The Network Autocorrelation Model using Two-mode Data: Affiliation Exposure and Potential Bias in the Autocorrelation Parameter

The network autocorrelation model has been a workhorse for modeling network influences on individual behavior. The standard network approaches to mapping social influence using network measures, however, are limited to specifying an influence weight matrix (W) based on a single mode network. Additionally, it has been demonstrated that the estimate of the autocorrelation parameter ρ of the network effect tends to be negatively biased as the density in W matrix increases. The current study introduces a two-mode version of the network autocorrelation model. We then conduct simulations to examine conditions under which bias might exist. We show that the estimate for the affiliation autocorrelation parameter (ρ) tends to be negatively biased as density increases, as in the one-mode case. Inclusion of the diagonal of W, the count of the number of events participated in, as one of the variables in the regression model helps to attenuate such bias, however. We discuss the implications of these results.     

Statistical power of the social network autocorrelation model

The network autocorrelation model has become an increasingly popular tool for conducting social network analysis. More and more researchers, however, have documented evidence of a systematic negative bias in the estimation of the network effect (ρ). In this paper, we take a different approach to the problem by investigating conditions under which, despite the underestimation bias, a network effect can still be detected by the network autocorrelation model. Using simulations, we find that moderately-sized network effects (e.g., ρ = .3) are still often detectable in modest-sized networks (i.e., 40 or more nodes). Analyses reveal that statistical power is primarily a nonlinear function of network effect size (ρ) and network size (N), although both of these factors can interact with network density and network structure to impair power under certain rare conditions. We conclude by discussing implications of these findings and guidelines for users of the autocorrelation model.     

Bayesian estimation of the network autocorrelation model

The network autocorrelation model has been extensively used by researchers interested modeling social influence effects in social networks. The most common inferential method in the model is classical maximum likelihood estimation. This approach, however, has known problems such as negative bias of the network autocorrelation parameter and poor coverage of confidence intervals. In this paper, we develop new Bayesian techniques for the network autocorrelation model that address the issues inherent to maximum likelihood estimation. A key ingredient of the Bayesian approach is the choice of the prior distribution. We derive two versions of Jeffreys prior, the Jeffreys rule prior and the Independence Jeffreys prior, which have not yet been developed for the network autocorrelation model. These priors can be used for Bayesian analyses of the model when prior information is completely unavailable. Moreover, we propose an informative as well as a weakly informative prior for the network autocorrelation parameter that are both based on an extensive literature review of empirical applications of the network autocorrelation model across many fields. Finally, we provide new and efficient Markov Chain Monte Carlo algorithms to sample from the resulting posterior distributions. Simulation results suggest that the considered Bayesian estimators outperform the maximum likelihood estimator with respect to bias and frequentist coverage of credible and confidence intervals.     

Structure and bias in the network autocorrelation model

In a recent paper (Mizruchi and Neuman, 2008), we showed that estimates of ρ in the network autocorrelation model exhibited a systematic negative bias and that the magnitude of this bias increased monotonically with increases in network density. We showed that this bias held regardless of the size of the network, the number of exogenous variables in the model, and whether the matrix W was normalized or in raw form. The networks in our simulations were random, however, which raises the question of the extent to which the negative bias holds in various structured networks. In this paper, we reproduce the simulations from our earlier paper on a series of networks drawn to represent well-known structures, including star, caveman, and small-world structures. Results from these simulations indicate that the pattern of negative bias in ρ continues to hold in all of these structures and that the negative bias continues to increase at increasing levels of density. Interestingly, the negative bias in ρ is especially pronounced at extremely low-density levels in the star network. We conclude by discussing the implications of these findings.     

Analytic strategies for longitudinal networks with missing data

Missing data are often problematic when analyzing complete longitudinal social network data. We review approaches for accommodating missing data when analyzing longitudinal network data with stochastic actor-based models. One common practice is to restrict analyses to participants observed at most or all time points, to achieve model convergence. We propose and evaluate an alternative, more inclusive approach to sub-setting and analyzing longitudinal network data, using data from a school friendship network observed at four waves (N = 694). Compared to standard practices, our approach retained more information from partially observed participants, generated a more representative analytic sample, and led to less biased model estimates for this case study. The implications and potential applications for longitudinal network analysis are discussed.     

