Decomposing the total variation in a nested random effects model of neighborhood, household, and individual components when the dependent variable is dichotomous: Implications for adolescent marijuana use
Multilevel modeling techniques have become a useful tool that enables substance abuse researchers to more accurately identify the contribution of multiple levels of influence on drug-related attitudes and behaviors. However, it is difficult to determine the relative importance of the different hierarchical levels because, in the case of dichotomous outcomes, the variance components estimation involves calculations using a log-odds metric at the lowest level of estimation. We present methods introduced by Goldstein and Rasbash [Goldstein, H., Rasbash, J., 1996. Improved approximations for multilevel models with binary responses. J. Roy. Stat. Soc. A 159, 505-513.] to convert the variance components from the log-odds to the probability metric. This method provides a more logical and interpretable way to examine variation for nonlinear outcomes, which tend to be heavily utilized in substance use research. Using data from the National Household Survey on Drug Abuse [Substance Abuse and Mental Health Services Administration (SAMHSA), 2001. 1999 National Household Survey on Drug Abuse. Data Collection Final Report. Office of Applied Studies (OAS), Rockville, MD. Available at http://www.samhsa.gov/oas/nhsda/1999/Collect/toc.htm. Accessed on July 1, 2003.], we partition variation among individual, household, and neighborhood levels for the binary outcome of past year marijuana use to illustrate this approach. We also conduct a stability analysis to examine the robustness across different estimation procedures commonly available in commercial multilevel software packages. Finally, we partition the variance components using a conventional continuously distributed outcome and compare the relative magnitudes across binary and continuous outcomes.