# Statistical Analysis of Social Networks

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Statistical Analysis of Social Networks Krista J. Gile University of Massachusetts, Amherst Octover 24, 2013

2 Collaborators: Social Network Analysis [1] Isabelle Beaudry, UMass Amherst Elena Erosheva, University of Washington Ian Fellows, FellStat Karen Fredriksen-Goldsen, University of Washington Krista J. Gile, UMass, Amherst Mark S. Handcock, UCLA Lisa G. Johnston, Tulane University, UCSF Corinne M. Mar, University of Washington Miles Ott, Carleton College Matt Salganik, Princeton University Amber Tomas, Mathematica Policy Research For details, see: gile

3 Career Path (how it felt) Social Network Analysis [2] M.S. Work people High School PhD, Postdoc Faculty College math

4 Career Path (employer version) Social Network Analysis [3] ratio: math/people High School College M.S. Work PhD Postdoc Faculty

5 Outline of Presentation Social Network Analysis [4] 1. What is a Social Network? 2. Why do we want to analyze a social network? 3. What can we know about a social network? 4. How do we analyze a social network? 5. Descriptive Analysis 6. Design-Based Inference 7. Model-based (likelihood) Inference 8. Examples 9. Discussion

6 Outline of Presentation Social Network Analysis [5] 1. What is a Social Network? 2. Why do we want to analyze a social network? 3. What can we know about a social network? 4. How do we analyze a social network? 5. Descriptive Analysis 6. Design-Based Inference 7. Model-based (likelihood) Inference 8. Examples 9. Discussion

7 (Cross-Sectional) Social Networks Social Network Analysis [6] Social Network: Tool to formally represent and quantify relational social structure. Relations can include: friendships, workplace collaborations, international trade Represent mathematically as a sociomatrix, Y, where Y ij = the value of the relationship from i to j (c) Sociogram (d) Sociomatrix

8 Social Networks that are harder: Social Network Analysis [7] Networks that change over time (ties, nodes, discrete, continuous, models, data) (effectively) Unbounded networks (the internet, social contacts in the world) Multiple social networks (friendships, co-work, leisure) Multi-modal networks (people and places) Valued networks (amount of trade, signed networks) Event networks ( , armed conflict)

9 Outline of Presentation Social Network Analysis [8] 1. What is a Social Network? 2. Why do we want to analyze a social network? 3. What can we know about a social network? 4. How do we analyze a social network? 5. Descriptive Analysis 6. Design-Based Inference 7. Model-based (likelihood) Inference 8. Examples 9. Discussion

10 Why do we want to analyze social networks? Social Network Analysis [9] Because it s cool and fun. Because we want information we can t get other ways. Learn about nodes Learn about relations Learn about processes Learn about the particular network Learn about the process the network came from

11 Outline of Presentation Social Network Analysis [10] 1. What is a Social Network? 2. Why do we want to analyze a social network? 3. What can we know about a social network? 4. How do we analyze a social network? 5. Descriptive Analysis 6. Design-Based Inference 7. Model-based (likelihood) Inference 8. Examples 9. Discussion

12 What can we know about a social network? Social Network Analysis [11] All nodes, all relations All nodes, some relations Some nodes, some relations Others we won t emphasize here: Attributes of nodes (where do your facebook contacts live?) Attributes of relations (who is your *best* friend?) Information on processes over the network (how much trade between countries?)

13 Partially-Observed Social Network Data Social Network Analysis [12] Some portion of the social network is often unobserved.

14 Partial Observation of Social Networks Sampling Design: Choose which part to observe: Ask 10% of employees about their collaborations Egocentric Adaptive Out-of-design Missing Data: Try to survey the whole company, but someone is out sick Boundary Specification Problem: Should a contractor be considered a part of the company? Social Network Analysis [13]

15 Partial Observation of Social Networks Sampling Design: Choose which part to observe: Ask 10% of employees about their collaborations Egocentric Adaptive Out-of-design Missing Data: Try to survey the whole company, but someone is out sick Boundary Specification Problem: Should a contractor be considered a part of the company? Social Network Analysis [14]

16 Partial Observation of Social Networks Sampling Design: Choose which part to observe: Ask 10% of employees about their collaborations Egocentric Adaptive Out-of-design Missing Data: Try to survey the whole company, but someone is out sick Boundary Specification Problem: Should a contractor be considered a part of the company? Social Network Analysis [15]

17 Partial Observation of Social Networks Sampling Design: Choose which part to observe: Ask 10% of employees about their collaborations Egocentric Adaptive Out-of-design Missing Data: Try to survey the whole company, but someone is out sick Boundary Specification Problem: Should a contractor be considered a part of the company? Social Network Analysis [16]

18 Partial Observation of Social Networks Sampling Design: Choose which part to observe: Ask 10% of employees about their collaborations Egocentric Adaptive Out-of-design Missing Data: Try to survey the whole company, but someone is out sick Boundary Specification Problem: Should a contractor be considered a part of the company? Social Network Analysis [17]

19 Partial Observation of Social Networks Sampling Design: Choose which part to observe: Ask 10% of employees about their collaborations Egocentric Adaptive Out-of-design Missing Data: Try to survey the whole company, but someone is out sick Boundary Specification Problem: Should a contractor be considered a part of the company? Social Network Analysis [18]

20 Partial Observation of Social Networks Sampling Design: Choose which part to observe: Ask 10% of employees about their collaborations Egocentric Adaptive Out-of-design Missing Data: Try to survey the whole company, but someone is out sick Boundary Specification Problem: Should a contractor be considered a part of the company? Social Network Analysis [19]

21 Partial Observation of Social Networks Sampling Design: Choose which part to observe: Ask 10% of employees about their collaborations Egocentric Adaptive Out-of-design Missing Data: Try to survey the whole company, but someone is out sick Boundary Specification Problem: Should a contractor be considered a part of the company? Social Network Analysis [20]

22 Partial Observation of Social Networks Sampling Design: Choose which part to observe: Ask 10% of employees about their collaborations Egocentric Adaptive Out-of-design Missing Data: Try to survey the whole company, but someone is out sick Boundary Specification Problem: Should a contractor be considered a part of the company? Social Network Analysis [21]

23 Partial Observation of Social Networks Sampling Design: Choose which part to observe: Ask 10% of employees about their collaborations Egocentric Adaptive Out-of-design Missing Data: Try to survey the whole company, but someone is out sick Boundary Specification Problem: Should a contractor be considered a part of the company? Social Network Analysis [22]???

