Multiple Membership Models Research Articles

Structure Induced by a Multiple Membership Transformation on the Conditional Autoregressive Model

The objective of disease mapping is to model data aggregated at the areal level. In some contexts, however, (e.g. residential histories, general practitioner catchment areas) when data is arising from a variety of sources, not necessarily at the same spatial scale, it is possible to specify spatial random effects, or covariate effects, at the areal level, by using a multiple membership principle (MM) (Petrof et al., 2020; Gramatica et al., 2021). A weighted average of conditional autoregressive (CAR) spatial random effects embeds spatial information for a spatially-misaligned outcome and estimate relative risk for both frameworks (areas and memberships). In this paper we investigate the theoretical underpinnings of these application of the multiple membership principle to the CAR prior, in particular with regard to parameterisation, properness and identifiability. We carry out simulations involving different numbers of memberships as compared to number of areas and assess impact of this on estimating parameters of interest. Both analytical and simulation study results show under which conditions parameters of interest are identifiable, so that we can offer actionable recommendations to researchers. Finally, we present the results of an application of the multiple membership model to diabetes prevalence data in South London, together with strategic implications for public health considerations.

Injection network drivers of HIV prevention service utilization among people who inject drugs: results of a community-based sociometric network cohort in New Delhi, India.

Injection drug networks may influence their network members' health-seeking behaviours. Using data from a sociometric injecting partner network of people who inject drugs (PWID) in New Delhi, India, we assessed the role of injecting partner (alter) behaviours on individual engagement in HIV prevention services. We enumerated injecting partner linkages among 2512 PWID using coupon referrals and biometric data from November 2017 to March 2020. Participants completed interviewer-administered questionnaires and provided information on injection behaviours, injecting partners, HIV/hepatitis C (HCV) testing and service engagement. Multilevel multiple-membership models (MMMM) evaluated individual PWID HIV testing, medication for opioid use disorder (MOUD) and syringe service engagement as a function of alter attributes, accounting for membership across multiple ego-networks. Logistic regression models assessed parallel associations among socially proximal injecting peers, defined as PWID ≤3 path length from ego. Median age was 26 years; 99% were male. PWID had median 2 injecting partners and 8 socially proximal peers; 14% reported HIV testing, 33% accessed MOUD and 13% used syringe services 6 months prior. In MMMM analyses, PWID with ≥1 versus 0 injecting partners who received HIV testing were significantly more likely to report HIV testing (adjusted odds ratio [aOR]: 2.27, 95% confidence interval [CI]: 1.68-3.16), MOUD (aOR: 1.99, 95% CI: 1.60-2.53) and syringe service use (aOR: 1.66, 95% CI: 1.21-2.39). We observed similar findings for individual MOUD and syringe service use. Having ≥1 versus 0 HIV-positive partners was associated with decreased HIV testing and MOUD but increased syringe service use (aOR: 1.54, 95% CI: 1.09-2.17). PWID with ≥1 versus 0 socially proximal peers who used non-sterile injection equipment reported increased HIV testing (aOR: 1.39, 95% CI: 1.01-1.92), MOUD (aOR: 1.40, 95% CI: 1.10-1.77) and syringe service use (aOR: 1.82, 95% CI: 1.23-2.68). We found differential associative relationships between individual HIV prevention service engagement and the health or risk behaviours of direct and indirect alters. Characterizing network exposure beyond direct injecting partnerships provided important context on possible mechanisms of behavioural influence. Findings could be leveraged to design peer-based interventions that promote network diffusion of health-seeking behaviours.

Modeling Historic Arsenic Exposures and Spatial Risk for Bladder Cancer.

