks

The peak of effectiveness of doctor-to-doctor contacts for the well- integrated doctors appeared in the earliest month for which it can be plotted-the second month-after which effectiveness sharply declined. For the relatively isolated doctors, by contrast, the networks were not so effective at first as were those for the integrated doctors, but they maintained their effectiveness longer

Conclusions

Why should these sociometric ties to colleagues who have used the drug be influential during the first months of the drug's availability, but not later? One possible answer lies in the greater uncertainty about the drug that must have prevailed when it was new. (Data not reported here show that those doctors who introduced gammanym early did so far more tentatively than those who introduced it later.) We know from work in the tradition of Sherif that it is precisely in situations which are objectively unclear that social validation of judg- ments becomes most important

Valente T. W., 1996, Social network thresholds in the diffusion of innovations, Social Networks, 18: 60-89.

The diffusion of innovations is the process by which a few members of a socialsystem initially adopt an innovation, then over time more individuals adopt until all(or most) members adopt the new idea (Ryan and Gross, 1943; Rogers, 1983;Valente, 1993)

• Threshold models• Critical mass models

The initial network approach to diffusion research was to count the number of times an individual was nominated as a network partner (in order to measure opinion leadership) and to correlate this variable with innovativeness as measured by an individual’s time-of-adoption of the innovation under study

This approach to studying diffusion networks was replaced by a more structural approach suggested by Granovetter (1973, 1982). Granovetter argued that weak ties (people loosely connected to others in the network) were necessary for diffusion to occur across subgroups within a system. Burt (1980, 1987) presented a third network approach to diffusion by arguing that structural equivalence (the degree of equality in network position) influenced the adoption of innovations.

The present research provides a fourth model of diffusion networks that incorporates threshold effects. Threshold models of collective behavior postulate that an individual engages in a behavior based on the proportion of people in the social system already engaged in the behavior (Granovetter, 1978).

An individual’s adoption of a new collective behavior is thus a function of the behavior of others in the group or system. Individuals with low thresholds engage in collective behavior before many others do, while individuals with high thresholds do so only after most of the group has engaged in the collective behavior.

The personal network conceptualization of thresholds provides a model of diffusion that creates adopter categories based on innovativeness relative to personal networks. The advantages of this approach are that it can be used (1) to determine the critical mass(2) To predict the pattern of diffusion of innovation(3) (3) to identify opinion leaders and followers in order to understand the two-step flow

hypothesis better.

A collective behavior threshold is the proportion of adopters in a system prior to an individual’s adoption. This system-level threshold is appropriate for collective behaviors such as a riot, since individuals’ behavior is observable (and thus information is complete).

Difficulties:

Individuals may not accurately monitor the adoption behavior of everyone else in the system, eg: family planning, recycling of cans or newspapers, and opinions regarding some issue.Innovations are often uncertain, ambiguous, and risky: Perceived uncertainty and riskencourage individuals to turn to others who have had prior experience with the innovation to learn more about it, to find out how much it costs, and to determine how effective it is

Exposure is the proportion of adopters in an individual’s personal network at a given time. Since adoption thresholds are the proportion of adopters in an individual’s personal network, the threshold is the exposure at the time-of-adoption.Exposure generally increases over time as more individuals in the social system adopt, and varies across individuals according to the adoption behavior of their network partners.

Innovativeness: individuals are innovative with respect to their personal network or innovative with respect to the social system. Those with high network thresholds who adopt early relative to the social system are only innovative relative to the social system,not relative to their personal communication network. Low network thresholdadopters are individuals who adopt early relative to their personal network yet may(though not necessarily) adopt late relative to the social system.

Adopters are classified as• early adopters: time-of-adoption is greater than one standard deviation earlier than the

average time-of-adoption• early majority and late majority: time-of-adoption is bounded by one standard deviation

earlier and later than the average• Laggards: individuals who adopted later than one standard deviation from the mean.