24 Outline of Presentation Social Network Analysis [23] 1. What is a Social Network? 2. Why do we want to analyze a social network? 3. What can we know about a social network? 4. How do we analyze a social network? 5. Descriptive Analysis 6. Design-Based Inference 7. Model-based (likelihood) Inference 8. Examples 9. Discussion

25 Frameworks for Statistical Analysis Social Network Analysis [24] Describe Describe Structure Mechanism Fully Observed Description Modeling Data (Statistical) Partially Observed Design-Based Likelihood Data Inference Inference

26 Outline of Presentation Social Network Analysis [25] 1. What is a Social Network? 2. Why do we want to analyze a social network? 3. What can we know about a social network? 4. How do we analyze a social network? 5. Descriptive Analysis 6. Design-Based Inference 7. Model-based (likelihood) Inference 8. Examples 9. Discussion

27 Descriptive Analysis Social Network Analysis [26] Centrality Balance Reachability and path length Clustering (e.g. Facebook [image from Bernie Hogan, Oxford])

28 Outline of Presentation Social Network Analysis [27] 1. What is a Social Network? 2. Why do we want to analyze a social network? 3. What can we know about a social network? 4. How do we analyze a social network? 5. Descriptive Analysis 6. Design-Based Inference 7. Model-based (likelihood) Inference 8. Examples 9. Discussion

29 The Horvitz-Thompson Estimator of a Total Social Network Analysis [28] I have a sample of students in a classroom and I want to estimate the total amount of money spent on textbooks in the class. ˆT HT = π i s i Where y i is the amount spent by student i, and π i is the probability i sampled. E( ˆT HT ) = i P op V ar( ˆT HT ) = y i y i π i = π i i P op j P op i P op ij y i π i y j π j y i = T Where ij = π ij π i π j Where ˇ ij = π ij π i π j π ij ˆ V ar( ˆT HT ) = i s j s ˇ ij y i π i y j π j

30 Social Network Analysis [29] Horvitz-Thompson Estimator for Number of Edges How many friendships are in a classroom? I choose a simple random sample of n students, from a classroom of N students. I look at the web space of each student in the sample, and identify all other students in the class with whom they share friendships I use this data to form a Horvitz-Thompson estimator for the total number of friendships in the classroom ˆT HT = i s V ar( ˆT HT ) = i s j / s or j>i j / s or j>i π ij k s l / s or l>k ij,kl y ij π ij y kl π kl y ij Where ij,kl = π ij,kl π ij π kl

31 The π ij s Social Network Analysis [30] π ij = 1 ( N 2 n ( N n ) ) = n(2n n 1) N(N 1) for i j π ij,kl = p(exactly one end of each sampled) + p(two end of one, one of the other sampled) + p(both ends of both sampled) ) ) = 2 2 ( N 4 n 2 ( N n) ( N 4 n 3 ( N n) + ( N 4 n 4 ( N n) ) for i, j, k, l unique.

32 Link-Tracing Designs and HT Estimation Social Network Analysis [31] Consider: π i = 1 ( N mi n ( N n) ) Where m i is the number of initial students that would have landed i in the sample. 1-Wave link-tracing: m i = 1+ number of friends of i, observed! 2-Wave link-tracing: m i = 1+ number of friends and friends of friends of i, NOT observed!

33 Social Network Analysis [32] Limitation: Sampling probabilities often not obserable Observable sampling probabilities under various sampling schemes for directed and undirected networks. Sampling Nodal Probabilities π i Dyadic Probabilities π ij Scheme Undirected Directed Undirected Directed Ego-centric X X X X One-Wave X k Wave, 1 < k < Saturated X Nodal and dyadic sampling probabilities are considered separately. X indicates observable sampling probabilities, while a blank indicates unobservable sampling probabilities.

34 Frameworks for Statistical Analysis Social Network Analysis [33] Describe Describe Structure Mechanism Fully Observed Description Modeling Data (Statistical) Partially Observed Design-Based Likelihood Data Inference Inference

35 Outline of Presentation Social Network Analysis [34] 1. What is a Social Network? 2. Why do we want to analyze a social network? 3. What can we know about a social network? 4. How do we analyze a social network? 5. Descriptive Analysis 6. Design-Based Inference 7. Model-based (likelihood) Inference 8. Examples 9. Discussion

36 Social Network Analysis [35] Modeling Social Network Data - Independence Models logitp (Y ij = 1 X) = β 0 + β 1 (same sex) + β 2 (i older than j) +.. Logistic regression form. Each pair (dyad) independent of all others. Scientific questions answered by comparing estimated coefficients, β i, to 0.

37 Social Network Analysis [36] More complex models: Exponential-family Random Graph Models Sometimes, we are interested in more complex relational structures. Need to look at whole graph at once, can t separate dyads. Exponential-family Random Graph Model (ERGM): (Holland and Leinhardt (1981), Snijders et al, (2006),... ) P β (Y = y) = c(β)e β 1g 1 (y)+β 2 g 2 (y)+... g(y) represent components of the social process c(β) is the normalizing constant

38 Social Network Analysis [37] Fitting Models to Partially Observed Social Network Data Two types of data: Observed relations (Y obs ), and indicators of units sampled (D). P (Y obs, D β, δ) = P (Y, D β, δ) Unobserved = P (D Y, δ)p (Y β) Unobserved β is the model parameter δ is the sampling parameter If P (D Y, δ) = P (D Y obs, δ) (adaptive sampling or missing at random) Then P (Y obs, D β, δ) = P (D Y, δ) P (Y β) Unobserved Can find maximum likelihood estimates by summing over the possible values of unobserved, ignoring sampling Sample with Markov Chain Monte Carlo (MCMC)

39 Social Network Analysis [38] Fitting Models to Partially Observed Social Network Data Two types of data: Observed relations (Y obs ), and indicators of units sampled (D). P (Y obs, D β, δ) = P (Y, D β, δ) Unobserved = P (D Y, δ)p (Y β) Unobserved β is the model parameter δ is the sampling parameter If P (D Y, δ) = P (D Y obs, δ) (adaptive sampling or missing at random) Then P (Y obs, D β, δ) = P (D Y, δ) P (Y β) Unobserved Can find maximum likelihood estimates by summing over the possible values of unobserved, ignoring sampling Sample with Markov Chain Monte Carlo (MCMC)

40 Outline of Presentation Social Network Analysis [39] 1. What is a Social Network? 2. Why do we want to analyze a social network? 3. What can we know about a social network? 4. How do we analyze a social network? 5. Descriptive Analysis 6. Design-Based Inference 7. Model-based (likelihood) Inference 8. Examples 9. Discussion

41 Example: Friendships in a School Social Network Analysis [40] From the National Longitudinal Survey on Adolescent Health - Wave 1: Each student asked to nominate up to 5 male and 5 female friends Sex and Grade available for 89 students, 70 students reported friendships.

42 Example: Friendships in a School Social Network Analysis [41] From the National Longitudinal Survey on Adolescent Health - Wave 1: Each student asked to nominate up to 5 male and 5 female friends Sex and Grade available for 89 students, 70 students reported friendships.

