Crafting Mosaics: Person-Centered Religious Influence and Selection in Adolescent Friendships

Abstract

This research addresses the intersection of two key domains of adolescents’ lives: religion and peer networks. Religion scholars argue that religion is multi-faceted and better understood by focusing on combinations of indicators (i.e. mosaics), versus a variable-centered approach. We adopt this framework and investigate the interplay between religion and peer networks, both in how religious mosaics are shaped by friends and how religious profiles affect friend selection dynamics. With data from two schools in the National Longitudinal Study of Adolescent Health, we estimate religious mosaics using latent class analysis (LCA) to identify profiles consisting of combinations of commonly available survey-based measures of religious attitudes, behaviors, and identities. Finding evidence of theoretically-expected profiles, we then use stochastic actor based models (SABMs) to investigate network dynamics for these LCA-based religious profiles. We demonstrate how the profile data can be integrated within the SABM framework to evaluate processes of friend selection and influence. Results show evidence of adolescents influencing one another’s religious mosaics, but not selecting friends on that basis.

Introduction

Adolescence and early adulthood are key moments in the life course where religious attitudes, behaviors, and identities change (Pearce and Denton 2011; Smith and Denton 2005; Smith and Snell 2009). During adolescence, individuals increasingly take control over decisions about their religiosity, which is reflected in substantial shifts in their religious identities, behaviors, and the primary influences of those changes. For example, adolescents’ religiosity has shown substantial declines (Regnerus and Uecker 2006; Uecker, Regnerus and Vaaler 2007), other less linear changes (Pearce and Denton 2011), and the capacity to establish or alter the trajectories of other domains of life—e.g., health (Ellison and Levin 1998; George, Ellison and Larson 2002; Trinitapoli and Weinreb 2012), educational performance (Lehrer 1999; Regnerus 2000), and delinquency (Pearce and Haynie 2004). Adolescence is also a time when peers take on an increasingly central role in both influencing important behavioral and identity changes (Steglich, Snijders, and Pearson 2010; Veenstra et al., 2013), and providing the primary social groups wherein such changes manifest (Schaefer et al., 2011; Ueno et al., 2012). Given the intersection of religious changes and heightened importance of peers during the adolescent period in the life course, there is ample reason to expect that peer processes and religious changes shape one another in adolescents’ lives (Cheadle and Schwadel 2012; Cook et al., 2017; Sepulvado et al., 2015).

Research on social networks has consistently found elevated similarity among peers on a wide range of behavioral and identity dimensions (McPherson, Smith-Lovin and Cook 2001)—including religiosity (Cheadle and Schwadel 2012). This similarity can arise from a variety of social processes; here we focus especially on peer influence, wherein adolescents adopt behaviors similar to those of their friends (Haas and Schaefer 2014; de la Haye et al., 2013), and homophilous selection, a process whereby friendships are more likely to form between similar vs. dissimilar peers (Schaefer, Kornienko, and Fox 2011). In light of the long-standing observation of such similarities, and the potential for similarity to arise through multiple social processes (Kandel 1978; Marsden 1988), scholars have sought to theoretically, methodologically, and empirically disentangle influence and selection processes from one another (Kossinets and Watts 2009; Steglich et al., 2010; Van Zalk et al., 2010). While others have examined selection and influence on adolescents’ religiosity (Cheadle and Schwadel 2012; Cook et al., 2017), we extend this by incorporating a recent fundamental re-conceptualization of adolescent religiosity into this research.

Given the importance of religion in social life, researchers have devoted considerable attention to identifying the most appropriate way(s) of conceptualizing how religion matters in people’s lives. Here, we follow the tradition initially developed in qualitative studies that aimed to capture how experiences of “lived religion” reflect the important dimensions of religion more faithfully than can strategies that conceptualize religion in terms of single variables (Ammerman 2007; McGuire 2008). Stemming from this literature, Lisa Pearce and colleagues demonstrated the capacity of in-depth religious surveys to capture some of religion’s multidimensionality highlighted in the lived religion approach, by identifying what they label as religious “mosaics” (Pearce and Denton 2011; Pearce et al., 2013). In brief, mosaics capture the ways individuals combine various religious behaviors and attitudes in patterned ways. We draw on this approach to use religious mosaics as the key conceptualization of religion when examining adolescents’ peer influence and friend selection patterns.

In this paper, we begin by providing an overview of network research on selection and peer influence. We then discuss the motivation for conceptualizing adolescent religion as mosaics, and how selection and influence may play out for religious mosaics. We make the case that it is advantageous to combine these perspectives and illustrate their integration through a dynamic network model. Our data come from two large schools in the National Longitudinal Study of Adolescent Health (“Add Health”; Bearman, Jones and Udry 1997). We follow the mosaic approach by identifying adolescents’ religious profiles, then estimate models of network and behavioral change (Snijders, van de Bunt, and Steglich 2010), to disentangle the effects of profile-based religious friend selection from influence. We discuss the implications of our findings for religious scholarship and identify pathways for advancing research on religion, networks, and their intersection using a mosaic-based approach.

Background

Adolescence and young adulthood is a time of rapid development, including changes in the ways individuals engage with and express their religious identities (Trinitapoli and Vaisey 2009; Uecker, Regnerus and Vaaler 2007). Given this dynamism, and the wide range of domains to which religion is salient, researchers have devoted considerable time to explaining the sources of religious identification, behavior, and change during adolescence (Smith and Denton 2005). In particular, Cheadle and Schwadel (2012) combine this focus on adolescent religious change with recent advances in the statistical modeling of social network data to show how adolescent friendships reflect both religious influence between friends and friend selection based on religious similarities for a range of common religion variables. Our focus here is similar: we investigate how networks contribute to religious identity, but demonstrate how the assessment of this question can benefit from incorporating the perspective of religious mosaics (Pearce and Denton 2011; Pearce et al., 2013).

