Social Effects in Blau Space:

Transcription

1 Social Effects in Blau Space: Miller McPherson and Jeffrey A. Smith Duke University

2 Abstract We develop a method of imputing characteristics of the network alters of respondents in probability samples of individuals using the homophily principle to estimate the properties of a respondent s core discussion network. These properties include a measure of the potential exposure to the attitudes, values, beliefs, and other characteristics of the respondent s network alters. Data from the General Social Survey data demonstrate that the imputed network characteristics are strongly related to individual level measures such as attitudes, beliefs, and other variables typical of survey analysis. In some cases, the imputed network variable drastically alters and even eliminates the effects of standard sociodemographic variables such as age and education. We follow with examples of health-related behavior from the Panel Study of income Dynamics

3 The Relational Approach N cases become N(N-1)/2 cases The metric is now distance Distance is created by Homophily

4 The Homophily Principle Applies to almost all social distinctions: Age, race, gender, beauty, height, weight, skin color. Has been found in almost all studies of social contact. Governs the large-scale organization of most kinds of interaction. Shapes the most elementary form of social structure: the probability of contact between two individuals. Produces localization of social entities.

5 Activities are localized in social space: Points are a representative sample of individuals. Boxes are a representative sample of associations.

6 What ties large scale systems together? The homophily principle simplifies transactions in Blau space, turning sociodemographic distance into network distance.

7 As the scale of the system grows larger, the Homophily principle becomes more and more powerful.

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11 Focus on Industrial Society Sizes in millions or billions High dimensional Blau space Differentiation of types of relationships Social entities operate at multiple levels

12 The number of potential connections in systems of varying size Connections (N(N-1)/2) System Size (N)

13 Estimated number of Confiding relationships on Earth 7,280,000,000,000

14 Ratio of Actual to Potential

15 Assumptions in the theory People have a finite capacity for processing information and finite time and energy The homophily principle organizes the flow of information across the system

16 Some implications of the theory: The localization of information through homophily leads to the formation of niches for social entities These social niches evolve and interact with each other dynamically The location of an individual inside a niche conditions the probability that the individual will be affiliated with the social entity

17 Core question for the present: Is the presence of socially transmissible characteristic in an individual the result of contagion in Blau space, or is it a result of human capital, material resources, or some atomistic process?

18 Activities are localized in social space: Points are a probability sample of individuals. Boxes are a probability sample of activities.

19 For example: Are highly educated people more tolerant because they have been trained by the educational institution to appreciate diversity [education causes tolerance]? Or, is it that educated people tend to be surrounded by other educated people who express tolerant views, and become more tolerant as a result [birds of a feather not only flock together, but they fly in parallel]?

20 Another example: Do highly educated people desire fewer children because there is something inherent in the educational process that inhibits childbearing [education causes a desire for smaller families]? Or, do highly educated people get their views on desired family size from their friends, who are also highly educated [social context affects desired family size]

21 Today s approach to the problem: 1. Parameterize Blau space in multiple dimensions. 2. Model the dependencies among social entities produced by proximity in Blau space. 3. Use the estimated dependencies to impute local social context 4. Compare the predictive power of social context and the conventional model

22 Parameterizing Blau space The General Social Survey asked respondents in 1985 and 2004 to name the persons with whom they discussed important matters, and to report the following social characteristics of those persons: Age, Race, Sex, Religion, Education.

23 Parameterizing, cont. The survey also collected information on those characteristics for the respondents, as well as a rich variety of attitudinal and belief variables.

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26 Parameterizing, cont. We create a dataset of all pairs of the GSS respondents in a given year, and assume that these pairs constitute a representative sample of pairs who do not discuss important matters with each other. Each of these pairs has a vector of Blau distances in Education, Age, Sex, Race, and Religion (e.g. D ij = Age i -Age j ). This dataset is the set of Controls, in our Case Control analysis.

27 Parameterizing, cont. We create a parallel dataset consisting of the pairs generated by the reports of each respondent on one of their core discussion partners. Again, each pair is characterized by the Blau distances in Education, Age, Sex, Race, and Religion. This dataset is the set of Cases.

28 Parameterizing, cont. We combine the cases and controls into a single dataset, and estimate the parameters in the following case control logistic regression model: Ln[P(tie ij )/[1-P(tie ij )] = ά + β( Dij ) where β( Dij ) represents the set of Blau distances and the associated parameters.

29 Case Control Analysis It is well known in the biometric literature that logistic regression provides consistent estimates up to a constant of proportionality for the parameters of models fitted to data sampled on the dependent variable (c.f. Hosmer and Lemeshow 1978, Pregibon 1974, Allison 2007). Our application fits into this model in the following way

30 Case Control Analysis, cont. The sample of relationships produced by the GSS study of core discussion networks is a representative sample of core confidant ties, since the respondents are a probability sample of the U.S.population.

31 Case Control Analysis, cont. The respondents in the GSS generate a sample of potential ties representative of the universe of core confidant ties that are unrealized, since the individuals are sampled independently (approximately). This result follows because the probability of obtaining a true network alter of any particular respondent in the actually measured core discussion networks is very small (p<.00001, with heroic assumptions about sampling design).