43 Example: Friendships in a School Social Network Analysis [42] From the National Longitudinal Survey on Adolescent Health - Wave 1: Each student asked to nominate up to 5 male and 5 female friends Sex and Grade available for 89 students, 70 students reported friendships.

44 Example: Friendships in a School Social Network Analysis [43] Scientific Question: manner? Do friendships form in an egalitarian or an hierarchal Methodological Question: Can we fit a network model to a network with missing data? Is the fit different from that of just the observed data? P (D Y, δ) = P (D Y obs, δ) (missing at random) Does observed status depend on unobserved characteristics?

45 Structure of Data Social Network Analysis [44] Up to 5 female friends and up to 5 male friends 89 students in school 70 completed friendship nominations portion of survey

46 Example: Friendships in a School Social Network Analysis [45] Fit an ERGM to the partially observed data, get coefficients like in logistic regression. Terms in the model: Density: Overall rate of ties Reciprocity: Do students tend to reciprocate nominations? Popularity by Grade: Do students in different grades receive different rates of ties? Popularity by Sex: Do boys and girls receive different rates of ties? Age:Sex Mixing: Rates of ties between older and younger boys and girls Propensity for ties within sex and grade to be transitive (hierarchal) Propensity for ties within sex and grade to be cyclical (egalitarian) Isolation: Propensity for students to receive no nominations

47 Percent of Possible Relations Realised Social Network Analysis [46] Observed Respondents to Respondents 8.2 Respondents to Non-Respondents 6.2 Non-Respondents to Respondents - Non-Respondents to Non-Respondents - 8.2% 6.2%

48 Social Network Analysis [47] Goodness of Fit: Percent of Possible Relations Realised Observed Fit Respondents to Respondents Respondents to Non-Respondents Non-Respondents to Respondents Non-Respondents to Non-Respondents % 6.2% 7.6% 8.0% 7.2% 9.3% (e) Observed (f) Fit

49 Social Network Analysis [48] Goodness of Fit: Percent of Possible Relations Realised Observed Original Diff. Popularity Respondents to Respondents Respondents to Non-Respondents Non-Respondents to Respondents Non-Respondents to Non-Respondents % 6.2% 7.6% 8.0% 8.1% 6.2% 7.2% 9.3% 7.4% 7.1% (g) Observed (h) Original (i) Differential Popularity

54 Conclusions, School Friendships Example Social Network Analysis [53] Nominations are reciprocated at a higher rate than random Males receive nominations from other males at a higher rate than females from females Nominations within grade are more likely than outside grade Nominations of older students are more likely than younger students Nominations within sex and grade are more consistent with a hierarchal rather than egalitarian structure More students receive no nominations than we would expect at random.

55 Frameworks for Statistical Analysis Social Network Analysis [54] Describe Describe Structure Mechanism Fully Observed Description Modeling Data (Statistical) Partially Observed Design-Based Likelihood Data Inference Inference

56 Injection Drug User Example Social Network Analysis [55] Simulations corresponding to U.S. Center for Disease Control study of Injection Drug Users in New York City Injection Drug Users (IDU) asked how many IDUs they know, and HIV tested. Given 2 coupons to pass to other IDUs they know, to invite them to join study. Sampling continues until sample size 500 (from simulated population 715).

57 Social Network Analysis [56]

58 Social Network Analysis [57]

59 Social Network Analysis [58]

60 Social Network Analysis [59]

61 Social Network Analysis [60]

62 Social Network Analysis [61]

63 Social Network Analysis [62]

64 Social Network Analysis [63]

65 Injection Drug User Example Social Network Analysis [64] Scientific Question: What proportion of Injection Drug Users in New York City are HIV positive? Methodological Question: Can we estimate population proportions from samples starting at a convenience sample of seeds? P (D Y, δ) = P (D Y obs, δ) (adaptive sampling) P (D Y, δ) = P (seeds Y, δ)p (D Y, δ, seeds) = P (seeds)p (D Y obs, δ, seeds) but typically P (seeds Y, δ) P (seeds Y obs, δ)

66 Structure of Analysis Social Network Analysis [65] Sample: Link-tracing sampling variant - Respondent-Driven Sampling Ask number of contacts - but not who. Can t identify alters. No matrix. Network used as sampling tool Existing Approach: Assume inclusion probability proportional to number of contacts (Volz and Heckathorn, 2008) Assume many waves of sampling remove bias of seed selection Our work: Design-based (describe structure, not mechanism) Fit simple network model to observed data (model-assisted) Correct for biases due to network-based sampling, and observable irregularities

67 Generalized Horvitz-Thompson Estimator Goal: Estimate proportion infected : N Social Network Analysis [66] µ = 1 N j=1 z i where z i = { 1 node i infected 0 node i uninfected. Generalized Horvitz-Thompson Estimator: i:s ˆµ = i =1 π 1 z i i i:s i =1 π 1 i where S i = { 1 node i sampled 0 node i not sampled π i = P (S i = 1). Key Point: Requires π i i : S i = 1

68 Simulate Population Simulation Study 1000, 835, 715, 625, 555, or 525 nodes 20% Infected Social Network Analysis [67] Simulate Social Network (from ERGM, using statnet) Mean degree 7 Homophily on Infection: R = Differential Activity: w = Simulate Respondent-Driven Sample P (infected to infected tie) P (uninfected to infected tie) mean degree infected mean degree uninfected 500 total samples 10 seeds, chosen proportional to degree 2 coupons each Coupons at random to relations Sample without replacement Repeat 1000 times! = 1 (or other) Blue parameters varied in study. = 5 (or other)

69 Social Network Analysis [68] Volz-Heckathorn, w=1 Estimated Proportion Infected % 60% 70% 80% 90% 95% Sample %:

70 Social Network Analysis [69] Varying Sample Percentage, w=1.4 Estimated Proportion Infected % 60% 70% 80% 90% 95% Sample %:

71 Successive Sampling Mapping Social Network Analysis [70] Nodal Inclusion Probability VH Probs. 50% Sample 60% Sample 70% Sample 80% Sample 90% Sample 95% Sample 100% Sample Nodal Degree

72 Social Network Analysis [71] Volz-Heckathorn, w=1.4 Estimated Proportion Infected % 60% 70% 80% 90% 95% Sample %:

73 Social Network Analysis [72] SS, w=1.4 Estimated Proportion Infected % 60% 70% 80% 90% 95% Sample %:

74 Social Network Analysis [73] All Infected Seeds, varying Homophily, 50% Expected Prevalence Estimate (Truth = 0.20) Mean VH SS R 1 3 5

75 Social Network Analysis [74] All Infected Seeds, varying number of seeds, 50% Expected Prevalence Estimate (Truth = 0.20) Max Wave Seeds Mean VH SS