Network Processes in Adolescent Friendships

Few findings in the social sciences are as consistent as people’s social contacts being highly structured to include others like themselves on a wide range of characteristics (McPherson, Smith-Lovin and Cook 2001). This pattern of assortativity has been documented for relationships ranging from strong close personal connections (e.g., marital homogamy and best friends) to weaker ties, including infrequent acquaintances. In fact, it is now hard to find examples of behaviors or attributes for which this pattern does not hold (though marital relationships are more often heterogamous on one dimension—gender). As a small sampling from the vast range of relationship assortativity documented in the literature: friendships are similar on demographic attributes such as race (Moody 2001; Goodreau et al. 2009), gender (Ridgeway and Smith-Lovin 1999), and age (Kossinets and Watts 2009); behaviors including substance use (Kirke 2004; Mercken et al. 2010), physical activity (de la Haye et al. 2011), aggression/prosociality (Dijkstra et al. 2012); psychological states such as depression (Schaefer et al., 2011), or attitudes such as school attachment (Paxton and Moody 2002), antipathy (Berger and Dijkstra 2013), identities including school “crowds” (Brown, Von Bank and Steinberg 2008), ethnic identity (Kornienko, Santos and Updegraff 2014), sexual identity (Ueno et al. 2012), and religion (Cheadle and Schwadel 2012; Cook et al., 2017) and the list could go on; for a review see McPherson, Smith-Lovin and Cook (2001).

Given the pervasiveness of assortativity, social scientists have long theorized its possible origins (Kandel 1978). When investigating the mechanisms responsible for assortativity, it is first necessary to take account of chance expectations. In particular, with any characteristic that is not equally distributed within a population, some level of relational homophily is to be expected simply by chance, which is known as baseline homophily (Blau 1977; Marsden 1988; McPherson, Smith-Lovin and Cook 2001). The goal of network studies is often to measure and identify the processes responsible for observed levels of homophily that exceed these baseline levels (Kandel 1978). In general, behavioral similarity can arise via two distinct processes: individuals can adopt the behaviors of their peers—for instance, through peer influence—and/or friendships can form and dissolve in ways that maximize behavioral similarities—homophilous selection (Steglich et al., 2010; Kandel 1978). Here, we first show that adolescent networks show assortativity on religion in excess of baseline expectations, then assess what processes account for the observed pattern.

Homophilous friend selection occurs when people form connections with others like themselves at rates greater than expected by chance (Kandel 1978). Homophilous selection can arise via numerous distinct mechanisms. For instance, McPherson and Smith-Lovin (1987) employ the notion of foci (Feld 1981) to explain how organizations such as voluntary associations or clubs can constrain relationship opportunities to others like oneself (Schaefer, Simpkins and Ettekal 2018). Alternatively, preferences for similar peers may lead people to select friends like themselves or, over time, dissolve friendships with dissimilar others (Van Zalk et al. 2010). Finally, network-based processes—e.g., transitivity (the tendency of two individuals who share a friend in common to themselves form a friendship)—can amplify homophily by reinforcing relationships and friendship groupings (Snijders 2011; Wimmer and Lewis 2011). The nature of adolescent religiosity—as a collective and often organization-based activity (i.e., foci)—makes these processes relevant and suggests a high likelihood of observing adolescents selecting friends or maintaining friendships with those who are religiously similar to themselves.

Friendship assortativity also arises via peer influence, wherein over time individuals increasingly adopt behaviors or attitudes similar to those of their friends (Snijders 2011; Kandel 1978). Scholars have theorized the importance of peer influence for adolescents’ behavioral change for decades on a wide range of outcomes (Kirke 2004; Van Zalk et al., 2010). Such influence can occur in many ways, often unintentionally, in light of adolescents’ basic psychological need for relatedness (Deci and Ryan 2011). Over time, adolescents imitate their friends as they learn to relate with one another (i.e., social learning). Adolescents may also seek to be like their friends as a way of exploring their identities and “trying on” different roles, which may receive reinforcement from friends. Our interest is not so much in discerning how peer influence occurs, but rather, whether peer influence processes are also at work in the realm of religious mosaics. Early peer influence research has been criticized for focusing too heavily on problem behaviors and negative outcomes, while paying inadequate regard to peer influences on prosocial outcomes (Brechwald and Prinstein 2011). Recent studies have begun to address this limitation and offer evidence of peer influence on a broader set of outcomes, including emotions (van Workum et al 2013), culture (Lewis and Kaufman 2018), and, most important for our purposes, identity (Kornienko et al., 2016; Rivas-Drake, et al., 2017).

Combined, this literature leads us to expect that over time we should also see adolescents becoming increasingly similar to their friends in the domain of religion. This could occur through selection, peer influence processes, or both. Recent developments in the statistical modeling of network data (e.g., Snijders 2011; Snijders et al., 2010; Steglich et al., 2010) allow researchers to empirically disentangle the relative importance of influence versus selection. Religion scholars have applied these models to adolescents’ religion (Cheadle and Schwadel 2012; Cook et al., 2017), finding evidence to support selection and influence. In light of these results, it is worth reconsidering how religiosity has been conceptualized in these studies and how well its measurement aligns with contemporary theorizing of adolescent religion.

Adolescents’ Religious Mosaics

Before modeling network selection and influence, it is important to conceptualize and measure religion in a way that best reflects recent literature on adolescent religion. Previous network scholarship demonstrates that measurement choices can substantially alter the capacity to identify and distinguish selection from influence effects. For example, in testing selection, Wimmer and Lewis (2011) demonstrate how homophily on race is better explained by using more precise measures of ethnicity versus broad racial categorizations. More pertinent here, studies of religion have found different selection and influence processes in operation depending upon whether attitudinal, behavioral or identity aspects of religion were measured (Cheadle and Schwadel 2012). While different variables may in fact exhibit different selection and influence patterns, recent scholarship on adolescents’ lived religious experiences suggest such variable-oriented approaches may not accurately capture the way religion is perceived and practiced. We therefore draw on Pearce and colleagues’ application of these ideas in the concept of religious “mosaics” to reframe how adolescent religiosity should be incorporated into studies of religious selection and influence processes.

