Using cross-classified multilevel models to disentangle school and neighborhood effects: An example focusing on smoking behaviors among adolescents in the United States
Introduction
There is much interest among epidemiologists in understanding multilevel phenomena, or how features of the physical and psychosocial environment in which individuals live, learn, work, and play influence individual health, disease, and behavior (Pickett and Pearl, 2001, Mair et al., 2008). The growth and interest in multilevel analyses has been facilitated by conceptual developments in multilevel theory (Bronfenbrenner and Morris, 2006, Stokols, 1996, Krieger, 2001, Dunn et al., 2014) as well as statistical advancements in multilevel statistical modeling (Diez Roux, 1998, Diez Roux, 2002, Raudenbush and Bryk, 2002, Subramanian et al., 2003). Although multilevel theory posits that multiple contexts (e.g., residential environments, schools, workplaces, hospitals, or other “areas”) influence individual and population health simultaneously, most empirical applications have studied contexts in isolation and the majority of studies have focused on neighborhoods. An emphasis on single contexts, and more specifically neighborhoods, is problematic for at least two reasons. First, it ignores the reality that individuals simultaneously belong to multiple settings that could each independently affect their health. For example, focusing on the influence of neighborhood factors on adolescent health behaviors ignores the influence of schools, which may be a more influential context in teens’ lives. Second, results from studies assessing a single context may be misleading, as the effect of one context can be over- or under-estimated depending on what context is ignored.
The objective of our study was to provide a methodological demonstration of cross-classified multilevel models (CCMM), also sometimes referred to as “multilevel cross-classified models, or ‘cross-classified random effect models”, in disentangling the role of two critical influences on adolescent tobacco use: schools and neighborhoods. CCMM allows researchers to incorporate non-hierarchical nesting structures, where individuals are simultaneously nested within multiple non-hierarchical settings. Thus, rather than modeling the effect of either the school or neighborhood setting, as would be done in a traditional two-level multilevel model (MLM), application of a CCMM enables researchers to simultaneously examine the fixed and random effects corresponding to the school and neighborhood settings. Simultaneous examination of schools and neighborhoods, in particular, is important because both settings can influence health behaviors through multiple pathways, including policies, normative behaviors, access to resources, and the like (Kawachi and Berkman, 2003, Bonnell et al., 2013). In this paper, our intention was to provide a methodological demonstration of the CCMM method and show where and how results from a CCMM might deviate from a traditional multilevel model focused on a single context. A methodological application and applied example of CCMM is warranted, given the underrepresentation of CCMM in the epidemiology literature relative to MLM (see for example Leyland and Naess, 2008, Lloyd et al., 2010, Utter et al., 2011, Riva et al., 2009, Moore et al., 2013, Virtanen et al., 2010, Basile et al., 2012).
Our demonstration proceeded in several steps. We first modeled our outcome using a traditional multilevel modeling (MLM) approach that included only one context (neighborhood or school) per model. In other words, we modeled the school as a random effect, ignoring the neighborhood in one MLM and then modeled the neighborhood as a random effect, ignoring the school in a second MLM. We then modeled tobacco use using CCMM, which simultaneously accounts for the influence of schools and neighborhoods. We compared both the fixed (i.e., population average effects) and random effects (i.e., variance in the outcome) in models assuming a two level hierarchy (MLM) versus those allowing for multiple non-hierarchical memberships (CCMM). The fixed effects we examined were individual-, school-, and neighborhood-level demographic indicators, including socioeconomic status and race/ethnicity. These fixed effect estimates are informative for determining the extent to which both the predictor of interest is associated with the outcome and the degree to which the predictor of interest reduces between-level variation. Finally, in our CCMM, we compared the relative variance contribution of schools and neighborhoods. By comparing variance contributions (i.e., random effects) across models, we are able to evaluate the extent to which inclusion of the fixed effect variables helped to explain the observed between-school and between-neighborhood variation in smoking.
To increase the use of CCMM, and make the processes of analyzing cross-classified data more transparent, we provide readers with instructions on how to implement the CCMM in MlwIN (refer to Technical Appendix: Part 1 online) and through MlwIN as implemented via STATA (refer to Technical Appendix: Part 2 online).
Section snippets
Data
Data for the study came from the National Longitudinal Study of Adolescent Health (Add Health), a nationally representative school-based longitudinal survey focusing on the health and behavior of adolescents in middle and high school (grades 7–12; ages 12–18) who were first interviewed in 1994–1995 (Wave 1) (Harris, 2013). To ensure selected schools were representative of US schools, researchers stratified schools by census region, urbanicity, size, type, and ethnic background of the student
Results
The AddHealth data were suited to cross-classified analyses. An average of 125.5 (sd=116.5) youth per school completed an In-Home survey (minimum=18; maximum=1012). In each neighborhood, an average of 7.6 (sd=18.5) youth completed an In-Home survey (minimum=1; maximum=260). There were 970 (of 2111) census tracts that contained only one youth respondent. There was an average of 20.2 (sd=22.0) census tracts per school (minimum=1; maximum=175), an average of 1.22 (sd=0.42) schools per census tract
Discussion
This paper demonstrated the value of cross-classified multilevel models (CCMM) to ascertain the quantitative importance of more than one context simultaneously. One very salient finding emerged from the current study. We found that two-level multilevel models that do not account for other non-nested contexts in which individuals are embedded can produce misleading results. In the current case, which focused on adolescent smoking, we found that the role of neighborhoods was overestimated.
Acknowledgments
This research uses data from Add Health, a program project directed by Kathleen Mullan Harris and designed by J. Richard Udry, Peter S. Bearman, and Kathleen Mullan Harris at the University of North Carolina at Chapel Hill, and funded by grant P01-HD31921 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development, with cooperative funding from 23 other federal agencies and foundations. Special acknowledgment is due Ronald R. Rindfuss and Barbara Entwisle for
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