Modeling social influence through network autocorrelation: constructing the weight matrix

Many physical and social phenomena are embedded within networks of interdependencies, the so-called ‘context’ of these phenomena. In network analysis, this type of process is typically modeled as a network autocorrelation model. Parameter estimates and inferences based on autocorrelation models, hinge upon the chosen specification of weight matrix W, the elements of which represent the influence pattern present in the network. In this paper I discuss how social influence processes can be incorporated in the specification of W. Theories of social influence center around ‘communication’ and ‘comparison’; it is discussed how these can be operationalized in a network analysis context. Starting from that, a series of operationalizations of W is discussed. Finally, statistical tests are presented that allow an analyst to test various specifications against one another or pick the best fitting model from a set of models.     

Weight matrices for social influence analysis: An investigation of measurement errors and their effect on model identification and estimation quality

Weight matrices, such as used in network autocorrelation models, are useful to investigate social influence processes. The objective of this paper is to investigate a key topic that has received relatively little attention in previous research, namely the issues that arise when observational limitations lead to measurement errors in these weight matrices. Measurement errors are investigated from two perspectives: when relevant ties are omitted, and when irrelevant ties are erroneously included as part of the matrix. The paper first shows analytically that these two situations result in biased estimates. Next, a simulation experiment provides evidence of the effect of erroneously coding the weight matrix on model performance and the ability of a network autocorrelation test to identify social influence effects. The results suggest that depending on the level of autocorrelation and the topology attributes of the underlying matrix, there is a window of opportunity to identify and model social influence processes even in situations where the ties in a matrix cannot be accurately observed.     

Are Italian consumer confidence adjustments asymmetric? A macroeconomic and psychological motives approach

This paper estimates the determinants of Italian consumer confidence indicator (CCI) using time series methods. We find there exists a long-run relationship between CCI and its determinants when an important political event ‘operation clean hands’, captured by a dummy, is considered. Using the asymmetric error correction model (Enders & Siklos, 2001), we find that consumers respond asymmetrically to different types of disequilibrium error under threshold autoregressive (TAR) adjustment specification. These findings are consistent with the psychological bias approach (Bovi, 2009).     

Missing data in networks: exponential random graph (p1) models for networks with non-respondents

Survey studies of complete social networks often involve non-respondents, whereby certain people within the “boundary” of a network do not complete a sociometric questionnaire—either by their own choice or by the design of the study—yet are still nominated by other respondents as network partners. We develop exponential random graph (p¹) models for network data with non-respondents. We model respondents and non-respondents as two different types of nodes, distinguishing ties between respondents from ties that link respondents to non-respondents. Moreover, if we assume that the non-respondents are missing at random, we invoke homogeneity across certain network configurations to infer effects as applicable to the entire set of network actors. Using an example from a well-known network dataset, we show that treating a sizeable proportion of nodes as non-respondents may still result in estimates, and inferences about structural effects, consistent with those for the entire network.If, on the other hand, the principal research focus is on the respondent-only structure, with non-respondents clearly not missing at random, we incorporate the information about ties to non-respondents as exogenous. We illustrate this model with an example of a network within and between organizational departments. Because in this second class of models the number of non-respondents may be large, values of parameter estimates may not be directly comparable to those for models that exclude non-respondents. In the context of discussing recent technical developments in exponential random graph models, we present a heuristic method based on pseudo-likelihood estimation to infer whether certain structural effects may contribute substantially to the predictive capacity of a model, thereby enabling comparisons of important effects between models with differently sized node sets.     

Union effects on productivity,personnel practices,and survival in the automotive parts industry

We estimate the effects of unions on productivity and compensation in the automotive engine and non-ornamental body parts manufacturing industry using data obtained from a detailed questionnaire and a series of personal interviews. We find no significant union productivity effect but a significant 30 percent compensation premium in firms organized by the United Auto Workers. Individual personnel policies were shown to differ significantly in the expected manner between the union and nonunion sectors. Finally, we use data on bankrupt firms to show how the failure to correct for sample selection bias might yield upwardly biased estimates of the union productivity effect. We would like to thank Elizabeth Savoca and an anonymous referee for their helpful suggestions.     

Blog bias: Reports,inferences, and judgments of credentialed bloggers at the 2004 nominating conventions

Public relations practitioners awarded bloggers media credentials in 2004 to the summer presidential nomination conventions. Using the Hayakawa–Lowry bias categories, this quantitative content analysis reviewed sentences posted by credentialed bloggers during the convention to examine blogger reports (attributed, unattributed), inferences (labeled, unlabeled), and judgments (attributed and favorable, unattributed and favorable, attributed and unfavorable, unattributed and unfavorable) to analyze potential bias in “coverage”.     