A growing body of literature advocates for a reconceptualization of religiosity away from variable-oriented notions, which have traditionally sought to succinctly capture the salient dimensions of people’s religion with a single variable (or some limited set of variables). The weakness of such “variable centered” approaches, as documented in qualitative work focusing on “lived” or “everyday” religion, is that it doesn’t reflect the ways that people experience and enact their religious identities to construct their own religious experience. As an alternative, the “lived religion” approach advocates that a more “person-centered” conceptualization of religion be used in research designs (Ammerman 2007; McGuire 2008). That is, for researchers to accurately capture religion as it is actually experienced requires describing the unique combinations of attitudes, behaviors, and identities in the way that individuals piece them together individually. In turn, once such profiles can be identified, the influence of religion on other aspects of one’s life should be examined in relation to those combinations, rather than focusing on particular religious variables (Pearce et al., 2013).

Survey researchers have subsequently attempted to leverage these theoretical insights about combinatorial conceptualizations of individuals’ religious experiences in ways that scale up for application to larger, more representative samples (Pearce and Denton 2011; Pearce et al., 2013). Descriptively, Pearce and colleagues use Latent Class Analysis to inductively estimate mosaics of religious profiles. Mosaics reflect the patchwork way that individuals combine varied religious dimensions into observable clusters. This work has then gone on to demonstrate how these mosaics provide additional leverage for explaining a range of behavioral outcomes (e.g., delinquency and academic performance), above and beyond the explanatory power available from the individual variables from which the mosaics were constructed (Pearce and Denton 2011). Here, we extend this approach further, by estimating profiles and examining their role in adolescent friendship dynamics.

Selection & Influence of Religious Mosaics

Our conceptualization of religious identity follows the religious mosaic approach described above. This approach moves beyond focusing on behaviors or attitudes singularly, given we have little reason to expect that individual variables form the basis on which peer influence and homophilous selection processes actually operate. In addition to the consistency with the conceptualization of religious mosaics, this shift to considering multiple measures in combination is also consistent with recent developments in network studies of selection and influence as well. These alterations have incorporated the recognition that behaviors and other attributes may operate in conjunction (Brechwald and Prinstein 2011: 168).

For example, Strang and Soule argue that diffusion actually entails individuals “translat[ing] concrete practices into abstractions for export and then unpack [t]he abstraction into a (suitably modified) concrete practice upon arrival” (1998:277). In other words, this perspective suggests that people don’t directly mimic the behaviors of their peers, even when influenced by them. Instead, an abstraction actually diffuses, and is interpreted—by the person being influenced—at both the sending and receiving ends. This perspective is consistent with making religious mosaics the focus of investigating the way adolescents’ religiosity and peer network processes are interrelated. To illustrate, it may be that while one adolescent’s frequent religious attendance may not directly influence the attendance of their peers, by signaling an identity of “highly religious” it may increase their peers’ reported religious salience (or other dimensions). Lewis and Kaufman (2018) make similar claims about how homophilous selection operates not on individual traits, but on clusters of cultural tastes.

In sum, religious mosaics are more consistent with recent developments in conceptualizing and measuring religion, and therefore the estimation of network selection and influence processes should incorporate this approach into how they are modeled, rather than only testing them with variable-centered approaches. Thus, while prior studies of religiosity and network dynamics have separately examined variables such as denominational affiliation, importance of religion, service attendance, and prayer frequency, among others (Cheadle and Schwadel 2012; Cook et al. 2017), a mosaic-based conceptualization of adolescents’ religion is readily adaptable into re-theorized accounts of how selection and influence operates in dynamic peer networks. We therefore assert that mosaics represent a more theoretically-grounded means to capture adolescent religious experience and therefore are the focus when evaluating network selection and influence processes. Thus, our primary research question is whether religious mosaics provide a basis for adolescents’ friend selection and peer influence processes.

Data

We use data from the Wave I in-home, and Wave II in-home surveys from the National Longitudinal Study of Adolescent Health (“Add Health”, Bearman, Jones and Udry 1997). Add Health contains information on complete networks for more than 100 schools at 1 wave, and 16 schools at 3 waves. Here, we focus on the two largest “saturated” schools with longitudinal complete network data.¹ These schools are of sufficient size to model friendship dynamics, while also reliably estimating school-specific religious profiles. The schools we use (frequently referred to by the pseudonyms “Jefferson” and “Sunshine” High School) represent two different social contexts. “Jefferson” is a mostly white school in the Midwest and “Sunshine” is a much larger, ethnically diverse school in the West; Table 1 provides descriptive overviews for each of these schools on key study and contextual variables.² These schools have become common for benchmarking social network change estimation (Green et al. 2013; Haas and Schaefer 2014), in part because they represent such different contexts.

Table 1.

Descriptive Statistics for Sample School Participants

	Jefferson HS N=502	Sunshine HS N=891
Demographics
Gender (% female)	47.2	50.3
Race (%)
White	94.4	3.8
African American	0	21.6
Hispanic	0.8	39.2
Asian American	0.6	23.9
Other	4.2	6.1
Age in Years	15.4 (0.99)	15.7 (0.81)
Grade Level	9.9 (0.78)	10.5 (0.50)
Religion
Service Attendance (1–5)	3.2 (1.44)	4.0 (1.19)
Importance (1–5)	3.5 (1.35)	4.3 (0.98)
Prayer (1–6)	3.9 (1.84)	5.1 (1.42)
Religious Tradition (%)
Evangelical Protestant	16.7	9.2
Mainline Protestant	32.2	16.8
Black Protestant	0	16.1
Roman Catholic	29.6	47.1
Other	3.6	5.8
None	17.9	5.1

NOTE: Unless otherwise noted, figures presented are means and (standard deviations).

Measures

We construct religious profiles from measures in Add Health that (a) are commonly available across a variety of national surveys, and (b) capture the domains that provide the theoretical basis for religious mosaics as developed by Pearce and colleagues. This results in our profiles being constructed from three variables in Add Health—frequency of religious attendance (i.e., behavior),³ religious salience (i.e., attitude), asked, “How important is religion to you?” (with Likert-scale response categories), and prayer frequency; descriptive statistics for these variables are included from Wave 1 for each school in Table 1. Given that the aim for including these indicators in our analysis is to mimic the theoretical motivation of Pearce and colleagues’ approach as closely as is possible with Add Health data, we label it the “replicate” strategy.⁴ In addition to this replicate approach, we use two alternative specifications to fit religious mosaics (described below).