32 Case Control Analysis, cont Thus, we have a representative sample of observed core discussion network ties, and a representative sample of non-ties, which may be combined in the case control study to allow us to estimate the parameters of our model of homophily in Blau space.

33 Estimated effects of Blau Distances Intercept Race Distance Religion Distance Education Distance Age Distance Gender Distance (All coefficients significant beyond.001)

34 Modeling Dependencies From the estimated logistic regression equation, we recover fitted probabilities of contact between persons i and j in our sample, given their distance in Blau space: P(contact ij D ij )=1/(1+e -(ά + β( Dij ) )

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40 Modeling Dependencies, cont. These probabilities are assembled into a row stochastic distance matrix P with which we can form the term PY i, the i th element of which is proportional to the expectation of Y for the potential network alters of respondent i, located in that respondent s position in Blau space.

41 Modeling Dependencies, cont. In concrete terms, the product PY i imputes the social context of ego s locale in Blau space. If Y is binary, then PY i estimates the proportion of potential alters which have attribute Y. If Y is continuous, PY i estimates the mean value of Y among ego s potential network alters. Since the y-intercepts from the case control analysis are biased, these estimates are correct up to a constant of proportionality, which is all that is required for the next stage of analysis.

42 Modeling Dependencies, cont. With our imputed network PY in hand, we then form the spatial/network regression model: Y i = ηx i + ΔPY j + Θ i Where ηx i represents the conventional survey analytic effects of X variables, Δ parameterizes the homophily effects in Blau space, and Θ i is stochastic.

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44 Return to our Tolerance Example: For our tolerance example cited earlier, the network regression model will be: Tolerance i = a + b 1 Education i + b 2 PTolerance j + error i

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47 Summary The social context variable not only is a substantial predictor of these survey measures of attitudes, but it actually destroys much of the effects of the conventional major predictors of those attitudes.

48 To emphasize, the model: Is applicable to any social survey variables, from any sample, as long as sociodemographic information is measured in that survey Does not require any information on networks in that survey

49 A Modest Claim If these results hold in general, then past studies of attributes in surveys like the GSS are almost certainly producing biased and inconsistent estimates due to the omission of social context. All prior studies of these survey variables may be producing illusory results due to the operation of social contagion in Blau space.

50 Some Implications The effects of sociodemographic variables may occur through social distance in Blau space, rather than through the traditionally conceived causal mechanisms Contagion in Blau space is a baseline phenomenon that should be accounted for before other effects are posited

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53 A Health Application to a Dataset with No Direct Network Variables Panel Study of Income Dynamics N=1112 Years 1999,2001,2003,2005 Growth Curves: Health, BMI, Ailments

54 Methods We compute the social context of a position in Blau space by constructing Ego s view of the health terrain We argue that Ego will tend to regress to the expected value of their social context over time, rather than to the grand mean over time.

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58 Regression to Social Context or Regression to the Grand Mean? Change in Count of Ailments Estimate Std. Error t value Pr(> t ) (Intercept) < 2e-16 *** Deviation from Alters e-16 *** Deviation from Overall Mean e-12 *** Change in Reported Health: Estimate Std. Error t value Pr(> t ) (Intercept) < 2e-16 *** Deviation from Alters e-16 *** Deviation from Overall Mean e-10 *** Change in BMI: Estimate Std. Error t value Pr(> t ) (Intercept) e-11 *** Deviation from Alters Deviation from Overall Mean *

59 Interpretations Network Neighborhood Contagion: The Cristakis Effect: Strong and Weak Ties Local Social Context: Family, Neighborhood, Workplace: Lifestyle Generalized Social Context: Position in Stratification System, Urban-Rural Location, Geography. Location in the Cultural System: Cultural Niches: Habitat and Habitus

60 Some limitations Statistical properties not well understood P term in Y i = ηx i + ΔPY i + Θ i is estimated, not fixed Assumed unity of network content All relations assumed to be from same distributional family P estimates based on very strong ties Strong ties are embedded in dense neighborhoods Assumes transmissible Y Genetically coded Y operates on different time scale Limited to entities with niches Will not explain uniformly distributed Y

61 Miller s Final Rant for the Day Homophily is not choice Social change is not rewiring, but is microevolution The action in Blau space is relational not attributional. All surveys of individuals are samples of the residue of networks: Each observation is a highly fallible information dump from a node in a high dimensional space organized by the homophily principle. The above implies that 1) survey observations are serially correlated in Blau space and 2) survey datasets actually have some number in the factorials of n and k dependent observations, rather than n independent observations, where n is the number of individuals, and k is the number of variables. Blau space is a lens that enables us to view the connections implicit in survey data with the high dimensional web of human networks. Micro-level networks, the bipartite (multipartite) networks of connections between individuals and and higher level social entities, and the connections among the higher level entities coevolve in Blau space. Human networks are instantiations of high dimensional objects that are mostly unobservable, not the zeros and ones in our models.

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