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SOST71032 Social Network AnalysisIntroduction toStatistical Network AnalysisDr Termeh ShafieDepartment of Social StatisticsSchool of Social SciencesThe University of ManchesterDay 4SOST71032 Social Network Analysis Introduction Day 4 1 / 15welcome to part II of the courseoverviewday 4:I introduction to statistical network analysisI parametric and non-parametric approachesI conditional uniform graph distributionsI random graph modelsI introduction to R (with András, Alejandro & Pete)day 5–6 (with András):I models for cross-sectional network data– exponential random graph modelsI models for longitudinal network data– stochastic actor oriented modelsSOST71032 Social Network Analysis Introduction Day 4 2 / 15soware: RI we use the statistical soware RI install R fromhttps://cran.r-project.org/I install Rstudio fromhttps://rstudio.com/I a (very) short introduction to R herewhat you need to know:I import dataI work with vectors, matrices, data frames and network objectsI using functionsI primary packages:statnet, igraph, snahelper, RsienaSOST71032 Social Network Analysis Introduction Day 4 3 / 15statistical network analysiswhat is statistical network analysis?what is statistics? descriptivesI simplify, present dataI describe, summarize datalooking at the dataand reporting what’s there(?part I of the course)inferenceI generalize from sample to populationI conclusion about the populationbased on your dataconcluding with respect to the underlyingpopulation from which the data is from(?part II of the course) SOST71032 Social Network Analysis Introduction Day 4 4 / 15statistical inferencethe science of changing your mind under uncertaintySOST71032 Social Network Analysis Introduction Day 4 5 / 15statistical inferencethe science of changing your mind under uncertainty– a default action (frequentist) or a prior belief (Bayesian)– hypotheses describe what the world might look like:the null hypothesis describes the world with the default actionthe alternative hypothesis is all other worldsdoes our evidence [data] make the null hypothesis look ridiculous or unlikely?SOST71032 Social Network Analysis Introduction Day 4 5 / 15statistical inferencethe science of changing your mind under uncertaintymaking decisions based on facts [parameters] means having informationabout all the facts…but most of the time we don’t have all the information!instead what we know [sample]is dierent from what we wish we knew [population]so we guess [estimate] under uncertaintySOST71032 Social Network Analysis Introduction Day 4 5 / 15statistical inferencethe science of changing your mind under uncertaintymaths [probabilities, distributions] allows usto express rules governing the null hypothesis worldand build a toy model of the null hypothesis worldfrom which we believe our data is fromsince we don’t have facts,we combine data with assumptions to make reasonable decisionsthere’s no magic that makes certainty out of uncertainty!SOST71032 Social Network Analysis Introduction Day 4 5 / 15statistical inferenceSOST71032 Social Network Analysis Introduction Day 4 6 / 15statistical inferencestatistical inferencerelies on the assumption that there is some randomness in the datawe need to model this randomnesswe will return to modelling this randomness later, but firstwhat is statistical network analysis?(i.e. what makes it statistical analysis of networks?)it’s all in the data…SOST71032 Social Network Analysis Introduction Day 4 7 / 15network datawhat is statistical network analysis?‘[…]the study of the collection, management, analysis,interpretation, and presentation of relational data.’[Brandes, Robins, McCranie, Wasserman, 2013]atomic data dyadic data network datamake use of the added informationthat network data gives in comparison to atomicSOST71032 Social Network Analysis Introduction Day 4 8 / 15network datawhat is statistical network analysis?features of network dataoverl

apping dyads interdependenciesimply challenges from a statistical perspectivedata availability improved over the last decadesI traditional data collection by questionnaires:”please name your best friends”I now more automatically logged from electronic communication:telephone calls, emails, social media, online markets, etc.=) opportunities and challengesSOST71032 Social Network Analysis Introduction Day 4 9 / 15statistical analysis of network dataresearch question about networks typically includeI how do networks work?I where could we best manipulate a network (diusion or brokerage)?I how similar are networks?I what are the building principles of these networks?I can we learn from real-life networks to build man-made eicient ones?from a statistical viewpoint, questions includeI how to best describe networks?I how to infer characteristics of nodes in the network?I how to infer missing linksI how to predict functions from networks?I how to find relevant sub-structures of a network?SOST71032 Social Network Analysis Introduction Day 4 10 / 15statistical inferencestatistical inferencerelies on the assumption that there is some randomness in the datawe need to model this randomnessto judge if a network summary is ’unusual’ or if a motif is ’frequent’,there is an underlying assumption of randomness in the networkSOST71032 Social Network Analysis Introduction Day 4 11 / 15network modelswhat is statistical network analysis?the elements of network modelsfrom Brandes et. al. 2013 What is Network Science?a specification ofI how the phenomena (in general i.e. more generally than this particularcase) is abstracted to a networkI how this conceptual network is represented in data(e.g. measured or observed)SOST71032 Social Network Analysis Introduction Day 4 12 / 15statistical models of network datawhat would happen, if we measured the data again?I at a dierent point in timeI on a dierent set of actorsI with dierent environmental factors…want to estimate expected outcome ± variability=) to explain and predict social relations and behaviourSOST71032 Social Network Analysis Introduction Day 4 13 / 15statistical models of network dataspecify realistic probability distributions for social networks,formalizing hypothetical dependencies in the data.statistical network models serve several purposes:explaining social relations and/or behaviour– search for rules that govern the evolution of social networkspredicting social relations and/or behaviour– learn from given data and predict the data yet to comerandom generation of networks that look like real data– algorithm engineering; empirical estimation of average runtime orperformance– simulation of network processes(e.g.,information spreading, spread of disease)SOST71032 Social Network Analysis Introduction Day 4 14 / 15statistical models of network dataspecify realistic probability distributions for social networks,formalizing hypothetical dependencies in the data.I sample graphs at random from this probability distributionI compare sampled to observed network on a feature of interestI if model is good fit, then sampled network resembles observedI modelled structural eects might explain emergence of networkhow do we determine this?I parametric methodsI non-parametric methods(topic of next video lecture)SOST71032 Social Network Analysis Introduction Day 4 14 / 15hypothesis testingnull hypothesisH0: observed network is created from specified model that does Xalternative hypothesisH1: observed network is not created from specified model that does Xif H0 is true we expect to see networks like those we simulate from model so:decision ruleif simulated networks look like the observed in only a(100%) of the caseswe would reject H0 on the a(100%) significance levelotherwise, we cannot reject the H0observed networkdistribution of measure under null modelsummary measureSOST71032 Social Network Analysis Introduction Day 4 15 / 15