Arsenic is a bladder carcinogen though less is known regarding the specific temporal relationship between exposure and bladder cancer diagnosis. In this study, we modeled time-varying mixtures of arsenic exposures at many historic temporal windows to evaluate their association with bladder cancer risk in the New England Bladder Cancer Study. We used arsenic exposure estimates up to 60 years prior to study entry and compared the goodness of fit of models using these mixtures to those using summary measures of arsenic exposures. We used the Bayesian index low rank kriging multiple membership model (LRK-MMM) to estimate the associations of these mixtures with bladder cancer and estimate cumulative spatial risk for bladder cancer using participants' residential histories. We found consistent evidence that modeling arsenic exposures as a time-varying mixture provided better fit to the data than using a single arsenic exposure summary measure. We estimated several positive though not significant associations of the time-varying arsenic mixtures with bladder cancer having odds ratios (ORs) of 1.03-1.14 and identified many significant and positive associations for an interaction among those who consumed water from a private dug well (ORs 1.28-1.60). Arsenic exposures 40-50 years before study entry received elevated importance weights in these mixtures. Additionally, we found two small areas of elevated cumulative spatial risk for bladder cancer in southern New Hampshire and in south central Maine. These results emphasize the importance of considering time-varying mixtures of exposures for diseases with long latencies such as bladder cancer.

Modeling historic environmental pollutant exposures and non-Hodgkin lymphoma risk

Environmental exposures to chemicals are suspected risk factors for non-Hodgkin lymphoma (NHL), but few studies have assessed historic environmental risk factors. In this study, we estimated the associations between NHL and 1) historic environmental pollutant emissions from the Risk Screening Environmental Indicators (RSEI) model, which uses a database from the Environmental Protection Agency of toxic release emissions to air, water, and land, and 2) chemical mixtures measured in house dust (groups of PCBs, PAHs, and two mixtures of pesticides) for study participants enrolled in the NCI-SEER population-based case-control study (1998–2000) at four SEER centers – Detroit, Iowa, Los Angeles County, and Seattle. We assigned 11 years of annual temporally-varying historic environmental exposure scores by intersecting residential locations from participants' residential histories with a fine grid from the RSEI model and by performing inverse distance weighting between facilities releasing specific carcinogenic chemicals and residential locations for spatially-precise exposure assignments. We used Bayesian index low-rank kriging multiple membership models to identify important lag times for RSEI scores, cumulative effects of RSEI scores, and specific carcinogenic chemical releases into the environment. We found a significant positive association between RSEI scores and NHL at the maximum time lag of 11 years (OR = 1.17, 95% CI (1.06, 1.32)) and a significant cumulative RSEI score effect (OR = 1.30, 95% CI (1.02, 1.84)) for long-term residents in Detroit, where benzene and trichloroethylene were the most important chemicals driving this association. Additionally, we identified significant inverse associations for two study centers and time lags that did not persist in cumulative exposure models. Large weights for dichloromethane and pentachlorophenol in models of cumulative exposure also support evidence for their association with NHL risk. These results underscore the importance of considering historic and cumulative environmental exposures and using residential histories for diseases with long latency periods such as NHL.

Estimating cumulative spatial risk over time with low-rankkriging multiple membership models.

Many health outcomes result from accumulated exposures to one or more environmental factors. Accordingly, spatial risk studies have begun to consider multiple residential locations of participants, acknowledging that participants move and thus are exposed to environmental factors in several places. However, novel methods are needed to estimate cumulative spatial risk for disease while accounting for other risk factors. To this end, we propose a Bayesian model (LRK-MMM) that embeds a multiple membership model (MMM) into a low-rank kriging (LRK) model in order to estimate cumulative spatial risk at the point level while allowing for multiple residential locations per subject. The LRK approach offers a more computationally efficient means to analyze spatial risk in case-control study data at the point level compared with a Bayesian generalized additive model, and as increased precision in spatial risk estimates by analyzing point locations instead of administrative areas. Through a simulation study, we demonstrate the efficacy of the model and its improvement upon an existing multiple membership model that uses area-level spatial random effects to estimate risk. The results show that our proposed method provides greater spatial sensitivity (improvements ranging from 0.12 to 0.54) and power (improvements ranging from 0.02 to 0.94) to detect regions of elevated risk for disease across a range of exposure scenarios. Finally, we apply our model to case-control data from the New England bladder cancer study to estimate cumulative spatial risk while adjusting for many covariates.