We construct friendship networks from the nominations respondents provided for up to five male and five female friends within the school at each wave (Bearman et al., 1997). This contrasts with many studies that use proxy reports of alter behavior, which tend to suffer from self-projection bias (Vaisey and Lizardo 2010). In addition to the study’s focal variables, we include a standard set of self-reported controls: gender (male is the reference category), age (in years at wave 1), race (non-Hispanic white=reference, non-Hispanic black, Hispanic, Asian, other),⁵ GPA, and parent’s highest level of completed education. Jefferson is a smaller school, where adolescents nominated more friends than in the larger Sunshine, resulting in networks of much higher density. Over time, students in each school each nominated fewer friends (a common observation in longitudinal network studies; adams 2019). Transitivity did not change appreciably between waves, while Sunshine students seem to have reduced their nominations to exclude less-close ties--as indicated by the increase in the reciprocity rate there across waves. The Jaccard index shows that these data are sufficiently stable for estimation with an SABM (Snijders et al 2010).

Methods

We follow (Pearce et al., 2013) by modeling religious mosaics with Latent Class Analysis (LCA) to identify the profiles of combinations observed across the three primary religious variables described above. LCA is a person-centered approach to identifying subgroups in a population who combine behaviors/attributes in common ways. LCA is particularly appropriate here in that it allows for multiple dimensions of variation across the religious indicators included. This stands in contrast to approaches that would treat each variable individually (for the reasons described above), or an index that would require assuming uniformity in how individuals combine these indicators (e.g., that increases/decreases in one component variable are equally likely or correlated with increases/decreases in another). This profile approach is consistent with the theoretical bases underpinning the search for religious mosaics (Pearce et al., 2013; Pearce and Denton 2011).

The basic form of the LCA model is:

$$P(Y_i=y|X_i=x)={\sum }_{l=1}^{n_c}\mathrm{\gamma l}{\prod }_{m=1}^M{\prod }_{k=1}^{r_M}\rho \begin{array}{c}I{(y}_m=k)\\ mk|l\end{array}$$ Equation 1.

which estimates the probabilistic class membership for each individual i, based on ρ (the probability of item response conditional on latent class) and γ (the probabilities of class membership). The first summation is over the number of classes, n_c. The first product is across question items M (here 3) and r_m, the number of possible responses for each item (5 our attendance and importance measures, and 6 for the prayer measure). That is, class membership is conditional on the probability of combining values across each included indicator in similar ways.

We use standard Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) criteria to identify the best fitting number of classes (Linzer and Lewis 2011; McCutcheon 1987; Vermut and Magidson 2002). It is increasingly common to fold the identification of LCA classes and estimation of those classes association with outcome variables into a single model-fitting approach, rather than a “classify-analyze” approach that splits these into two separate modeling steps (Bray et al 2015). However, we use the classify-analyze approach here for two reasons. First, no modeling approach akin to the stochastic actor-based model for network dynamics that we employ (described below) is available to combine the LCA fitting into a single model. Second, the classify-analyze approach is an acceptable procedure when class probabilities are high (e.g., >.80) (Jung and Wickrama 2008).⁶ We use this classify-analyze approach to assign individuals to the class with the largest posterior probability, Pr(Ci= k|Yi), and then estimate network models using this nominal variable. Note especially that each indicator (M) can vary independently from the others, in a way consistent with the person-centered multidimensionality of religion as conceptualized by the mosaic approach. In practice, this allows for an exploratory analysis of the myriad possible combinations between these variables’ response categories, reducing the sets in the output classes to correspond only with the prevalent combinations observed within the population.

We estimate a series of nested LCA solutions using the poLCA package in R (Linzer and Lewis, 2014). We use a variety of model fit indices to determine which model best replicates the data (i.e., G2 likelihood ratio, AIC and BIC), which aligns with Pearce and colleagues’ method. Our model uses the “replicate” set of variables described above: religious importance, religious attendance, and prayer frequency. With these variables, we estimate LCA solutions for two through six class solutions to empirically identify best-fitting class solutions. We estimate each LCA model separately at Wave I and Wave II for each school.

Alternate LCA Specifications

In addition to the replicate strategy described above, we also fit two alternative specifications for the LCA-model estimation of religious profiles. The first alternative replaces the measure of prayer frequency with a measure that asks individuals to report on their denominational affiliation (“What religion are you?”).⁷ This variable—and the alternative specification using it—are important for three reasons. First, for studies not focused on religion, it is among the most common questions asked, and therefore among the most widely available variables on religion in social science research. Social scientific studies of religion frequently focus on measuring some combination of three dimensions: religious identity, behavior, and attitudes (Cornwall et al. 1986; Smith and Denton 2005). Furthermore, in practice these dimensions have most often been operationalized respectively with single variables: religious affiliation (i.e., denomination type), frequency of religious attendance (e.g., at weekly services), and self-identified importance (e.g., by asking how important one’s religion is when making daily or important decisions – on a Likert scale). Only the first of these differs from the replicate approach described above. Despite some critiques of this variable-centered approach to measuring religion (Hadaway, Marler and Chaves 1993; 1998; Steensland et al. 2000),⁸ the ubiquity of this approach to conceptualizing key measures of religion has led researchers to frequently incorporate measures reflecting these dimensions into a wide range of surveys, even when religion is not the project’s focus.⁹ As such, this specification addresses how readily this approach might be adaptable into other survey data where religion captures these more common dimensions.

Second, by substituting religious affiliation for prayer frequency, the combination of variables used to construct religious profiles brings the included variables more directly in line with the three dimensions of religion most commonly identified as important (Cornwall et al., 1987); religious affiliation aligns with the notion of religious “identity” not represented in any of the other variables described above. Drawing on these motivations, we label this first alternative LCA specification as the “canonical” approach. Specifically, this variable set adds religious affiliation to variables of service attendance and reported religious salience. We follow all other steps in the analytic approach exactly as described above, for this canonical LCA profile specification. The canonical profiles provide a comparison to the replicate approach allowing us to ask how readily religious mosaic profiles are estimable from limited religious information, particularly the variables most commonly available in studies not focused on religion. Comparing the network results across these two strategies also addresses how similarly the approach developed here could be expected to operate similarly in other research where only one or the other combination of variables are possible.