Stability of psychological symptoms: drug use consequences and intervening processes

We integrate aspects of coping response, impaired ability, and motivational explanations for the causes and consequences of drug abuse, all which were cast previously as competing or alternative paradigms. We projected a model of 1) continual daily drug use as a consequence of early adolescent psychological symptoms and 2) continual daily drug use as an influential variable in maintaining or exacerbating these symptoms over the young adult life-course. Gender, race, and education also were modeled explicitly according to their presumed theoretical importance. Finally, we modeled contemporaneous factors such as physical health and employment status as the common consequences of the shared independent variables in order to reduce bias in the estimated structural relationships. We found that continual daily drug use is significantly dependent on early psychopathology and increases psychological symptoms significantly. Daily proximate drug use has direct negative effects on education. Education, in turn, improves both mental and physical symptoms significantly. During young adulthood, psychological symptoms are related significantly to contemporaneous unemployment and physical health limitations; thus modeling these symptoms as common consequences reduces potentially biased estimates of the effect of shared independent variables.     

A comparison of estimators for the network autocorrelation model based on observed social networks

Network autocorrelation models (NAMs) are widely used to study a response variable of interest among subjects embedded within a network. Although the NAM is highly useful for studying such networked observational units, several simulation studies have raised concerns about point estimation. Specifically, these studies have consistently demonstrated a negative bias of maximum likelihood estimators (MLEs) of the network effect parameter. However, in order to gain a practical understanding of point estimation in the NAM, these findings need to be expanded in three important ways. First, these simulation studies are based on relatively simple network generative models rather than observed networks, thereby leaving as an open question how realistic network topologies may affect point estimation in practice. Second, although there has been strong work done in developing two-stage least squares estimators as well as Bayesian estimators, only the MLE has received extensive attention in the literature, thus leaving practitioners in question as to best practices. Third, the performance of these estimators need to be compared using both bias and variance, as well as the coverage rate of each estimator's corresponding confidence or credible interval. In this paper we describe a simulation study which aims to overcome these shortcomings in the following way. We first fit real social networks using the exponential random graph model and used the Bayesian predictive posterior distribution to generate networks with realistic topologies. We then compared the performance of the three different estimators mentioned above.     

Measurement error in network data: A re-classification

Research on measurement error in network data has typically focused on missing data. We embed missing data, which we term false negative nodes and edges, in a broader classification of error scenarios. This includes false positive nodes and edges and falsely aggregated and disaggregated nodes. We simulate these six measurement errors using an online social network and a publication citation network, reporting their effects on four node-level measures – degree centrality, clustering coefficient, network constraint, and eigenvector centrality. Our results suggest that in networks with more positively-skewed degree distributions and higher average clustering, these measures tend to be less resistant to most forms of measurement error. In addition, we argue that the sensitivity of a given measure to an error scenario depends on the idiosyncracies of the measure's calculation, thus revising the general claim from past research that the more ‘global’ a measure, the less resistant it is to measurement error. Finally, we anchor our discussion to commonly-used networks in past research that suffer from these different forms of measurement error and make recommendations for correction strategies.     

Measuring and explaining tax evasion: Improving self-reports using the crosswise model

Due to its sensitive nature, tax compliance is difficult to study empirically, and valid information on tax evasion is rare. More specifically, when directly asked on surveys, respondents are likely to underreport their evasion behavior. Such invalid responses not only bias prevalence estimates but may also obscure associations with individual predictors. To generate more valid estimates of tax evasion, we used a new method of data collection for sensitive questions, the crosswise model (CM). The CM is conceptually based on the randomized response technique (RRT), but due to its advanced design, it is better suited for large surveys than classical RRTs. In an experimental online survey, we compared the CM (N = 862) to standard direct questioning (DQ; N = 305). First, our results showed that the CM was able to elicit a higher proportion of self-stigmatizing reports of tax evasion by increasing privacy in the data collection process. Second, on average, we found stronger effects of our predictor variables on tax evasion in the CM condition compared with the DQ condition such that an egoistic personality and the opportunity for tax evasion predicted actual tax evasion only in the CM condition.     