76 Network-Model Estimator Social Network Analysis [75] Key Points: Goal: Estimate inclusion probabilities to use to weight sampled nodes If we knew the network, we could simulate sampling to estimate inclusion probabilities Approach: 1. Use (weighted) information in the data to estimate network structure 2. Use simulated sampling over estimated network to estimate inclusion probabilities 3. Iterate steps (1) and (2)

77 Simulation Study Social Network Analysis [76] Set-up: High sample fraction (500 of 715) Infected have more relations than uninfected (twice as many) Initial sample biased (all infected) Truth: 20% Infected Comparison of Estimators: Mean : Naive Sample Mean SH: Salganik-Heckathorn: based on MME of number of cross-relations VH: Existing Volz-Heckathorn Estimator (2008) SS: Another new estimator, not discussed here Net: New Network-Based Estimator

78 Social Network Analysis [77] All Infected Seeds, varying Homophily Expected Prevalence Estimate (Truth = 0.20) Mean VH SS R 1 3 5

79 Social Network Analysis [78] All Infected Seeds, varying Homophily Expected Prevalence Estimate (Truth = 0.20) Mean SH VH SS R 1 3 5

80 Social Network Analysis [79] All Infected Seeds, varying Homophily Expected Prevalence Estimate (Truth = 0.20) Mean SH VH SS MA R 1 3 5

81 Social Network Analysis [80] All Infected Seeds, varying number of seeds (waves) Expected Prevalence Estimate (Truth = 0.20) Max Wave Seeds Mean VH SS

82 Social Network Analysis [81] All Infected Seeds, varying number of seeds (waves) Expected Prevalence Estimate (Truth = 0.20) Max Wave Seeds Mean SH VH SS

83 Social Network Analysis [82] All Infected Seeds, varying number of seeds (waves) Expected Prevalence Estimate (Truth = 0.20) Max Wave Seeds Mean SH VH SS MA

84 Social Network Analysis [83] HIV Prevalence among IDU in an Eastern European City Estimated Prevalence Random Correct Seeds & Seeds Seeds Offspring Mean SH VH SS MA (+/ 1se)

85 Wave Total Social Network Analysis [84] Recruitment Rates Uninfected Recruiter Avg Infected Recruiter Avg Legend: Number of Recruits:

86 Social Network Analysis [85] HIV Prevalence among IDU in an Eastern European City Estimated Prevalence Random Correct Seeds & Seeds Seeds Offspring Mean SH VH SS MA (+/ 1se)

87 Social Network Analysis [86] HIV Prevalence among IDU in an Eastern European City Estimated Prevalence Random Correct Seeds & Seeds Seeds Offspring Mean SH VH SS MA (+/ 1se)

88 Methodological Social Network Analysis [87] Network-Model estimator corrects for differential activity by infection status, unlike sample mean. Network-Model estimator uses appropriate sample weights for simulated high sample fraction, unlike sample mean or Volz-Heckathorn estimator. Network-Model estimator corrects for seed bias, unlike any existing method.

89 Outline of Presentation Social Network Analysis [88] 1. What is a Social Network? 2. Why do we want to analyze a social network? 3. What can we know about a social network? 4. How do we analyze a social network? 5. Descriptive Analysis 6. Design-Based Inference 7. Model-based (likelihood) Inference 8. Examples 9. Discussion

90 Discussion Social Network Analysis [89] Examples School Friendships: Describe process generating relations. Missing data Injecting Drug User: Describe nodes in actual population. Network for sampling Network data have many types of complexity (nested nodes/edges, time, attributes, boundaries, sampling No single dominant approach Can only correct for what we can measure - data and scientific question related Room for future research: deeper, also broader.

91 References Social Network Analysis [90] Missing Data and Sampling Little, R. J.A. and D. B. Rubin, Second Edition (2002). Statistical Analysis with Missing Data, John Wiley and Sons, Hoboken, NJ. Thompson, S.K., and G.A. Seber (1996). Adaptive Sampling John Wiley and Sons, Inc. New York. Modeling Social Network Data with Exponential-Family Random Graph Models Handcock, M.S., D.R. Hunter, C.T. Butts, S.M. Goodreau, and M. Morris (2003) statnet: An R package for the Statistical Modeling of Social Networks. URL: Holland, P.W., and S. Leinhardt (1981), An exponential family of probability distributions for directed graphs, Journal of the American Statistical Association, 76: Snijders, T.A.B., P.E. Pattison, G.L. Robins, and M.S. Handcock (2006). New specifications for exponential random graph models. Sociological Methodology, Inference with Partially-Observed Network Data Frank, O. (1971). The Statistical Analysis of Networks Chapman and Hall, London. Frank, O., and T.A.B. Snijders (1994). Estimating the size of hidden populations using snowball sampling. Journal of Official Statistics, 10: Gile, K.J. (2008). Inference from Partially-Observed Network Data. PhD. Dissertation. University of Washington, Seattle. Gile, K. and M.S. Handcock (2006). Model-based Assessment of the Impact of Missing Data on Inference for Networks. Working paper, Center for Statistics and the Social Sciences, University of Washington. Handcock, M.S., and K. Gile (2007). Modeling social networks with sampled data. Technical Report, Department of Statistics, University of Washington. Thompson, S.K. and O. Frank (2000). Model-Based Estimation With Link-Tracing Sampling Designs. Survey Methodology, 26: Other Harris, K. M., F. Florey, J. Tabor, P. S. Bearman, J. Jones, and R. J. Udry (2003). The National Longitudinal Study of Adolescent Health: Research design. Technical Report, Carolina Population Center, University of North Carolina at Chapel Hill. Thank you for your attention!

### Using Link-Tracing Data to Inform Epidemiology

Using Link-Tracing Data to Inform Epidemiology Krista J. Gile Nuffield College, Oxford joint work with Mark S. Handcock University of Washington, Seattle 23 October, 2008 For details, see: Gile, K.J. (2008).