Incorporating student mobility in studying academic growth in math: comparing several alternative multilevel formulations

ABSTRACT Increasing pupil mobility has led to widespread concern among parents, educators, and policymakers regarding its negative effects on academic performance. An important issue in examining mobility effects in longitudinal school achievement comparisons is providing accurate estimates. The presence of pupil mobility suggests that we should model pupils as belonging to the series of schools attended and not just their first or final school. We discuss several challenges in accounting for student mobility and, because of the presence of mobile pupils, how to represent the contribution of multiple schools attended on estimating academic growth properly. We then contrast several previous longitudinal multilevel models utilized with two cross-classified multiple membership (CCMM) models, which have been proposed to cumulate annual school effects on pupils’ academic growth better given the complexity of the multilevel data structure. We discuss our results in terms of their theoretical and practical implications for research on school academic improvement.

Between-Year and Within-Year School Mobility: Different Effects by Race/Ethnicity

The current study investigated the effects of school mobility on the academic achievement of different racial/ethnic groups in four cohorts of students from a very large urban school district. In this study, I compared within-year and between-year mobility and, most importantly, account for all the schools students attended over the study period. Using a multiple membership model (MMM), the findings confirmed that, for all student groups, academic achievement was affected more by within-year school mobility than between-year school mobility. Black students had the highest mobility rates, both for between- and within-year mobility. Although Asian-American students achieved higher reading and math scores on average, they were more negatively impacted by within-year school mobility compared to other groups. The current study was able to pinpoint the students most at risk for negative outcomes following within-year mobility. The findings are discussed in the context of policy recommendations that can be adopted by school districts.

On the impact of residential history in the spatial analysis of diseases with a long latency period: A study of mesothelioma in Belgium.

Mesothelioma is a rare cancer caused by exposure to asbestos. Belgium has a known long history of asbestos production, resulting in one of the highest mesothelioma mortality rates worldwide. While the production of asbestos has stopped completely, the long latency period of mesothelioma, which can fluctuate between 20 and 40 years after exposure, causes incidences still to be frequent. Mesothelioma's long incubation time affects our assessment of its geographical distribution as well. Since patients' residential locations are likely to change a number of times throughout their lives, the location where the patients develop the disease is often far from the location where they were exposed to asbestos. Using the residential history of patients, we propose the use of a convolution multiple membership model (MMM), which includes both a spatial conditional autoregressive and an unstructured random effect. Pancreatic cancer patients are used as a control population, reflecting the population at risk for mesothelioma. Results show the impact of the residential mobility on the geographical risk estimation, as well as the importance of acknowledging the latency period of a disease. A simulation study was conducted to investigate the properties of the convolution MMM. The robustness of the results for the convolution MMM is assessed via a sensitivity analysis.

Peer, school, and country variations in adolescents’ health behaviour: A multilevel analysis of binary response variables in six European cities

Adolescents often display similar health behaviour to their peers. Peer effects on health behaviour may be influenced by the school context, and by the country of residence. According to the complex contagion theory, these effects for risky health behaviour may be different from protective health behaviour. This paper combines social network analysis and multilevel analysis to estimate the relative share of variation of risky and protective health behaviours at different levels of the population structure: individuals, peer (friendship) networks, and schools. To achieve these aims, multiple membership models are applied to estimate variations in smoking, drinking, cannabis use, and physical activity at the individual, peer, and school levels, taking into account the differences between countries. The data come from a social network survey carried out in 50 schools in six medium-sized European cities. Networks of peers were found to have similar risky health behaviour when it comes to smoking, drinking, and cannabis use. This was not true, however, for positive health behaviour, i.e. physical activity. For smoking, drinking, and cannabis use, the peer network accounted for almost half of the total behaviour variance. In comparison, the school variance was quite small for all health behaviour. The results suggest that interventions are best carried out at the peer-network level, particularly for behaviour vulnerable to complex contagion, such as smoking and cannabis use.