The third importance of the religious affiliation variable is that, unfortunately, Add Health employed a skip pattern wherein anyone who reported no religious affiliation was not subsequently asked the rest of the religious questions. This constrains our ability to capture as full a range of profiles as would be available from more complete data. We discuss the implications of this limitation in the Results section when comparing our LCA classes to those of Pearce and colleagues. Moreover, because of this skip pattern, we knew in advance that we would not be able to fully replicate the class solutions identified by Pearce and colleagues. That is, while Pearce and colleagues find five-class solutions, one of theirs was not identifiable with Add Health data.¹⁰ As such, to draw—somewhat a priori—on their findings (while above we follow their methods), we also extract the 4-class solution using the “replicate” variables that conceptually align with Pearce and colleagues.¹¹ We label this second alternative specification as the Rep4 (4-class replicate LCA solution).

Fitting the LCA Solutions in a Stochastic Actor-Based Model

Once class assignments have been made, we use these to examine religion-friendship dynamics. Table 2 demonstrates the presence of assortativity on the LCA-class memberships,¹² which is what we seek to explain here. We use a stochastic actor-based model (SABM), with religious selection and influence on latent class membership as the key parameters of interest. An SABM allows for the simultaneous modeling of changes in network and attribute data. These models can address the central aim here—separating peer influence from homophilous selection, while also properly accounting for the interdependence between network observations (which would not be possible with e.g., logistic regression), and controlling for endogenous network processes (e.g., tendencies towards reciprocity and triadic closure, described in more detail below). The SABM involves maximization over two separate functions representing network selection and behavior change (i.e. religious measures). First, the network function estimates effects that shape the likelihood of tie presence or absence, and takes the form:

$$f_i(\beta ,x)={\sum }_k{\beta }_k{s}_{ki}(x)+\epsilon (x,z,t,j)$$ Equation 2.

where f_i(β,x) is the value of the network function for actor (i) with respect to all potential alters (j), given: the current set of parameter estimates (β), and state of the network (x), for k effects, represented as s_ki, which may be based on the network (x) and individual attributes (z). In addition, the model incorporates some random disturbance (ε) associated with each of x, z, t, and j. The key effect of interest in the network function here is homophily on religion. Homophily effects estimate how likely individuals are to nominate someone who is more similar on religiosity versus someone who is more dissimilar. For the categorical measures (e.g., LCA class) we use the same effect, which codes dyads as 1 if their scores match, and 0 otherwise. For the continuous indicators (prayer, attendance, and importance) we use the similarity effect, which is a transformation of the absolute value between scores for two dyad members. This effect ranges from 0 (greatest dissimilarity) to 1 (identical scores) across dyads. For the continuous measures, we also included related effects for how religiosity affects the tendency to send (ego effects) and receive (alter effects) ties.

Table 2.

Network Descriptive Statistics

	Jefferson HS		Sunshine HS
	Wave I	Wave II	Wave I	Wave II
# of ties	1721	1345	1381	1014
Density	0.007	0.006	0.002	0.002
Outdegree mean (sd)	3.43 (2.21)	2.67 (2.18)	1.55 (1.66)	1.14 (1.51)
Jaccard	0.269		0.240
Reciprocity	0.446	0.457	0.354	0.411
Transitivity	0.207	0.214	0.232	0.263
LCA-Class Assortativity (OR)	1.32***	1.25***	1.16***	1.20***

^***p<0.001

NOTE: Numbers are for the specified network, except outdegree (which are the mean and standard deviation across individuals in the network), and assortativity (Odds-ratio).

Several other effects were included in the model to control for selection based on other individual attributes (i.e., sex, grade, SES), dyadic attributes (extracurricular activity and course overlaps), and network processes. Important network processes to include as controls in these models are reciprocity (the tendency for individuals to send ties to those who they currently receive ties from), transitivity (the tendency for individuals who share a friend in common to have an elevated chance of themselves becoming friends), and popularity effects (the “Matthew effect” of disproportionately connecting to those already having higher numbers of friends). A final set of controls capture the “foci” of opportunities for friendship formation described above--those indicating which adolescents participated in the same extracurricular activities and courses (Schaefer et al., 2011). In combination, these effects represent how likely i is to select j (i.e., add a new tie to j or maintain an existing tie to j).

Second, the behavior objective function takes a similar form:

$$f_i^z(\beta ,x,z)={\sum }_k{\beta }_k^z{s}_{ki}^z(x,z)+\epsilon (x,z,t,\delta )$$ Equation 3.

where f_i^z (β, x, z) is the value of the behavioral objective function for actor (i) for behavior (z), and all other elements are as in Equation 2, with the exception of δ which is the error associated with behavior change.¹³ The key effect here is peer influence on religion, which captures whether friends are more likely to become (or remain) more religiously similar over time than adolescents who are not friends. Additional effects in these models controlled for the effects of race, sex, age, SES, parent’s religiosity, and two-parent family on level of religion.

Estimating the peer influence effect in the behavior function requires a different specification for continuous versus categorical religion measures. For continuous religion measures, we use the behavior function shown in Equation 3 and measured peer influence with the total similarity effect. Total similarity was calculated as the sum of the absolute differences between ego’s score and the scores of the friends nominated by ego. The sum was reverse-coded and centered based on the average level of similarity across all dyads (Ripley et al. 2013).

For categorical religion profiles that result from LCA, we specify religious classes in the behavior function using a two-mode network (Snijders, Lomi and Torló 2013). In the two-mode representation adolescents have a score for each class (or category of affiliation), with a “1” coded for the class they were assigned to, and a “0” coded for all other classes. The key predictor in this part of the function is the number of friends who belong to each category or class of religion. Thus, the likelihood of choosing each category of the religious profiles is determined by the number of friends who made that same choice. We controlled for how youths’ sociodemographic characteristics affected their religious choice by including interactions between dummy variables representing classes and each sociodemographic control variable. We also included dummy variables for all classes except one in order to control for the overall probability of belonging to each class.