### Inference from Link-Tracing Network Samples

Inference from Link-Tracing Network Samples Krista J. Gile University of Massachusetts, Amherst October 21, 2013 For more information: Krista J. Gile Inference from Link-Tracing Network Samples: Review,

### Design-Based Estimators for Snowball Sampling

Design-Based Estimators for Snowball Sampling Termeh Shafie Department of Statistics, Stockholm University SE-106 91 Stockholm, Sweden Abstract Snowball sampling, where existing study subjects recruit

### On the Concept of Snowball Sampling

On the Concept of Snowball Sampling arxiv:1108.0301v1 [stat.ap] 1 Aug 2011 Mark S. Handcock Krista J. Gile August 2, 2011 Confusion over the definition of snowball sampling reflects a phenomena in the

### Handling attrition and non-response in longitudinal data

Longitudinal and Life Course Studies 2009 Volume 1 Issue 1 Pp 63-72 Handling attrition and non-response in longitudinal data Harvey Goldstein University of Bristol Correspondence. Professor H. Goldstein

### New Specifications for Exponential Random Graph Models

New Specifications for Exponential Random Graph Models Garry Robins University of Melbourne, Australia Workshop on exponential random graph models Sunbelt XXVI April 2006 http://www.sna.unimelb.edu.au/

### arxiv: v1 [stat.ap] 5 Oct 2010

The Annals of Applied Statistics 2010, Vol. 4, No. 1, 5 25 DOI: 10.1214/08-AOAS221 c Institute of Mathematical Statistics, 2010 MODELING SOCIAL NETWORKS FROM SAMPLED DATA 1 arxiv:1010.0891v1 [stat.ap]

### Imputation of missing network data: Some simple procedures

Imputation of missing network data: Some simple procedures Mark Huisman Dept. of Psychology University of Groningen Abstract Analysis of social network data is often hampered by non-response and missing

### Unequal edge inclusion probabilities in link-tracing network sampling with implications for Respondent-Driven Sampling

Electronic Journal of Statistics Vol. 10 (2016) 1109 1132 ISSN: 1935-7524 DOI: 10.1214/16-EJS1138 Unequal edge inclusion probabilities in link-tracing network sampling with implications for Respondent-Driven

### Exponential Random Graph Models for Social Network Analysis. Danny Wyatt 590AI March 6, 2009

Exponential Random Graph Models for Social Network Analysis Danny Wyatt 590AI March 6, 2009 Traditional Social Network Analysis Covered by Eytan Traditional SNA uses descriptive statistics Path lengths

### IEMS 441 Social Network Analysis Term Paper Multiple Testing Multi-theoretical, Multi-level Hypotheses

IEMS 441 Social Network Analysis Term Paper Multiple Testing Multi-theoretical, Multi-level Hypotheses Jiangtao Gou Department of Statistics, Northwestern University Instructor: Prof. Noshir Contractor

### Sampling from Rare/Hiddent Populations. From Adaptive Cluster Sampling to Adaptive Web Sampling

Outline Sampling from Rare/Hidden Populations: From Adaptive Cluster Sampling to Adaptive Web Sampling Department of Statistics National Cheng Kung University, Taiwan VCQS, Aug/18/211 Outline Outline 1

### ONS Methodology Working Paper Series No 4. Non-probability Survey Sampling in Official Statistics

ONS Methodology Working Paper Series No 4 Non-probability Survey Sampling in Official Statistics Debbie Cooper and Matt Greenaway June 2015 1. Introduction Non-probability sampling is generally avoided

### Respondent Driven Sampling with Online Recruitment and Adaptive Follow-ups

Respondent Driven Sampling with Online Recruitment and Adaptive Follow-ups Presenter: Deirdre Middleton, MPH ICF International Co-authors: Christian Evans, MA ICF International Naomi Freedner, MPH ICF

### Application of Social Network Analysis to a Public Health Emergency Preparedness-Funded Workforce Program

North Carolina Preparedness & Emergency Response Research Center (NCPERRC) Application of Social Network Analysis to a Public Health Emergency Preparedness-Funded Workforce Program Christine A. Bevc, PhD,

### Snowball sampling for estimating exponential random graph models for large networks

*Title Page (WITH author details) Snowball sampling for estimating exponential random graph models for large networks Alex D. Stivala a,, Johan H. Koskinen b, David A. Rolls a, Peng Wang a, Garry L. Robins

### Network Analytics in Marketing

Network Analytics in Marketing Prof. Dr. Daning Hu Department of Informatics University of Zurich Nov 13th, 2014 Introduction: Network Analytics in Marketing Marketing channels and business networks have

### Equivalence Concepts for Social Networks

Equivalence Concepts for Social Networks Tom A.B. Snijders University of Oxford March 26, 2009 c Tom A.B. Snijders (University of Oxford) Equivalences in networks March 26, 2009 1 / 40 Outline Structural

### Social Networks 31 (2009) 240 254. Contents lists available at ScienceDirect. Social Networks

Social Networks 31 (2009) 240 254 Contents lists available at ScienceDirect Social Networks j o u r n a l h o m e p a g e : www.elsevier.com/locate/socnet A comparative study of social network models:

### Collecting Network Data in Surveys

Collecting Network Data in Surveys Arun Advani and Bansi Malde September 203 We gratefully acknowledge funding from the ESRC-NCRM Node Programme Evaluation for Policy Analysis Grant reference RES-576-25-0042.

### Statistical Models for Social Networks

Statistical Models for Social Networks 1 Statistical Models for Social Networks Tom A.B. Snijders University of Oxford, University of Groningen Key Words Social networks, Statistical modeling, Inference

### Social Media Mining. Network Measures

Klout Measures and Metrics 22 Why Do We Need Measures? Who are the central figures (influential individuals) in the network? What interaction patterns are common in friends? Who are the like-minded users

### PROBABILISTIC NETWORK ANALYSIS

½ PROBABILISTIC NETWORK ANALYSIS PHILIPPA PATTISON AND GARRY ROBINS INTRODUCTION The aim of this chapter is to describe the foundations of probabilistic network theory. We review the development of the

### A model-based approach to goodness-of-fit evaluation in item response theory

A MODEL-BASED APPROACH TO GOF EVALUATION IN IRT 1 A model-based approach to goodness-of-fit evaluation in item response theory DL Oberski JK Vermunt Dept of Methodology and Statistics, Tilburg University,

### Statistical and computational challenges in networks and cybersecurity

Statistical and computational challenges in networks and cybersecurity Hugh Chipman Acadia University June 12, 2015 Statistical and computational challenges in networks and cybersecurity May 4-8, 2015,

### An Application of the G-formula to Asbestos and Lung Cancer. Stephen R. Cole. Epidemiology, UNC Chapel Hill. Slides: www.unc.

An Application of the G-formula to Asbestos and Lung Cancer Stephen R. Cole Epidemiology, UNC Chapel Hill Slides: www.unc.edu/~colesr/ 1 Acknowledgements Collaboration with David B. Richardson, Haitao

### Statistics in Applications III. Distribution Theory and Inference

2.2 Master of Science Degrees The Department of Statistics at FSU offers three different options for an MS degree. 1. The applied statistics degree is for a student preparing for a career as an applied

### Variance Estimation, Design Effects, and Sample Size Calculations for Respondent-Driven Sampling

Journal of Urban Health: Bulletin of the New York Academy of Medicine, Vol. 83, No. 7 doi:10.1007/s11524-006-9106-x * 2006 The New York Academy of Medicine Variance Estimation, Design Effects, and Sample

### An approach of detecting structure emergence of regional complex network of entrepreneurs: simulation experiment of college student start-ups

An approach of detecting structure emergence of regional complex network of entrepreneurs: simulation experiment of college student start-ups Abstract Yan Shen 1, Bao Wu 2* 3 1 Hangzhou Normal University,

### HISTORICAL DEVELOPMENTS AND THEORETICAL APPROACHES IN SOCIOLOGY Vol. I - Social Network Analysis - Wouter de Nooy

SOCIAL NETWORK ANALYSIS University of Amsterdam, Netherlands Keywords: Social networks, structuralism, cohesion, brokerage, stratification, network analysis, methods, graph theory, statistical models Contents

### Introduction to social network analysis

Introduction to social network analysis Paola Tubaro University of Greenwich, London 26 March 2012 Introduction to social network analysis Introduction Introducing SNA Rise of online social networking

### Missing Data Dr Eleni Matechou

1 Statistical Methods Principles Missing Data Dr Eleni Matechou matechou@stats.ox.ac.uk References: R.J.A. Little and D.B. Rubin 2nd edition Statistical Analysis with Missing Data J.L. Schafer and J.W.