How to consider fractional counting and field normalization in the statistical modeling of bibliometric data: A multilevel Poisson regression approach

Abstract The numerical-algorithmic procedures of fractional counting and field normalization are often mentioned as indispensable requirements for bibliometric analyses. Against the background of the increasing importance of statistics in bibliometrics, a multilevel Poisson regression model (level 1: publication, level 2: author) shows possible ways to consider fractional counting and field normalization in a statistical model (fractional counting I). However, due to the assumption of duplicate publications in the data set, the approach is not quite optimal. Therefore, a more advanced approach, a multilevel multiple membership model, is proposed that no longer provides for duplicates (fractional counting II). It is assumed that the citation impact can essentially be attributed to time-stable dispositions of researchers as authors who contribute with different fractions to the success of a publication’s citation. The two approaches are applied to bibliometric data for 254 scientists working in social science methodology. A major advantage of fractional counting II is that the results no longer depend on the type of fractional counting (e.g., equal weighting). Differences between authors in rankings are reproduced more clearly than on the basis of percentiles. In addition, the strong importance of field normalization is demonstrated; 60% of the citation variance is explained by field normalization.

Neighborhood affluence protects against antenatal smoking: Evidence from a spatial multiple membership model

ABSTRACTA spatial multiple membership model formalizes the effect of neighborhood affluence on antenatal smoking. The data are geocoded New Jersey birth certificate records linked to United States census tract-level data from 1999 to 2007. Neighborhood affluence shows significant spatial autocorrelation and local clustering. Better model fit is observed when incorporating the spatial clustering of neighborhood affluence into multivariate analyses. Relative to the spatial multiple membership model, the multilevel model that ignores spatial clustering produced downwardly biased standard errors; the effective sample size of the key parameter of interest (neighborhood affluence) is also lower. Residents of communities located in high-high affluence clusters likely have better access to health-promoting institutions that regulate antenatal smoking behaviors.

Dynamic network partnerships and social contagion drive cooperation.

Both reciprocity and positive assortment (like with like) are predicted to promote the evolution of cooperation, yet how partners influence each other's behaviour within dynamic networks is not well understood. One way to test this question is to partition phenotypic variation into differences among individuals in the expression of cooperative behaviour (the 'direct effect'), and plasticity within individuals in response to the social environment (the 'indirect effect'). A positive correlation between these two sources of variation, such that more cooperative individuals elicit others to cooperate, is predicted to facilitate social contagion and selection on cooperative behaviour. Testing this hypothesis is challenging, however, because it requires repeated measures of behaviour across a dynamic social landscape. Here, we use an automated data-logging system to quantify the behaviour of 179 wire-tailed manakins, birds that form cooperative male-male coalitions, and we use multiple-membership models to test the hypothesis that dynamic network partnerships shape within-individual variation in cooperative behaviour. Our results show strong positive correlations between a bird's own sociality and his estimated effect on his partners, consistent with the hypothesis that cooperation begets cooperation. These findings support the hypothesis that social contagion can facilitate selection for cooperative behaviour within social networks.

Teacher Effects on Chilean Children’s Achievement Growth: A Cross-Classified Multiple Membership Accelerated Growth Curve Model

We investigated teacher effects (magnitude, predictors, and cumulativeness) on primary students’ achievement trajectories in Chile, using multilevel cross-classified (accelerated) growth models (four overlapping cohorts, spanning Grades 3 to 8; n = 19,704 students, and 851 language and 812 mathematics teachers, in 156 schools). It was found that teacher effects on achievement growth are large, exceeding school effects. Also, the contribution of teachers to student achievement growth was found to accumulate over time. The study advances the field by exploring teacher effects in the context of an emerging economy, contributing further evidence on the properties of teacher effects on student achievement growth and demonstrating the combined use of accelerated longitudinal designs, growth curve approaches, and cross-classified and multiple membership models.