In addition to the effects described above, models also include a series of standard network structural controls: reciprocity, transitivity, an interaction between reciprocity and transitivity, 3-cycles (non-hierarchical triad closure), actors at distance-2 (an indicator of the lack of triad closure), indegree – popularity (how number of incoming ties affects the likelihood of receiving future ties), outdegree – popularity (how number of outgoing ties affects the likelihood of receiving future ties), and indegree – activity (how number of incoming ties affect the likelihood of sending future ties. These latter three measures were transformed using a square-root function to give greater weight to differences at lower levels of degree.

Alternate SABM Specifications

While our focus is on the SAB models that allow us to estimate mosaic-based religious selection/influence, we also estimate a series of preliminary models examining the same patterns for each of the individual variables with which the LCA profiles are constructed. These allow us to (1) be sure our models are properly calibrated to reproduce similar results on this set of variables in previous work (Cheadle and Schwadel 2012; Cook et al., 2017), and to show where their results diverge from those in our proposed approach. Those preliminary models include: (1) four separate SABM specifications, one for each of the individual variables used across the replicate and canonical LCA estimations, and (2) a single composite model including all four variables into a single model. In addition to these preliminary models and the SABM of primary interest—using the best fitting LCA solution from the replicate class variable—we also specify SABMs for each of the alternate LCA specifications described above (the canonical variable set and the 4-class solution with the replicate variable set).

Results

Identifying Latent Classes of Religiosity Among Adolescents

We estimated a total of four separate LCA models (two schools, by two waves of data) for the replicate and each alternative specification. All model fit statistics are shown in Table 3. When using the replicate variables, in each school, across both wayves, the three-class solution had the lowest BIC (Nagin 2005).¹⁴ Thus, we examined the class probabilities to determine whether the class probabilities were high enough to proceed using the classify-analyze approach for these three classes. All class probabilities were > .80 for the three class solutions, but fell below this cut-off when adding additional classes. Therefore, we chose the three-class solution to interpret as the model demonstrating best fit to the data. In what follows, we discuss the findings primarily only as they relate to this three-class replicate LCA solution, and mention the alternate specifications only where they differ substantially from those.

Table 3.

Fit Statistics for LCA Models

	Wave 1				Wave 2
	G2	BIC	AIC	Range of Avg. Class Probabilities	G2	BIC	AIC	Range of Avg. Class Probabilities
	Jefferson High School
Replicate Variables1
Two Classes	423.95	4693.47	4568.48	1.00 – 1.00	397.70	3731.59	3619.24	1.00 – 1.00
Three Classes	131.26	4494.74	4303.79	.84 – 1.00	143.14	3563.29	3392.68	.42 – 1.00
Four Classes	47.27	4502.42	4247.80	.69 – 1.00	79.15	3585.56	3356.69	.56 – 1.00
Five Classes	26.31	4559.36	4254.84	.55 – 1.00	44.86	3637.52	3350.40	.46 – 1.00
Six Classes	12.96	4635.82	4269.50	.42 – 1.00	44.85	3723.78	3378.40	.38 – 1.00
Canonical Variables2
Two Classes	218.40	4388.20	4269.04	1.00 – 1.00	180.41	3487.77	3375.42	1.00 – 1.00
Three Classes	85.05	4344.65	4163.69	.81 – 1.00	80.76	3474.37	3303.76	.73 – 1.00
Four Classes	57.98	4407.36	4164.62	.63 – 1.00	45.50	3525.37	3296.50	.55 – 1.00
Five Classes	44.03	4483.20	4178.67	.57 – 1.00	29.66	3595.79	3308.67	.54 – 1.00
Six Classes	35.78	4564.74	4198.42	.45 – 1.00	19.69	3672.07	3326.69	.44 – 1.00
	Sunshine High School
Replicate Variablesa
Two Classes	541.36	8339.11	8200.93	1.00 – 1.00	468.86	5919.74	5792.13	.88 – .97
Three Classes	125.05	8022.45	7812.61	.85 – 1.00	143.65	5688.69	5494.92	.79 – 1.00
Four Classes	56.33	8053.38	7771.89	.71 – 1.00	57.46	5696.68	5436.74	.61 – 1.00
Five Classes	33.99	8130.69	7777.55	.62 – 1.00	44.21	5777.59	5451.48	.56 – 1.00
Six Classes	21.23	8217.59	7792.79	.56 – 1.00	25.09	5852.64	5460.37	.44 – 1.00
Canonical Variablesb
Two Classes	297.52	8723.31	8585.12	1.00 – 1.00	299.24	6179.74	6052.07	1.00 – 1.00
Three Classes	104.05	8629.48	8419.64	.80 – 1.00	120.43	6097.00	5903.15	.77 – 1.00
Four Classes	54.30	8679.39	8397.90	.62 – 1.00	68.16	6138.95	5878.88	.64 – 1.00
Five Classes	37.58	8762.32	8409.18	.49 – 1.00	51.89	6216.88	5890.61	.61 – 1.00
Six Classes	22.36	8846.75	8421.95	.41 – 1.00	37.93	6297.12	5904.64	.50 – 1.00

NOTE. Bolded indicates best-fitting model. G² = Likelihood ratio test statistic. BIC = Bayesian Information Criterion. AIC = Akaike Information Criterion.

¹“Replicate Variables” indicates the solutions using variables consistent with the conceptual model employed by Pearce and colleagues—i.e., limited to behavioral and attitudinal variables. Here that includes religious importance, religious attendance and prayer frequency.

²“Canonical Variables” replaces prayer frequency in the “replicate” set with religious affiliation to match the limited set of variables most often available in surveys not primarily concerned with religion.

Three Classes of Religiosity

Table 4 shows the posterior response probabilities statistics for each school, by class solutions, for each set of variables at Wave 1.¹⁵ Using the replicate set of variables (i.e., attendance, importance, prayer), the three classes were qualitatively and quantitatively distinct, following a similar pattern across schools and waves. The smallest class in both schools (i.e., Class 1) comprised adolescents who were not religious, that is, did not identify with any religious tradition. As noted above, because of Add Health skip patterns, these individuals were assumed to not attend religious services, pray, or attribute any importance to religion. The other two classes were quantitatively distinct. Adolescents in Class 2, the largest class in Sunshine High School (79.1% of the sample), were highly religious (i.e., attended services and prayed frequently and rated religiosity as fairly important), whereas adolescents in Class 3, the largest class in Jefferson High School (54.9% of the sample), were moderately religious (i.e., attended services and prayed fairly infrequently and rated the importance of religiosity as neutral).