### Inferential Network Analysis with Exponential Random. Graph Models

Inferential Network Analysis with Exponential Random Graph Models Skyler J. Cranmer Bruce A. Desmarais April 15, 2010 Abstract Methods for descriptive network analysis have reached statistical maturity

### Missing data in randomized controlled trials (RCTs) can

EVALUATION TECHNICAL ASSISTANCE BRIEF for OAH & ACYF Teenage Pregnancy Prevention Grantees May 2013 Brief 3 Coping with Missing Data in Randomized Controlled Trials Missing data in randomized controlled

### Discovering Long Range Properties of Social Networks with Multi-Valued Time-Inhomogeneous Models

Discovering Long Range Properties of Social Networks with Multi-Valued Time-Inhomogeneous Models Danny Wyatt Dept. of Computer Science and Engineering University of Washington danny@cs.washington.edu Tanzeem

### Sensitivity Analysis in Multiple Imputation for Missing Data

Paper SAS270-2014 Sensitivity Analysis in Multiple Imputation for Missing Data Yang Yuan, SAS Institute Inc. ABSTRACT Multiple imputation, a popular strategy for dealing with missing values, usually assumes

### A comparison of networks and off- line social. networks: A study of a medium- sized bank*

A comparison of email networks and off- line social networks: A study of a medium- sized bank* Rebeka Johnson Balázs Kovács András Vicsek University of Lugano Rebeka.Johnson@usi.ch University of Lugano

### Week 3. Network Data; Introduction to Graph Theory and Sociometric Notation

Wasserman, Stanley, and Katherine Faust. 2009. Social Network Analysis: Methods and Applications, Structural Analysis in the Social Sciences. New York, NY: Cambridge University Press. Chapter III: Notation

### Missing Data. A Typology Of Missing Data. Missing At Random Or Not Missing At Random

[Leeuw, Edith D. de, and Joop Hox. (2008). Missing Data. Encyclopedia of Survey Research Methods. Retrieved from http://sage-ereference.com/survey/article_n298.html] Missing Data An important indicator

### Statistical Rules of Thumb

Statistical Rules of Thumb Second Edition Gerald van Belle University of Washington Department of Biostatistics and Department of Environmental and Occupational Health Sciences Seattle, WA WILEY AJOHN

### Chenfeng Xiong (corresponding), University of Maryland, College Park (cxiong@umd.edu)

Paper Author (s) Chenfeng Xiong (corresponding), University of Maryland, College Park (cxiong@umd.edu) Lei Zhang, University of Maryland, College Park (lei@umd.edu) Paper Title & Number Dynamic Travel

### An extension of the factoring likelihood approach for non-monotone missing data

An extension of the factoring likelihood approach for non-monotone missing data Jae Kwang Kim Dong Wan Shin January 14, 2010 ABSTRACT We address the problem of parameter estimation in multivariate distributions

### Service courses for graduate students in degree programs other than the MS or PhD programs in Biostatistics.

Course Catalog In order to be assured that all prerequisites are met, students must acquire a permission number from the education coordinator prior to enrolling in any Biostatistics course. Courses are

### NEW VERSION OF DECISION SUPPORT SYSTEM FOR EVALUATING TAKEOVER BIDS IN PRIVATIZATION OF THE PUBLIC ENTERPRISES AND SERVICES

NEW VERSION OF DECISION SUPPORT SYSTEM FOR EVALUATING TAKEOVER BIDS IN PRIVATIZATION OF THE PUBLIC ENTERPRISES AND SERVICES Silvija Vlah Kristina Soric Visnja Vojvodic Rosenzweig Department of Mathematics

### 1.204 Final Project Network Analysis of Urban Street Patterns

1.204 Final Project Network Analysis of Urban Street Patterns Michael T. Chang December 21, 2012 1 Introduction In this project, I analyze road networks as a planar graph and use tools from network analysis

Statistics Graduate Courses STAT 7002--Topics in Statistics-Biological/Physical/Mathematics (cr.arr.).organized study of selected topics. Subjects and earnable credit may vary from semester to semester.

### Social network analysis with R sna package

Social network analysis with R sna package George Zhang iresearch Consulting Group (China) bird@iresearch.com.cn birdzhangxiang@gmail.com Social network (graph) definition G = (V,E) Max edges = N All possible

### Exploring Big Data in Social Networks

Exploring Big Data in Social Networks virgilio@dcc.ufmg.br (meira@dcc.ufmg.br) INWEB National Science and Technology Institute for Web Federal University of Minas Gerais - UFMG May 2013 Some thoughts about

### 2. Making example missing-value datasets: MCAR, MAR, and MNAR

Lecture 20 1. Types of missing values 2. Making example missing-value datasets: MCAR, MAR, and MNAR 3. Common methods for missing data 4. Compare results on example MCAR, MAR, MNAR data 1 Missing Data

### It is important to bear in mind that one of the first three subscripts is redundant since k = i -j +3.

IDENTIFICATION AND ESTIMATION OF AGE, PERIOD AND COHORT EFFECTS IN THE ANALYSIS OF DISCRETE ARCHIVAL DATA Stephen E. Fienberg, University of Minnesota William M. Mason, University of Michigan 1. INTRODUCTION

### Why Do I Really Want to Be a Nurse? People start to develop career goals at an early age, which often change. I came

Why Do I Really Want to Be a Nurse? People start to develop career goals at an early age, which often change. I came into college with the ultimate dream of going to medical school to be physician. After

### Protocols for Randomized Experiments to Identify Network Contagion

Protocols for Randomized Experiments to Identify Network Contagion A.C. Thomas Michael Finegold March 14, 2013 Abstract Identifying the existence and magnitude of social contagion, or the spread of an

