Prologue

Symposium on Dynamic Network Models

Many phenomena in social life are organized as social networks, and hardly anyone would disagree that social network concepts and methods have advanced substantive research in sociology. Without question, there has been a growth in social network studies over the past few decades, and SM has played an important role in publishing a number of methodological innovations in the study of social networks. A social network perspective points to the interconnections among actors as a key component of social interaction, with a primary focus on the relational aspects of social processes. Increasingly, sociologists are studying human lives and social networks through time, and more work is being done at the intersection of social networks and life course studies (e.g., Alwin, Felmlee, and Kreager, forthcoming). Given these considerations, we decided to build the symposium for this volume around the theme of modeling lives “together through time,” an idea in part stimulated by an article we received that focuses on the analysis of relationships through time. The article “Dynamic Network Actor Models: Investigating Coordination Ties through Time” by Christoph Stadtfeld, James Hollway, and Per Block places these matters within the framework of a model of coordination ties, network ties that are established only when both actors agree on its creation (e.g., through cooperative arrangements, marriage, or political coordination). The authors argue that coordination ties are common but are difficult to investigate with available statistical models. One of the most important sections of the paper reviews a variety of other statistical models (e.g., SIENA) and their limitations. This paper introduces a dynamic network actor model (DyNAM) for the study of coordination networks over time. This model builds on stochastic actor-oriented models (Snijders 1996, 2001) and statistical network models for time-stamped data (Butts 2008). The authors make explicit the specific characteristics of the dynamic coordination mentioned, introduce software, and sketch out a variety of potential model specifications that researchers might investigate in the framework of their model. The DyNAM model is applied to two empirical examples: The first is concerned with the formation of romantic relationships in a high school over 18 months, and the second is the formation of international fisheries treaties from 1947 to 2010.

This article on coordination ties through time is accompanied by commentaries written by Tom A. B. Snijders and Carter T. Butts. These commentaries focus on both the strengths and limitations of the proposed approach, and they are accompanied by a response from the authors. We believe this symposium raises a number of questions about how sociologists study “linked lives” over time. Ultimately, these models will contribute to knowledge in the role played by social networks, as well as their adaptation and change, in the course of individual lives.

More on Social Network Models

As noted previously, social network research also has experienced remarkable growth in recent years, and SM has played an important role in publishing scholarship focused on the methods of network research. Indeed, in addition to the symposium in this volume, we include a related paper using network models. “Exponential-family Random Graph Models for Rank-order Relational Data” by Pavel N. Krivitsky and Carter T. Butts deals with the case of rank-order or “ipsative” relational data, in which social network preferences are rank-ordered rather than measured in a continuous scale. Such data, in which each actor ranks other actors according to some criterion, are not uncommon, and the authors argue that model-based approaches to rank-order network data have been limited. The approach taken by the authors proposes a general framework for representing such data and defines a class of exponential-family graph models (ERGMs) for rank-order relational data. The paper shows how the now well-known ERGM framework can be generalized to the case of rank-order sociometric data. Particularly because of their suitability for data collected in observational settings, rank-order ERGMs provide a useful tool for considering both new and classic problems in social psychology and the study of decision making.

With respect to the emphasis on social network methods, we also note that the paper in the section on survey measurement, contributed by Ashton Verdery and his collaborators, is fundamentally about the measurement of social networks and could have arguably been included in this section instead. Although it is summarized in the following, it is worth noting here that in addition to introducing some new survey measures of social network ties, Verdery and colleagues focus specifically on clustering coefficients, which measure the extent to which most ties between people appear in pockets of interconnection. Their paper argues that the concept of network clustering can have high payoff in the future study of hidden populations.

Multiplicative Models for Continuous Dependent Variables

This section includes a pair of papers that make an important contribution to understanding current practices involving transformations of continuous dependent variables. The paper “Multiplicative Models for Continuous Dependent Variables: Estimation on Unlogged versus Logged Form” by Trond Petersen provides a unified treatment of this topic and compares two common approaches for modeling a positive and continuous outcome. One is to use generalized linear models for positive outcomes, such as gamma or Poisson regressions. The other is to first transform the outcome onto the log scale and then use simple linear regressions. The paper shows that these two approaches typically generate different coefficient estimates that are not always consistent with one another. As Petersen points out, this is because the first models the conditional mean of the original outcome whereas the second models the conditional mean of the logged outcome (or equivalently, the geometric mean of the original outcome). Petersen includes a framework for understanding the assumptions underlying a variety of the forms of the model and explicates the conditions under which the two approaches yield the same results. The paper provides guidance to readers regarding the most relevant sources for more information, and it will be helpful to the mathematically unsophisticated researcher regarding the choice of scaling continuous dependent variables. In the companion paper in this section, “A New Way to View the Magnitude of the Difference between the Arithmetic Mean and the Geometric Mean and the Difference between the Slopes When a Continuous Dependent Variable Is Expressed in Raw Form vxersus Logged Form,” Leo A. Goodman provides supplementary derivations that assist in the understanding of the Petersen paper. His paper gives the exact conditions for differences among the models discussed by Petersen and provides an understanding of the conditions under which the two approaches yield the same results.