Table 4.

Posterior Response Probabilities (rhos) for LCA Class Solutions at Wave 1

	Affiliation (%)a						Attendance M(SD)b	Importance M(SD)a	Prayer M(SD)c	% of Sampled
	NR	EP	MP	BP	RC	OT
Jefferson High School (N=502)
Total	17.91	16.70	32.19	0.00	29.58	3.62	3.20(1.44)	3.46(1.35)	3.94(1.85)
3-Class LCA, Replicate Variablese
I							1.00(0.00)	1.00(0.00)	1.00(0.00)	15.32
II							4.55(0.73)	4.52(0.50)	5.46(0.64)	29.72
III							2.92(0.76)	3.54(0.70)	3.81(1.36)	54.95
3-Class LCA, Canonical Variablesf
I	100.0	0.00	0.00	0.00	0.00	0.00	1.00(0.00)	1.00(0.00)		15.32
II	0.00	32.26	32.90	0.00	31.61	3.23	4.83(0.37)	4.54(0.50)		24.97
III	0.00	13.04	43.08	0.00	38.74	5.14	2.98(0.76)	3.66(0.74)		59.71
4-Class LCA, Replicate Variablese
I							1.00(0.00)	1.00(0.00)	1.00(0.00)	15.32
II							4.66(0.77)	4.65(0.48)	5.58(0.53)	23.91
III							2.70(0.73)	2.80(0.72)	2.38(0.70)	9.91
IV							3.27(0.85)	3.89(0.38)	4.54(1.06)	50.86
Sunshine High School (N=891)
Total	5.10	9.17	16.76	16.08	47.11	5.78	4.02(1.19)	4.32(0.98)	5.05(1.42)
3-Class LCA, Replicate Variablesa
I							1.00(0.00)	1.00(0.00)	1.00(0.00)	3.59
II							4.51(0.78)	4.69(0.47)	5.67(0.65)	79.14
III							3.07(0.81)	3.82(0.63)	3.92(1.21)	17.27
3-Class LCA, Canonical Variablesc
I	100.0	0.00	0.00	0.00	0.00	0.00	1.00(0.00)	1.00(0.00)		3.59
II	0.00	10.57	17.79	18.62	46.48	6.54	4.57(0.78)	4.78(0.41)		74.36
III	0.00	7.44	17.36	12.81	57.44	4.95	3.23(0.79)	3.79(0.49)		22.06
4-Class LCA, Replicate Variablese
I							1.00(0.00)	1.00(0.00)	1.00(0.00)	3.59
II							4.61(0.74)	4.78(0.42)	5.66(0.65)	72.38
III							3.58(0.61)	4.01(0.29)	4.78(1.11)	17.69
IV							2.41(0.66)	3.55(0.86)	3.52(1.52)	6.34

^aNR = no religious affiliation. EP = Evangelical Protestant. MP = Mainline Protestant. BP = Black Protestant. RC = Roman Catholic. OT = Other.

^bRange = 1–5

^cRange = 1–6

^dSample percentages based on predicted class membership by modal posterior probability.

^e“Replicate Variables” indicates the solutions using variables consistent with the conceptual model employed by Pearce and colleagues—i.e., limited to behavioral and attitudinal variables. Here that includes religious importance, religious attendance and prayer frequency.

^f“Canonical Variables” replaces prayer frequency in the “replicate” set with religious affiliation to match the limited set of variables most often available in surveys not primarily concerned with religion

Using the alternative specification with the “canonical” set of variables (i.e., importance, attendance, affiliation), the best-fitting model was also a three-class solution. The three classes included adolescents who: (1) had no religious affiliation, (2) were very religious--about equally divided across religious affiliation (but, notably more Evangelical Protestants than the third class), rated religiosity as very important, and attended services frequently, or (3) were moderately religious (largely Mainline Protestant or Roman Catholic), rated religiosity as fairly important, but attended services comparatively infrequently.

In the second alternative specifications, we examined the four-class solution using the replicate variables to determine whether Pearce and colleagues’ classes could be replicated. As noted above, this was not the best-fitting solution for the “replicate” set of variables, so these results should only be interpreted in light of how they align with Pearce and colleagues’ findings, and not as a primary assessment of our research questions here. The four-class solution included the same not-at-all and highly- religious classes as identified in the three-class solutions. But how the “moderate” classes differed from those extremes varied across the schools. First, there was a moderate class identified in each class that was relatively consistent across all indicators. However, in Jefferson this class reported only slightly higher importance, prayer, and attendance than the irreligious group (akin to the “Avoider” class identified by Pearce and colleagues). In Sunshine, the overall level of religiosity is higher than in Jefferson, and this “consistently moderate” class is much closer to the highly religious class, lagging only slightly behind them across all three indicators. The fourth class in each school combines reporting religion as relatively important and relatively frequent prayer, but reports only modest participation in religious services. This final class, while not exactly matching the distributions, approximates some characteristics of the “Adapters” class identified by Pearce et al. (2013)—those combining differing levels of religiosity across indicators. This suggests that while this solution is not the best fit to Add Health data, the substantive patterns here are suggestive that combinations here, as in Pearce et al. (2013), are not simply coordinated levels of religiosity that operate in lock-step across each indicator.

Network Dynamics

Estimating network selection and influence effects assumes the presence of network assortativity to be explained. Since religious mosaics are categorical, we estimated the observed level of assortativity using the α segregation index (Moody 2001) for each school and wave.¹⁶ The resulting odds ratios (see bottom row, Table 2) indicate that in each school, at both waves, ties are significantly more likely to form between two adolescents in the same LCA class compared to friendships between pairs with different LCA classes.

As described above, we ran a series of SAB models to test selection and influence on religion, while controlling for a range of potential confounding factors. Across models, estimates of our controls were as expected and consistent with prior studies using these data. For the sake of brevity, Figure 1 presents only the SAB model estimates for the parameters of selection and influence on the corresponding religion measures (results with full controls are provided in Supplementary Tables A1 and A2). Of greatest interest for the present purpose is Model C1, Panel C of Figure 1. These models correspond to our primary research question—how religious mosaics exert selection and/or influence effects—as modeled with the best fitting three-class LCA solution using the replicate set of variables. Panels A and B present the preliminary models described above for each of the included religion indicators from a model specifying their effects in separate models (A1–4) and a single composite model (B).