EXTERNAL SOURCES

1. Reanalysis of Coleman, including the external influence of number of scientific journals they read

2. Spread of adoption of hybrid seed corn. Data: The year in which farmers recalled having first planted hybrid corn was the time-of-adoption. Network data were collected by

asking farmers to name• their three best friends• the three most influential• people in their community• the three most influential people regarding various farm innovations• the best person to organize a cooperative project.External influence: n. of visit to the closest city

3. Adoption of family planning methods among all married women of childbearingage in 25 Korean villages in 1973 (Ri = 1047). Network data were obtained by asking the women to name five people from whom they sought advice about (1)family planning, (2) general information, (3) abortion, (4) health, (5) the purchaseof consumer goods, and (6) children’s education.The external influence variable is a respondents’ media campaign exposure

Innovative in respect to the system

Innovative in respect to the network

External influence scores are almost always highest for individuals who are most innovative relative to the system and their personal network. These are the earliest adopters (innovators), who are the first to adopt the innovation. Their early adoption is associated with high external influence.

Second, the upper-triangle scores in Table 3 are usually greater than the respective lower-triangle scores, indicating that external influence tends to make individuals innovative relative to the social system more than relative to their personal network.

Within each phase one would expect tha very low thresholds would have the highest external influence score, followed by low thresholds, followed by high thresholds, and finally very high thresholds. This is not the case. In fact, generally the diagonal element has the largest or second largest external influence score. This indicates that individuals who are consistent in their innovativeness (at both macro- and micro-levels) tend to have the highest external influence in their adoption phase.

Laggards can be partitioned into those who did not adopt because they did not hear about the innovation (rows 10-12, column I), and those who did not adopt because of resistance (rows 10-12, column 4)

Results

The long-standing theory of diffusion has been that the media. salesmen, campaigns, targeted literature, and other factors make individuals aware of innovations, but interpersonal persuasion is necessary to convince individuals to adopt.Thus, the two-step flow hypothesis was created which stated that the media inform opinion leaders who, in a second step, influence opinion followers.

Social network thresholds permit specification of this two-step flow by postulatingthat opinion leaders are those individuals with lower thresholds who influencethose with higher thresholds to adopt. Thus, innovativeness relative to one’spersonal network should be associated with opinion leadership.

Opinion leadership is measured by the number of network nominations received.

For early adopters. it is normative for them to adopt early relative to their personal network, and these individuals are more likely to be opinion leaders. For example, doctors who adopt early relative to both system and network receive an average of 3.08 nominations. Early adopter doctors (system level) with low thresholds receive an average of 2.0 network nominations. compared with early adopter doctors who have high thresholds and who receive only 1.5 network nominations.

In sum, it seems that the diffusion of innovations in these three datasets followed three different patterns, perhaps as the result of three different influence processes.

For the medical innovation data, doctors connected to the broader medical community in Chicago or New York may have been the first to adopt and became opinion leaders for their phase of diffusion. Subsequent adoption was probably based on opinion leadership within stages of diffusion. Thus, the medical innovation data support the two-step flow model in which external influence leads to opinion leadership within phases of diffusion, but not across phases.

For Brazilian farmers, cosmopolitan contact, as measured by visits to the nearest city, had the strongest influence on the adoption of hybrid corn, and interpersonal influence within villages seemed to be less structured. Thus, for Brazilian farmers it may be that being cosmopolitan was associated with earlier adoption, but was not associated with opinion leadership.

For Korean women the classic two-step flow model seemed to operate, in which consistency between system network thresholds was associated with opinion leadership.This opinion leadership was also associated with external influence from the family planning media campaign. Finally, the earliest adopters were considered opinion leaders for the entire village. not just individuals who adopted in their same stage of diffusion.

RECAP

Various fields of applicationsVarious methods: qualitative/quantitativeVarious network approaches: longitudinal, whole networks, egonetsSocial relations, personal attributes, external influences

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Differences in models of diffusions

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