Social Network Analysis

Statistical Analysis with Missing Data

Statistical Analysis With Missing Data (2nd ed.) (Book)

Contrasting treatment‐specific survival using double‐robust estimators

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active "network community" and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online "networking communities" such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data.

Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.

https://dash.harvard.edu/bitstream/handle/1/4645865/Goldenberg_NetSurvey.pdf?sequence=1

A Survey of Statistical Network Models

Survey researchers routinely conduct studies that use different methods of data collection and inference. But for at least the past 60 years, the probabilitysampling framework has been used in most surveys. More recently, concerns about coverage and nonresponse coupled with rising costs have led some to wonder whether non-probability sampling methods might be an acceptable alternative, at least under some conditions (Groves 2006; Savage and Burrows 2007). A wide range of non-probability designs exist and are being used in various settings, including case control studies, clinical trials, evaluation research

Summary Report of the AAPOR Task Force on Non-probability Sampling

Respondent-Driven Sampling (RDS) employs a variant of a link-tracing network sampling strategy to collect data from hard-to-reach populations. By tracing the links in the underlying social network, the process exploits the social structure to expand the sample and reduce its dependence on the initial (convenience) sample.The current estimators of population averages make strong assumptions in order to treat the data as a probability sample. We evaluate three critical sensitivities of the estimators: to bias induced by the initial sample, to uncontrollable features of respondent behavior, and to the without-replacement structure of sampling.Our analysis indicates: (1) that the convenience sample of seeds can induce bias, and the number of sample waves typically used in RDS is likely insufficient for the type of nodal mixing required to obtain the reputed asymptotic unbiasedness; (2) that preferential referral behavior by respondents leads to bias; (3) that when a substantial fraction of the target population is sampled the current estimators can have substantial bias.This paper sounds a cautionary note for the users of RDS. While current RDS methodology is powerful and clever, the favorable statistical properties claimed for the current estimates are shown to be heavily dependent on often unrealistic assumptions. We recommend ways to improve the methodology.

/pdf/respondent-driven-sampling-an-assessment-of-current-46md85b8s5.pdf

Respondent‐driven sampling: an assessment of current methodology

Respondent-Driven Sampling (RDS) employs a variant of a link-tracing network sampling strategy to collect data from hard-to-reach populations. By tracing the links in the underlying social network, the process exploits the social structure to expand the sample and reduce its dependence on the initial (convenience) sample. 
The primary goal of RDS is typically to estimate population averages in the hard-to-reach population. The current estimates make strong assumptions in order to treat the data as a probability sample. In particular, we evaluate three critical sensitivities of the estimators: to bias induced by the initial sample, to uncontrollable features of respondent behavior, and to the without-replacement structure of sampling. 
This paper sounds a cautionary note for the users of RDS. While current RDS methodology is powerful and clever, the favorable statistical properties claimed for the current estimates are shown to be heavily dependent on often unrealistic assumptions.

Respondent-Driven Sampling: An Assessment of Current Methodology

Network models are widely used to represent relational information among interacting units and the structural implications of these relations. Recently, social network studies have focused a great deal of attention on random graph models of networks whose nodes represent individual social actors and whose edges represent a specified relationship between the actors. Most inference for social network models assumes that the presence or absence of all possible links is observed, that the information is completely reliable, and that there are no measurement (e.g., recording) errors. This is clearly not true in practice, as much network data is collected though sample surveys. In addition even if a census of a population is attempted, individuals and links between individuals are missed (i.e., do not appear in the recorded data). In this paper we develop the conceptual and computational theory for inference based on sampled network information. We first review forms of network sampling designs used in practice. We consider inference from the likelihood framework, and develop a typology of network data that reflects their treatment within this frame. We then develop inference for social network models based on information from adaptive network designs. We motivate and illustrate these ideas by analyzing the effect of link-tracing sampling designs on a collaboration network.

/pdf/modeling-social-networks-from-sampled-data-gf85ce9qga.pdf

Modeling social networks from sampled data.

COMMENT: ON THE CONCEPT OF SNOWBALL SAMPLING Mark S. Handcock* Krista J. Gile † The need for notes by Goodman (2011) and Heckathorn (2011) re- flects a phenomenon in the sociology of science: that multidisciplinary fields tend to produce a plethora of inconsistent terminology. Often the meaning of a term evolves over time, or different terms are used for the same concept. More confusing is the use of the same term for different concepts. As the two notes point out, the term “snowball sampling” suffers from this treatment. The term “snowball sampling” has likely been in informal use for a long time, but it certainly predates Coleman (1958) and Trow (1957). The earliest systematic work dates to the 1940s from the Columbia Bureau of Applied Social Research, led by Paul Lazarsfeld. The bu- reau became interested in the empirical study of personal influence via media (Barton 2001). This led to the consideration of interpersonal en- vironments and to the identification of opinion leaders and followers. However, standard sampling of individuals was regarded as ineffective in studying the relations between opinion leaders and followers as pairs related in this way were seldom both selected in the sample (Lazarsfeld et al. 1944:49–50). To address this, Robert Merton asked individuals in an initial diverse sample to name the people who influenced them. From these, a second wave of influential people were interviewed as a *University of California, Los Angeles University of Massachusetts, Amherst

/pdf/comment-on-the-concept-of-snowball-sampling-4hw58byga0.pdf

Krista J. Gile

Papers

Summary Report of the AAPOR Task Force on Non-probability Sampling

Respondent‐driven sampling: an assessment of current methodology

Respondent-Driven Sampling: An Assessment of Current Methodology

Modeling social networks from sampled data.

Comment: on the concept of snowball sampling