Assessment of Multiple Membership Multilevel Models: An Application to Interviewer Effects on Nonresponse

ABSTRACTMultilevel multiple membership models account for situations where lower level units are nested within multiple higher level units from the same classification. Not accounting correctly for such multiple membership structures leads to biased results. The use of a multiple membership model requires selection of weights reflecting the hypothesized contribution of each level two unit and their relationship to the level one outcome. The Deviance Information Criterion (DIC) has been proposed to identify such weights. For the case of logistic regression, this study assesses, through simulation, the model identification rates of the DIC to detect the correct multiple membership weights, and the properties of model variance estimators for different weight specifications across a range of scenarios. The study is motivated by analyzing interviewer effects across waves in a longitudinal study. Interviewers can substantially influence the behavior of sample survey respondents, including their decision to participate in the survey. In the case of a longitudinal survey several interviewers may contact sample members to participate across different waves. Multilevel multiple membership models are suitable to account for the inclusion of higher-level random effects for interviewers at various waves, and to assess, for example, the relative importance of previous and current wave interviewers on current wave nonresponse. To illustrate the application, multiple membership models are applied to the UK Family and Children Survey to identify interviewer effects in a longitudinal study. The paper takes a critical view on the substantive interpretation of the model weights and provides practical guidance to statistical modelers. The main recommendation is that it is best to specify the weights in a multiple membership model by exploring different weight specifications based on the DIC, rather than prespecifying the weights.

Structural Role Complementarity in Entrepreneurial Teams

To refine the understanding of the social network characteristics of entrepreneurial teams, we present a new construct: structural role complementarity. In particular, we examine the variation between team members’ respective abilities to act as network brokers. Based on the cofounding networks of 9,461 entrepreneurs and 2,446 large-scale industrial enterprises over 45 years in Russia’s emerging economy (1869–1913), our findings show that variation among team members’ brokering ability significantly predicts the starting capital raised by their firm. The effect is moderated by the team’s average brokering potential. When both the team’s average and variation in brokering potential is high, firms raise greater starting capital. By using multiple membership models, we demonstrate that greater starting capital is largely attributable to team factors rather than the attributes of the individual team members. We also take advantage of discriminatory laws that were passed in 1887 in an instrumental variable analysis to address potential endogeneity issues.The online appendix is available at https://doi.org/10.1287/mnsc.2017.2874 .This paper was accepted by Olav Sorenson, organizations.

Estimating multiple-membership logit models with mixed effects: indirect inference versus data cloning

ABSTRACTMultiple-membership logit models with random effects are models for clustered binary data, where each statistical unit can belong to more than one group. The likelihood function of these models is analytically intractable. We propose two different approaches for parameter estimation: indirect inference and data cloning (DC). The former is a non-likelihood-based method which uses an auxiliary model to select reasonable estimates. We propose an auxiliary model with the same dimension of parameter space as the target model, which is particularly convenient to reach good estimates very fast. The latter method computes maximum likelihood estimates through the posterior distribution of an adequate Bayesian model, fitted to cloned data. We implement a DC algorithm specifically for multiple-membership models. A Monte Carlo experiment compares the two methods on simulated data. For further comparison, we also report Bayesian posterior mean and Integrated Nested Laplace Approximation hybrid DC estimates. Simulations show a negligible loss of efficiency for the indirect inference estimator, compensated by a relevant computational gain. The approaches are then illustrated with two real examples on matched paired data.