### ESTIMATION OF THE EFFECTIVE DEGREES OF FREEDOM IN T-TYPE TESTS FOR COMPLEX DATA

m ESTIMATION OF THE EFFECTIVE DEGREES OF FREEDOM IN T-TYPE TESTS FOR COMPLEX DATA Jiahe Qian, Educational Testing Service Rosedale Road, MS 02-T, Princeton, NJ 08541 Key Words" Complex sampling, NAEP data,

### Grappling with Grouping III Social Network Analysis

Grappling with Grouping III Social Network Analysis David Henry University of Illinois at Chicago Allison Dymnicki American Institutes for Research Acknowledgments Families and Communities Research Group

### Statistical Analysis of Complete Social Networks

Statistical Analysis of Complete Social Networks Introduction to networks Christian Steglich c.e.g.steglich@rug.nl median geodesic distance between groups 1.8 1.2 0.6 transitivity 0.0 0.0 0.5 1.0 1.5 2.0

### Partitioning of Variance in Multilevel Models. Dr William J. Browne

Partitioning of Variance in Multilevel Models Dr William J. Browne University of Nottingham with thanks to Harvey Goldstein (Institute of Education) & S.V. Subramanian (Harvard School of Public Health)

### USING SPECTRAL RADIUS RATIO FOR NODE DEGREE TO ANALYZE THE EVOLUTION OF SCALE- FREE NETWORKS AND SMALL-WORLD NETWORKS

USING SPECTRAL RADIUS RATIO FOR NODE DEGREE TO ANALYZE THE EVOLUTION OF SCALE- FREE NETWORKS AND SMALL-WORLD NETWORKS Natarajan Meghanathan Jackson State University, 1400 Lynch St, Jackson, MS, USA natarajan.meghanathan@jsums.edu

### Four factors influencing effectiveness in communication networks

Four factors influencing effectiveness in email communication networks Ofer Engel Department of Management London School of Economics and Political Science Houghton Street, London WC2A 2AE, UK o.engel@lse.ac.uk

### Earn 57% of all the undergraduate degrees awarded. Much less likely than men to major in computer science, physical sciences, and engineering

Mary Madden, Ph.D. College of Education and Human Development University of Maine Maine Girls Collaborative Project Earn 57% of all the undergraduate degrees awarded Much less likely than men to major

### Health 2011 Survey: An overview of the design, missing data and statistical analyses examples

Health 2011 Survey: An overview of the design, missing data and statistical analyses examples Tommi Härkänen Department of Health, Functional Capacity and Welfare The National Institute for Health and

### Introduction to Biostatistics PhD programs

Introduction to Biostatistics PhD programs Takumi Saegusa University of Washington Department of Biostatistics April 17 2013 Takumi Saegusa (UW Biostat) Biostat PhD April 17 2013 1 / 35 Outline What is

### Homophily in Online Social Networks

Homophily in Online Social Networks Bassel Tarbush and Alexander Teytelboym Department of Economics, University of Oxford bassel.tarbush@economics.ox.ac.uk Department of Economics, University of Oxford

### Inequality, Mobility and Income Distribution Comparisons

Fiscal Studies (1997) vol. 18, no. 3, pp. 93 30 Inequality, Mobility and Income Distribution Comparisons JOHN CREEDY * Abstract his paper examines the relationship between the cross-sectional and lifetime

### How to Develop a Sporting Habit for Life

How to Develop a Sporting Habit for Life Final report December 2012 Context Sport England s 2012-17 strategy aims to help people and communities across the country transform our sporting culture, so that

### MINFS544: Business Network Data Analytics and Applications

MINFS544: Business Network Data Analytics and Applications March 30 th, 2015 Daning Hu, Ph.D., Department of Informatics University of Zurich F Schweitzer et al. Science 2009 Stop Contagious Failures in

### Postdocs: All Sectors (N=533)

www.aip.org/statistics One Physics Ellipse College Park, MD 20740 301.209.3070 stats@aip.org March 2013 Recent Physics Doctorates: Skills Used & Satisfaction with Employment Data from the degree recipient

### Asking Hard Graph Questions. Paul Burkhardt. February 3, 2014

Beyond Watson: Predictive Analytics and Big Data U.S. National Security Agency Research Directorate - R6 Technical Report February 3, 2014 300 years before Watson there was Euler! The first (Jeopardy!)

### HIV Infection Among Those with an Injection Drug Use*-Associated Risk, Florida, 2014

To protect, promote and improve the health of all people in Florida through integrated state, county, and community efforts. HIV Infection Among Those with an Injection Drug Use*-Associated Risk, Florida,

### TRACKING, WEIGHTING, AND SAMPLE SELECTION MODELING TO CORRECT FOR ATTRITION

TRACKING, WEIGHTING, AND SAMPLE SELECTION MODELING TO CORRECT FOR ATTRITION Kimberly A. McGuigan, Phyllis L. Ellickson, Ronald D. Hays and Robert M. Bell, RAND Kimberly A. McGuigan, RAND, 1700 Main Street,

### BOOSTING - A METHOD FOR IMPROVING THE ACCURACY OF PREDICTIVE MODEL

The Fifth International Conference on e-learning (elearning-2014), 22-23 September 2014, Belgrade, Serbia BOOSTING - A METHOD FOR IMPROVING THE ACCURACY OF PREDICTIVE MODEL SNJEŽANA MILINKOVIĆ University

### The Comparisons. Grade Levels Comparisons. Focal PSSM K-8. Points PSSM CCSS 9-12 PSSM CCSS. Color Coding Legend. Not Identified in the Grade Band

Comparison of NCTM to Dr. Jim Bohan, Ed.D Intelligent Education, LLC Intel.educ@gmail.com The Comparisons Grade Levels Comparisons Focal K-8 Points 9-12 pre-k through 12 Instructional programs from prekindergarten

Talking Mentoring Leadership Minority Dental Faculty Development: Leading Change: Leadership Training Strategies for Inclusion and Academic/Community Partnerships Joan Y. Reede, MD, MPH,MS,MBA Harvard

### Imputing Attendance Data in a Longitudinal Multilevel Panel Data Set

Imputing Attendance Data in a Longitudinal Multilevel Panel Data Set April 2015 SHORT REPORT Baby FACES 2009 This page is left blank for double-sided printing. Imputing Attendance Data in a Longitudinal

### CSV886: Social, Economics and Business Networks. Lecture 2: Affiliation and Balance. R Ravi ravi+iitd@andrew.cmu.edu

CSV886: Social, Economics and Business Networks Lecture 2: Affiliation and Balance R Ravi ravi+iitd@andrew.cmu.edu Granovetter s Puzzle Resolved Strong Triadic Closure holds in most nodes in social networks

### SAS Software to Fit the Generalized Linear Model

SAS Software to Fit the Generalized Linear Model Gordon Johnston, SAS Institute Inc., Cary, NC Abstract In recent years, the class of generalized linear models has gained popularity as a statistical modeling