Figure 1. Religious Selection & Influence Parameters from Stochastic Actor Based Models.

NOTE: The letters indicate SAB model estimates for friend selection (S) and peer influence (I) effects respectively for the specified religion measures, with error bars providing the 95% confidence intervals. Models in Panel A were estimated for each individual measure separately. The model in Panel B included all 4 religion indicators in a single estimation. The three models in Panel C were estimated separately for each latent class specification: 3-class replicate (Rep3), 3-class canonical (Can3), and 4-class replicate (Rep4).

Model C1 shows that peer influence operates on replicate-variable derived religious profiles. For example, in Jefferson HS the influence estimate of 0.26 indicates that for each additional friend an adolescent has in a particular LCA class, the odds of choosing that class increase by 30% (exp[0.26]), all else being equal. This effect is stronger in Sunshine HS, with a 139% increase (exp[0.87]) in selecting a specified LCA class from each additional friend the adolescent has in that class. Thus, in both schools we see that adolescents are more likely to adopt an LCA class over time when they have more friends in that class, relative to other classes.

These same models also tested for whether adolescents select friends with the same religious class assignment as themselves. The results indicate that in neither school was selection based on common class membership significant. Thus, we have no evidence that adolescents choose friends with the same religious identity as themselves. Instead, observed assortativity on religious class can be attributed to interpersonal influence processes, or is accounted for by the other effects controlled in the model.

SAB models relying on the alternate LCA specifications show similar results. The canonical three-class solution (Model C2) pattern is the same as Model C1 across both schools. The four-class solution (Model C3) also shows influence but not selection on class membership; however, the effect of peer influence in Jefferson High School (two-tailed p=.07) did not reach the conventional level of significance. In combination, the results for the class profile models suggest that adolescents are increasingly likely to adopt the latent religious class memberships of their friends over time, but do not select friends based on those classes.

Discussion and Conclusions

Our aim was to determine whether religious mosaics provide a basis for peer influence and/or homophilous friend selection. To address this question we first estimate LCA solutions using the “replicate” variables that most closely resemble the behavioral orientation employed by Pearce et al (2013). This model identified three classes, which roughly correspond to adolescents with no, high, and moderate levels of religion. These results suggest it is worthwhile for survey researchers to continue exploring additional empirical and theoretically oriented strategies for incorporating these notions of religious mosaics into future research. Even in the face of limited religious measures, there may be added value to exploring the mosaic conceptualization of religion.

With these religious profiles in hand, we found evidence that religious mosaics are intertwined with adolescents’ friendship processes. In particular, we found evidence for peer influence effects, but not selection, related to religious mosaics.¹⁷ Over time, adolescents tended to become more like their friends on the ways their religious attributes clustered together. Thus, we found evidence of the expected pattern of peer influence on religious mosaics. The absence of selection effects here could suggest that religious selection genuinely does not operate among adolescents, works in other ways (e.g., only on individual variables; see Panels A/B of Figure 1), or could reflect the imperfect measures (especially due to the skip patterns) available in Add Health. In the remainder of the paper, we discuss the implications of these findings for future studies of adolescent religion and peer networks.

For conceptualizing and measuring religion, our LCA results suggest that it is possible to incorporate the theoretical aims that correspond with the “lived religion” orientation into studies even where religion isn’t the focus and only limited information on religion is available. While Pearce et al. (2013) demonstrate the robustness of their approach when using a portion of the variables available in NSYR, our approach provides additional support that mosaics are broadly usable for conceptualizing and modeling adolescent religion. Perhaps future work can resolve some of the misalignment between our identified classes and those from the NSYR (e.g., how much these differences were simply driven by Add Health’s unfortunate skip pattern). Additionally, it is important to consider whether mosaics change as populations age, and how the peer-based religious effects identified here (i.e., influence but not selection on mosaics) may shift across stages of the life course.

While not our focus here, the empirical cases we drew on also suggest future research should investigate whether and how the modeled effects differ across contexts. We observed large differences in the distribution of classes between the two schools examined—the highly religious class was by far the largest in Sunshine HS, while the more moderately religious class was the majority in Jefferson HS. Despite this discrepancy, the composition of classes differed only modestly between the schools. Namely, the four-class solution identified a group of religious “Adapters” in each school who attended services infrequently and who indicated religion was either fairly important (Sunshine High School) or less important (Jefferson High School). Perhaps most striking is that religious profiles showed consistent network patterns across schools, variables used, and number of classes identified—a consistent pattern of religious peer influence but not religion-based friend selection. There is accumulating evidence in religious (Ammerman 1997) and network (adams and Schaefer 2016) scholarship suggesting that an important avenue for future research is to more carefully consider how such contextual differences may alter what we know from studies of single cases, or models that assume similar patterns across entire populations.

One such possibility for network scholarship would be to consider whether influence and/or selection processes may differ across groups. For example, in highly religious schools (like Sunshine), the salience of religion for selection may be stronger for the less religious (who are the numeric minority), or vice versa in less religious schools. Such a result may explain the lack of selection effects observed here—if, in effect a strong religious selection process among the highly religious class and a true absence of effect among the irreligious canceled each other out. Heterogenous effects, either by group or context, are not frequently considered in networks research. For one exception, Goodreau et al (2009) found that racial friendship homophily was stronger for those groups that were numeric minorities within their schools. Unfortunately, estimating such contextual differences likely requires many more schools than are currently available in Add Health, but would be a fruitful avenue for future research.

In summary, religion is a multidimensional construct that cannot simply be reduced to individual and/or variable level assessment. People combine various aspects of religion into unique constellations, which are shaped by others in their contexts. We demonstrated how to employ recent methodological advances in the modeling of categorical variables as two-mode networks (Snijders et al 2013) to investigate how peers are involved in developing these norms (e.g., potentially through influence and selection). We found suggestive empirical evidence for how these play out in two different school contexts. We encourage future research to further elaborate whether and how adolescents’ religious mosaics shape and are shaped by their friendship networks.