Imputation of attributes in networked data using Bayesian autocorrelation regression models

Misspecification in network autocorrelation models poses a challenge for parameter estimation, which is amplified by missing data. Model misspecification has been a focus of recent work in the statistics literature and new robust procedures have been developed, in particular cutting feedback. This paper shows how this helps in a misspecified network autocorrelation model. Where model misspecification is mild and the traits are fully observed, Bayesian imputation is routine. In settings with high missingness, Bayesian inference can fail, but a closely related cut model is robust. We illustrate this on a data set of graduate students using a Facebook-like messaging app.     

Linked Ego Networks: Improving estimate reliability and validity with respondent-driven sampling

Respondent-driven sampling (RDS) is currently widely used for the study of HIV/AIDS-related high risk populations. However, recent studies have shown that traditional RDS methods are likely to generate large variances and may be severely biased since the assumptions behind RDS are seldom fully met in real life. To improve estimation in RDS studies, we propose a new method to generate estimates with ego network data, which is collected by asking respondents about the composition of their personal networks, such as “what proportion of your friends are married?”. By simulations on an extracted real-world social network of gay men as well as on artificial networks with varying structural properties, we show that the precision of estimates for population characteristics is greatly improved. The proposed estimator shows superior advantages over traditional RDS estimators, and most importantly, the method exhibits strong robustness to the recruitment preference of respondents and degree reporting error, which commonly happen in RDS practice and may generate large estimate biases and errors for traditional RDS estimators. The positive results henceforth encourage researchers to collect ego network data for variables of interests by RDS, for both hard-to-access populations and general populations when random sampling is not applicable.     

I can’t smile without you: Spousal correlation in life satisfaction

This paper tests whether one partner’s happiness significantly influences the happiness of the other partner. Using 10 waves of the British Household Panel Survey, it utilizes a panel-based GMM methodology to estimate a dynamic model of life satisfaction. The use of the GMM-system estimator corrects for correlated effects of partner’s life satisfaction and solves the problem of measurement error bias. The results show that, for both genders, there is a positive and statistically significant spillover effect of life satisfaction that runs from one partner to the other partner in a couple. The positive bias on the estimated spillover effect coming from assortative mating and shared social environment at cross-section is almost offset by the negative bias coming from systematic measurement errors in the way people report their life satisfaction. Moreover, consistent with the spillover effect model, couple dissolution at t + 1 is negatively correlated with partners’ life satisfaction at t.     

Categorical attribute based centrality: E–I and G–F centrality

In a paper examining informal networks and organizational crisis, Krackhardt and Stern (1988) proposed a measure assessing the extent to which relations in a network were internal to a group as opposed to external. They called their measure the E–I index. The measure is now in wide use and is implemented in standard network packages such as UCINET ( Borgatti et al., 2002). The measure is based on a partition-based degree centrality measure and as such can be extended to other centrality measures and group level data. We explore extensions to closeness, betweenness and eigenvector centrality, and show how to apply the technique to sets of subgroups that do not form a partition. In addition, the extension to betweenness suggests a linkage to the Gould and Fernandez brokerage measures, which we explore.     

"I'LL DIE WITH THE HAMMER IN MY HAND": JOHN HENRYISM AS A PREDICTOR OF HAPPINESS

This paper examines the association between John Henryism - a behavioral predisposition to cope actively with psycho-social environmental stressors - and happiness. On the basis of previous research on aspiration and goal regulation, we predicted that John Henryism would be negatively associated with happiness when controlling for demographic factors and attainment in various domains of life. We tested the prediction in a sample of hypertensive participants (n = 758) drawn from an inner-city, mainly African-American, safety-net hospital in Jefferson County, Alabama. Bivariate analysis revealed no association between John Henryism and attainment in six domains of life: marriage, children, education, employment, income, and health. However, a significant negative association between John Henryism and happiness was found both in bivariate analysis (Spearman’s ρ = -0.335; p < .001) and when controlling for demographic factors and attainment using ordinal logistic regression analysis. There was a significant interaction effect between John Henryism and gender: being male was positively associated with happiness among participants with low John Henryism, but negatively associated with happiness among participants with high John Henryism. While further study would be required in order to establish the extent to which these findings can be generalized as well as their causal underpinnings, the results support the hypothesis that John Henryism is negatively associated with happiness, especially among men, and underscore the limitations of using self-report measures of happiness as proxies for well-being for purposes of public policy.