LITMIR.BIZ

Скачать книгу

properties are obtained by aggregating information from the individual members of the collective (e.g., proportion of Hispanics in a city). Structural properties are based on the relational characteristics of collective members (e.g., friendship density in a classroom). Finally, global properties are characteristics of the collective itself that are not based on the properties of the individual members. Presence of an antismoking policy in a school would be a global property of the school, for example.

      Using this framework, it becomes clear that fallacies are a problem of inference, not of measurement. That is, it is perfectly admissible to characterize a higher level collective using information obtained from lower level members. The types of fallacies described above come about when relationships discovered at one particular level are inappropriately assumed to occur in the same fashion at some other (higher or lower) level.

      There is broad interest in social and physical context across the social sciences, and this can be seen most clearly in the ecological richness of various social science theories and conceptual frameworks. In sociology and criminology, the theory of neighborhood disorder proposes that various physical and social indicators of environmental disorder are related to a variety of individual and relational outcomes, including crime, violence, policing styles, and depression (Sampson, Morenoff, & Gannon-Rowley, 2002). Political scientists have consistently viewed political participation (e.g., voting, petitioning, contacting elected officials) as being driven by a number of contextual processes and factors, including organizational culture, media exposure, and peer influence (Uhlaner, 2015). Policy science generally views policy development and implementation as a process embedded in local, regional, and national political and geographic contexts. For example, the political stream of Kingdon’s influential multiple streams framework is defined by referring to predominately contextual structures and processes including national mood, legislative body makeup, and interest group activities (Béland & Howlett, 2016). An alternative model of the policy process, the advocacy coalition framework, more explicitly positions policy activity as an output from the policy subsystem, which is in turn made up of three types of collectives: (1) coalitions, (2) governmental bodies, and (3) institutions (Sabatier & Weible, 2007).

      Finally, implementation science (sometimes called dissemination and implementation science) is a relatively new social science that focuses on how evidence-based programs, practices, and policies can be better disseminated, implemented, and maintained to benefit population health. Early frameworks used in implementation science view implementation processes and outcomes as situated within social and organizational contexts. For example, Rogers’s diffusion of innovations theory has been used extensively to study how new discoveries are passively diffused and actively disseminated across social and organizational networks and systems (Rogers, 2003; Valente, 1996). Figure 1.1 presents an expanded social–ecological framework for implementation science (Luke, Morshed, McKay, & Combs, 2017). This framework, adapted from Glass and McAtee (2006), suggests that relational, organizational, and social contexts are important for studying and understanding implementation outcomes.

      

Description

      Figure 1.1 A social–ecological model for implementation science.

      Source: Adapted from Glass and McAtee (2006).

      Statistical Reasons for Multilevel Models

      Despite the contextual richness of the theories and frameworks used by social scientists, they have often tended to utilize traditional individual-level statistical tools for their data, even if their data and hypotheses are multilevel in nature. One approach has been to disaggregate group-level information to the individual level so that all predictors in a multiple regression model are tied to the individual unit of analysis. This leads to at least two problems. First, all of the unmodeled contextual information ends up pooled into the single individual error term of the model (Duncan, Jones, & Moon, 1998). This is problematic because individuals belonging to the same context will presumably have correlated errors, which violates one of the basic assumptions of multiple regression (i.e., no autocorrelation of residuals). This is often called clustering, and it implies that observations within some larger unit are related to one another. For example, you might see clustering of student test scores within a classroom. If students are not randomly assigned to classes, if teacher ability varies across classrooms, or if classroom environments (e.g., class size) vary systematically, then you would expect to see clustering of scores.

      The second statistical problem is that by ignoring context, the model assumes that the regression coefficients apply equally to all contexts, “thus propagating the notion that processes work out in the same way in different contexts” (Duncan et al., 1998, p. 98).

      One partial solution to these statistical problems is to include an effect in the model that corresponds to the grouping of the individuals. This leads to an analysis of variance (ANOVA) or analysis of covariance (ANCOVA) approach to modeling. Unfortunately, there are still a number of issues with this approach. First, in the case where there are many groups, these models will have many more parameters, resulting in greatly reduced power and parsimony. Second, these group parameters are often treated as fixed effects, which ignores the random variability associated with group-level characteristics. Finally, ANOVA methods are not very flexible in handling missing data or greatly unbalanced designs.

      Scope of This Book

      Based on the previous discussion, the purpose of this monograph is to provide a relatively nontechnical introduction to multilevel modeling statistical techniques for social and health scientists. After this introduction, the book is split into two major sections. Chapters 2 through 4 discuss how to plan, build, and assess the basic two-level multilevel model, and describe the steps in fitting a multilevel model, including data preparation, model estimation, model interpretation, hypothesis testing, testing of model assumptions, centering, and power analysis. Chapters 5 through 7 constitute the second section of the book, covering extensions and more advanced topics. Chapter 5 covers useful extensions to the basic multilevel model, including modeling noncontinuous and nonnormal dependent variables, building three-level models, and building cross-classified models. Chapter 6 covers the use of mixed-effects models for longitudinal data. Finally, Chapter 7 provides some guidance on a couple of general multilevel modeling topics, including tips for presenting multilevel model results and general resources for analysts. The presentation of the topics covered in this book only assumes familiarity with multiple regression, and the text makes extensive use of example data and analyses.

      The primary focus of this book is the application of mixed-effects modeling techniques for multilevel and longitudinal models. Mixedeffect models are powerful and flexible approaches that can handle a number of theoretical and statistical challenges. In particular, mixedeffects models can deal with the type of clustered data that more traditional multiple regression models cannot handle. Multilevel and longitudinal data sets are typified by clustered data (e.g., students nested in classrooms or observations nested within individuals), so that makes a mixed-effects modeling approach ideal in these situations.

      A useful definition to serve as a basis for the rest of the presentation is as follows: A multilevel model is a statistical model applied to data collected at more than one level in order to elucidate relationships at more than one level. The statistical basis for multilevel modeling has been developed over the past several decades from a number of different disciplines and has been called various things, including hierarchical linear models (Raudenbush & Bryk, 2002), random coefficient models (Longford, 1995), mixed-effects

Скачать книгу