Some further aspects of sampling: Comment on Williams and Bornmann

The numerical-algorithmic procedures of fractional counting and field normalization are often mentioned as indispensable requirements for bibliometric analyses. Against the background of the increasing importance of statistics in bibliometrics, a multilevel Poisson regression model (level 1: publication, level 2: author) shows possible ways to consider fractional counting and field normalization in a statistical model (fractional counting I). However, due to the assumption of duplicate publications in the data set, the approach is not quite optimal. Therefore, a more advanced approach, a multilevel multiple membership model, is proposed that no longer provides for duplicates (fractional counting II). It is assumed that the citation impact can essentially be attributed to time-stable dispositions of researchers as authors who contribute with different fractions to the success of a publication’s citation. The two approaches are applied to bibliometric data for 254 scientists working in social science methodology. A major advantage of fractional counting II is that the results no longer depend on the type of fractional counting (e.g., equal weighting). Differences between authors in rankings are reproduced more clearly than on the basis of percentiles. In addition, the strong importance of field normalization is demonstrated; 60% of the citation variance is explained by field normalization.

School composition, family poverty and child behaviour

PurposeThere is little research on the role of school composition in young children’s behaviour. School composition effects may be particularly important for children in disadvantaged circumstances, such as those growing up in poverty. We explored the role of school academic and socio-economic composition in internalising problems, externalising problems and prosocial behaviour at age 7 years, and tested if it moderates the effect of family poverty on these outcomes.MethodsWe used data from 7225 7-year-olds of the Millennium Cohort Study who attended state primary schools in England and for whom we had information on these outcomes. In multiple membership models, we allowed for clustering of children in schools and moves between schools since the beginning of school, at age 5. Our school academic and socio-economic composition variables were school-level achievement and % of pupils eligible for free school-meals, respectively. Poverty (family income below the poverty line) was measured in all sweeps until age 7. We explored the roles of both timing and duration of poverty.ResultsThe effects of poverty were strong and robust to adjustment. School socio-economic composition was associated with individual children’s internalising and externalising problems, even in adjusted models. School composition did not interact with poverty to predict any of the outcomes.ConclusionsNeither the academic nor the socio-economic composition of the school moderated the effect of family poverty on children’s behaviour in primary school. However, children attending schools with more disadvantaged socio-economic intakes had more internalising and externalising problems than their counterparts.

Testing mediation effects in cross-classified multilevel data.

In this article, we propose an approach to test mediation effects in cross-classified multilevel data in which the initial cause is associated with one crossed factor, the mediator is associated with the other crossed factor, and the outcome is associated with Level-1 units (i.e., the 2(A)➔2(B)➔1 design). Multiple-membership models and cross-classified random effects models are used to estimate the indirect effects. The method is illustrated using real data from the Early Childhood Longitudinal Study-Kindergarten Cohort (1998). The results from the simulation study show that the proposed method can produce a consistent estimate of the indirect effect and reliable statistical inferences, given an adequate sample size.

Incorporating Mobility in Growth Modeling for Multilevel and Longitudinal Item Response Data

ABSTRACTMultilevel data often cannot be represented by the strict form of hierarchy typically assumed in multilevel modeling. A common example is the case in which subjects change their group membership in longitudinal studies (e.g., students transfer schools; employees transition between different departments). In this study, cross-classified and multiple membership models for multilevel and longitudinal item response data (CCMM-MLIRD) are developed to incorporate such mobility, focusing on students' school change in large-scale longitudinal studies. Furthermore, we investigate the effect of incorrectly modeling school membership in the analysis of multilevel and longitudinal item response data. Two types of school mobility are described, and corresponding models are specified. Results of the simulation studies suggested that appropriate modeling of the two types of school mobility using the CCMM-MLIRD yielded good recovery of the parameters and improvement over models that did not incorporate mobility properly. In addition, the consequences of incorrectly modeling the school effects on the variance estimates of the random effects and the standard errors of the fixed effects depended upon mobility patterns and model specifications. Two sets of large-scale longitudinal data are analyzed to illustrate applications of the CCMM-MLIRD for each type of school mobility.