### Markov Processes in a Longitudinal Social Network Analysis and Smoking Behavior

Markov Processes in a Longitudinal Social Network Analysis and Smoking Behavior Hsieh-Hua Yang Chang Jung Christian University Chyi-in Wu Institute of Sociology, Academia Sinica Abstract Social network

### Imputation of Missing Links and Attributes in Longitudinal Social Surveys

Imputation of Missing Links and Attributes in Longitudinal Social Surveys Vladimir Ouzienko and Zoran Obradovic Center for Data Analytics and Biomedical Informatics Temple University Philadelphia, PA 922,

### Missing Data & How to Deal: An overview of missing data. Melissa Humphries Population Research Center

Missing Data & How to Deal: An overview of missing data Melissa Humphries Population Research Center Goals Discuss ways to evaluate and understand missing data Discuss common missing data methods Know

### The Applied and Computational Mathematics (ACM) Program at The Johns Hopkins University (JHU) is

The Applied and Computational Mathematics Program at The Johns Hopkins University James C. Spall The Applied and Computational Mathematics Program emphasizes mathematical and computational techniques of

### INTRODUCTION TO SURVEY DATA ANALYSIS THROUGH STATISTICAL PACKAGES

INTRODUCTION TO SURVEY DATA ANALYSIS THROUGH STATISTICAL PACKAGES Hukum Chandra Indian Agricultural Statistics Research Institute, New Delhi-110012 1. INTRODUCTION A sample survey is a process for collecting

### Secondary school students use of computers at home

British Journal of Educational Technology Vol 30 No 4 1999 331 339 Secondary school students use of computers at home Susan Harris Susan Harris is a Senior Research Officer at the National Foundation for

### ARTICLE IN PRESS Social Networks xxx (2013) xxx xxx

G Model ARTICLE IN PRESS Social Networks xxx (2013) xxx xxx Contents lists available at SciVerse ScienceDirect Social Networks journa l h o me page: www.elsevier.com/locate/socnet Exponential random graph

### 2006 RESEARCH GRANT FINAL PROJECT REPORT

2006 RESEARCH GRANT FINAL PROJECT REPORT Date: June 26, 2009 AIR Award Number: RG 06-479 Principal Investigator Name: Patricia Cerrito Principal Investigator Institution: University of Louisville Secondary

### Lecture 6. Artificial Neural Networks

Lecture 6 Artificial Neural Networks 1 1 Artificial Neural Networks In this note we provide an overview of the key concepts that have led to the emergence of Artificial Neural Networks as a major paradigm

### Monitoring the Behaviour of Credit Card Holders with Graphical Chain Models

Journal of Business Finance & Accounting, 30(9) & (10), Nov./Dec. 2003, 0306-686X Monitoring the Behaviour of Credit Card Holders with Graphical Chain Models ELENA STANGHELLINI* 1. INTRODUCTION Consumer

### Gaussian Processes to Speed up Hamiltonian Monte Carlo

Gaussian Processes to Speed up Hamiltonian Monte Carlo Matthieu Lê Murray, Iain http://videolectures.net/mlss09uk_murray_mcmc/ Rasmussen, Carl Edward. "Gaussian processes to speed up hybrid Monte Carlo

### Earnings in private jobs after participation to post-doctoral programs : an assessment using a treatment effect model. Isabelle Recotillet

Earnings in private obs after participation to post-doctoral programs : an assessment using a treatment effect model Isabelle Recotillet Institute of Labor Economics and Industrial Sociology, UMR 6123,

### How To Use A Monte Carlo Study To Decide On Sample Size and Determine Power

How To Use A Monte Carlo Study To Decide On Sample Size and Determine Power Linda K. Muthén Muthén & Muthén 11965 Venice Blvd., Suite 407 Los Angeles, CA 90066 Telephone: (310) 391-9971 Fax: (310) 391-8971

### Dealing with Missing Data

Dealing with Missing Data Roch Giorgi email: roch.giorgi@univ-amu.fr UMR 912 SESSTIM, Aix Marseille Université / INSERM / IRD, Marseille, France BioSTIC, APHM, Hôpital Timone, Marseille, France January

### Multilevel Modeling of Complex Survey Data

Multilevel Modeling of Complex Survey Data Sophia Rabe-Hesketh, University of California, Berkeley and Institute of Education, University of London Joint work with Anders Skrondal, London School of Economics

### Collective behaviour in clustered social networks

Collective behaviour in clustered social networks Maciej Wołoszyn 1, Dietrich Stauffer 2, Krzysztof Kułakowski 1 1 Faculty of Physics and Applied Computer Science AGH University of Science and Technology

### A Composite Likelihood Approach to Analysis of Survey Data with Sampling Weights Incorporated under Two-Level Models

A Composite Likelihood Approach to Analysis of Survey Data with Sampling Weights Incorporated under Two-Level Models Grace Y. Yi 13, JNK Rao 2 and Haocheng Li 1 1. University of Waterloo, Waterloo, Canada

### SEXUAL PREDATORS ON MYSPACE:

SEXUAL PREDATORS ON MYSPACE: A DEEPER LOOK AT TEENS BEING STALKED OR APPROACHED FOR SEXUAL LIAISONS Short Report 2006-01 Larry D. Rosen, Ph.D. California State University, Dominguez Hills July 2006 I recently

### Lecture 10-12: Non-Experimental, Observational, Quasi- Experimental, and Developmental Designs

Lecture 10-12: Non-Experimental, Observational, Quasi- Experimental, and Developmental Designs I. INTRODUCTION A. Experimental vs. Correlational research For the most part we have been discussing Experimental

### We study the drivers of the emergence of opinion leaders in a networked community where users establish

Published online ahead of print March 18, 2013 MANAGEMENT SCIENCE Articles in Advance, pp. 1 17 ISSN 0025-1909 (print) ISSN 1526-5501 (online) http://dx.doi.org/10.1287/mnsc.1120.1685 2013 INFORMS The

### 10. Analysis of Longitudinal Studies Repeat-measures analysis

Research Methods II 99 10. Analysis of Longitudinal Studies Repeat-measures analysis This chapter builds on the concepts and methods described in Chapters 7 and 8 of Mother and Child Health: Research methods.

### SYSM 6304: Risk and Decision Analysis Lecture 5: Methods of Risk Analysis

SYSM 6304: Risk and Decision Analysis Lecture 5: Methods of Risk Analysis M. Vidyasagar Cecil & Ida Green Chair The University of Texas at Dallas Email: M.Vidyasagar@utdallas.edu October 17, 2015 Outline

### Handling missing data in Stata a whirlwind tour

Handling missing data in Stata a whirlwind tour 2012 Italian Stata Users Group Meeting Jonathan Bartlett www.missingdata.org.uk 20th September 2012 1/55 Outline The problem of missing data and a principled