Causal Inference

The two papers included in this section deal with causal inferences in important and interesting ways. Arvid Sjölander develops a model for observational data that draws on the “case-time-control design” from the epidemiological literature (Suissa 1995). The paper “The Case-time-control Method for Nonbinary Exposures” proposes a solution to the problem of estimating fixed effects models for nonrepeated events where the exposure variables are continuous. As the author points out, there are two formulations of the case-time-control method in the extant literature. One formulation requires that the exposure is binary, and the other requires that there are no more than two time points per individual. Building on this work, Sjölander proposes a solution for continuous predictor (exposure) variables and two or more time points for observations. The author derives the asymptotic properties of the resulting estimator and assesses its finite sample properties in a simulation study. Although to our knowledge not many sociologists have employed the case-time-control method, there are many potential applications. In the words of one editorial board member, “this expands the sociologist’s toolkit.”

The paper “Estimating Moderated Causal Effects with Time-varying Treatments and Time-varying Moderators: Structural Nested Mean Models and Regression with Residuals” by Geoffrey T. Wodtke and Daniel Almirall tackles a similar problem—namely, one’s ability to infer causation using models that include time-varying treatments and time-varying moderators. Their paper focuses on the situation of “treatment effect moderation,” by which is meant “variation in the effects of a treatment across observed subgroups defined in terms of covariates measured prior to treatment exposure” (not the same as interaction). This article introduces to sociology moderated intermediate causal effects and the structural nested mean model for analyzing effect moderation in the longitudinal setting. It discusses problems with conventional regression and presents a new approach to estimation (regression with residuals) that avoids these problems.

In the tradition and terminology developed by Holland (1986), Wodtke and Almirall propose models that specify that both the treatment and effect moderators vary over time and may influence one another through a dynamic process of selection and feedback. Their paper introduces the concept of “moderated intermediate causal effects,” and the authors point out that with the proliferation of rich prospective panel data, it is now possible to study time-dependent processes without the restrictions of point-in-time research questions. To illustrate the techniques, the authors use an example from the Panel Study of Income Dynamics (PSID), examining whether the effects of time-varying exposures to poor neighborhoods on the risk of adolescent childbearing are moderated by time-varying family income. To accomplish this, they employ structural nested mean models (SNMM) and regression with residuals (RWR), arguing that conventional regression models can lead to bias.

Decomposing Segregation

The study of segregation has been central to demographic approaches in sociology. Within that tradition, numerous studies have been conducted that focus on residential and school segregation by race and occupational segregation by gender. The paper by Kazuo Yamaguchi, “Decomposition Analysis of Segregation,” focuses attention on the problem of the confounding of the unique effect of the group variable (e.g., race) with the effects of covariates on segregation. The goal is to partition the extent of segregation into that which can be explained by the covariates and the remaining extent of segregation, the explained and unexplained components, respectively. The paper introduces two new statistical methods for the decomposition analysis of segregation. Both models rely on Rubin’s conception of modeling counterfactual outcomes and inverse-probability-of-treatment weighting. One method is an extension of the DiNardo-Fortin-Lemieux (DFL) supply-driven decomposition method (DiNardo, Fortin, and Lemieux 1996) and the other an extension of it that includes demand-based constraints. The author applies both models to the case of Japanese gender segregation in occupation and produces some surprising results.

Survey Measurement

Two papers involving issues of survey measurement are included in this volume, one proposing a new set of survey measures that permits improvements in assessing network structure in respondent-driven sampling studies and one dealing with the question of the accuracy of retrospective data. The first paper, by Ashton M. Verdery and colleagues (Jacob C. Fisher, Nalyn Siripong, Kahina Abdesselam, and Shawn Bauldry), “New Survey Questions and Estimators for Network Clustering with Respondent-driven Sampling Data,” focuses on survey question methods used in conjunction with respondent-driven sampling (RDS). RDS is an increasingly popular method for sampling hard-to-survey populations characterized by stigmatized, sensitive, and hidden attributes that employs information about social network ties and peer recruitment (see Heckathorn 1997; Salganik and Heckathorn 2004). RDS is typically used to estimate the prevalence of specific behaviors within a population at risk, and it is rarely used to draw inferences about the structural properties of the networks in those populations. This is in part because typical RDS studies are not designed to provide this type of information and therefore have limited opportunity to measure network structure beyond recruiter-recruit relationships. Few studies of hidden populations using RDS have directly examined network structure, and the paper by Verdery and colleagues introduces a new set of survey data collection protocols, developed in computer science for random walk surveys (RWS) (see Hardiman and Katzir 2013), that can be used in RDS studies. Building on this work, the authors recommend that researchers using RDS surveys begin asking the types of questions that would allow the estimation of clustering coefficients. They further demonstrate the utility of the approach by using simulations and implementation in six empirical surveys. As a network phenomenon, network clustering may play an important role in the transmission of diseases and the adoption of behaviors through social networks, and this chapter reinforces these possibilities.

