Abstract
This book illustrates strategies for the development and testing of multilevel models bearing on social problems, all of which deal directly or indirectly on aspects of human development, measured by social and economic indicators. It confronts social problems by ideally following these five steps: analyze the roots of the social problem both theoretically and empirically; formulate a study design that captures the nuances of the problem; gather empirical data bearing on the social problem that enable the design to be operationalized by forming identifiable and repeatable measures; model the multilevel data using appropriate multilevel statistical methods to uncover potential causes and any bias to their effects; and use the results to sharpen theory and to formulate evidence-based policy recommendations for implementation and testing. Applying this process, the core chapters present multilevel models focusing on political extremism, global human development, violence against minorities, the substantive complexity of work, reform of urban schools, and problems of health care. The reader will be better able to conduct state-of-the-art studies on these and other topics by gaining an understanding of these chapters and by using the available data sets and analytic programs to replicate and advance the analyses.
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- 1.
To avoid confusing the levels of causality with the levels of the variables in the multilevel models, I spell their levels of causality (i.e., zero, one, and two) whereas I designate the hierarchical levels of the multilevel models and their variables using numbers (i.e., level-1, level-2, and level-3).
- 2.
Rubin ([1984] 2006, 27) has reprinted William Cochran’s reading list for Statistics 284, circa 1968. The books and studies on this list exemplify classic causality and robust dependence; they were a starting point for Rubin’s subsequent advancement of statistical theory and method.
- 3.
Rubin ([1984] 2006, 7) gives this example of an observational study:
An analysis of health records for samples of smokers and nonsmokers from the U.S. population is an observational study. The obvious problem created by observational studies is that there may exist systematic differences between the treatment groups besides treatment exposure, and so any observed differences between the groups (e.g., between smokers and nonsmokers) with respect to an outcome variable (e.g., incidence of lung cancer) might be due to confounding variables (e.g., age, genetic susceptibility to cancer) rather than to the treatments themselves. Consequently, a primary objective in the design and analysis of observational studies is to control, through sampling and statistical adjustment, the possible biasing effects of those confounding variables that can be measured: a primary objective in the evaluation of observational studies is to speculate about the remaining biasing effects of those confounding variables that cannot be measured.
- 4.
Computer simulation studies find that variables that only affect treatment assignment but not the response (i.e., instrumental variables) are best not included as a covariate, but those variables that affect the response but not treatment assignment can be included. (Presentation to the Boston Chapter of the American Statistical Association by Til Stürmer, MD, MPH, May 4, 2010.)
- 5.
See the data for 2009 and the time series in the Stephen Roth report (2010).
- 6.
Heckman, Pearl, Robins, and Rubin and their colleagues are developing comprehensive general theories of causality. These general theories would incorporate the three notions of causality as special cases and would extend their conceptualizations and procedures, thus forming a new level-three notion of generalized causal relations.
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Smith, R.B. (2011). Gauging Causality in Multilevel Models. In: Multilevel Modeling of Social Problems. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9855-9_16
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