The second paper in the section on survey measurement, “Retrospective Reporting of First Employment in the Life-courses of U.S. Women” by Rachel M. Shattuck and Michael S. Rendall, focuses on methods for assessing the accuracy of women’s reporting of their first spell of employment. This paper is motivated in part by the life course perspective, which emphasizes that people’s lives are uniquely shaped by the timing and sequencing of events (Elder 1985). To locate events (and transitions) in time and understand how earlier events may influence later outcomes, it is essential to have accurate information about both the past and the present. With the exception of prospective longitudinal research designs, analysts must often employ retrospective measures about events in the past, a strategy that poses a number of problems (Giele and Elder 1998). Survey methodologists have devoted considerable attention to the development of methods for the reporting of early life events (see Belli, Stafford, and Alwin 2008; Freedman et al. 1988). The accuracy of such retrospective measurement is the focus of Shattuck and Rendall’s paper. Building on prior research concerning retrospective reports of life course events, the authors employ a “benchmark-survey approach,” focusing on retrospective reports of women’s first substantial involvement in the labor force. Shattuck and Rendall employ retrospective measures of first jobs from three nationally representative surveys for a specific range of birth cohorts and compare them with their chosen benchmark. The three studies are (1) the 2006–2010 National Survey of Family Growth (NSFG), (2) the Survey of Income and Program Participation (SIPP), and (3) the National Longitudinal Study of Adolescent to Adult Health (Add Health)—compared to the benchmark. Their study uses an independent annual panel survey, the National Longitudinal Survey of Youth, 1997 cohort (NLSY97), as the benchmark data source. They conclude that retrospective reports are reasonably accurate in providing summary indicators of women’s first jobs. This study represents a valuable contribution to the study of the accuracy of retrospective measurement, raising a number of questions about how to evaluate the accuracy of survey data and proposing several explanations for inaccuracies in retrospective reporting.

Data Visualization

Visualization has always been an important set of tools for understanding social data, and in the modern era of “big data,” visualization of results of data analysis becomes even more important. “Visualizing Latent Class Models with Analysis-of-distance Biplots” by Zsuzsa Bakk and Niel J. le Roux proposes some visualization tools for latent class (LC) models. Given the widespread use of LC models, there has been an accompanying interest in LC visualization tools. This has not been a neglected topic as papers on this subject have been published in Sociological Methodology (Magidson and Vermunt 2001; Van der Heijden, Gilula, and Van der Ark 1999). Building on this prior work, Bakk and le Roux argue that there is a need for better visualization tools, linked in part to alleged shortcomings of currently available tools. The tools proposed by these authors build on their prior experience and an existing literature on the development and practice of biplots. Such tools can assist in the interpretation of LC models by giving a graphical understanding of the properties of the model. Bakk and le Roux propose using categorical analysis-of-distance (AoD) biplots to visualize the posterior classifications arising from an LC model. Using such multivariate plots, it is possible to visualize in two or three dimensions the profile of multiple LCs. The authors illustrate their approach empirically for three or more classes and compare their proposed methods with state-of-the-art tools: the univariate profile plot and the multivariate ternary plot. They make a case for the viewpoint that their proposed biplot enhances the interpretation of the latent classes. They outline several topics for future research.

In closing, we wish to draw attention to the passage from “Great Books and Small Groups” in Sociologists at Work (Davis 1964) cited in the epigraph to the dedication—namely, the idea that while sociologists’ interests and preoccupations may be capricious, their methods cumulate. In reviewing the past 50 years of methodology in sociology, we remain mindful of Jim’s idea about the cumulative nature of methods and methodology. Traditionally, the community of sociological methodologists has emphasized the view that SM is primarily a place for the publication of innovative approaches or new solutions to old problems in the field. At the same time, there is abundant evidence that the articles SM has published over the years have reflected the kind of cumulative development of knowledge to which Davis referred. This is certainly true of many of the papers included in the present volume. With this in mind, we move forward with the pledge to publish work that demonstrates both innovation and cumulativeness in sociological methodology.