The Impact of Measurement Error in Predictor Variables in Multilevel Models: An Empirical Investigation of Statistical Bias and Sampling Error (original) (raw)
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Multilevel Modeling: A Review of Methodological Issues and Applications
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Multilevel models are often used to evaluate hypotheses about relations among constructs when data are nested within clusters (Raudenbush & Bryk, 2002), although alternative approaches are available when analyzing nested data (Binder & Roberts, 2003; Sterba, 2009). The overarching goal of this article is to suggest when it is appropriate and advantageous to analyze such nested data within a single-level framework and when utilization of multilevel models presents advantages. The decision hinges on the research questions to be addressed, the scope of the data, and the measurement structure of any constructs hypothesized at the cluster level (Kozolowski & Klein, 2000; Marsh et al., 2012). We demonstrate models using several different data sets, including single-level and multilevel hierarchical linear models and confirmatory factor models. For these demonstrations, observational data from students nested within schools are used, as well as data from a classroom-based cluster randomized trial. Researchers in educational settings often find themselves with data that are nested such that students are nested within classrooms, classrooms are nested within schools, and schools are nested within districts. Educational intervention studies are conducted using cluster randomized designs where classrooms or schools are randomized to conditions or as multisite trials with individuals randomized within multiple schools. In addition, survey data might be obtained from students who are nested in classrooms and schools, multiple students may be rated by the same teachers, and districts may have ratings or questionnaire data from teachers nested within schools. These data present opportunities for a researcher to pose questions that are not answerable using data that are not nested. On the other hand, the nested structure may not be explicitly part of a research question because it may not be of interest. That is, the nested structure is an aspect that needs to be accounted for statistically but the driving research question is not contingent on having nested data. Whether multilevel models are necessary depends on the research question (i.e., the analysis choice hinges on the parameters of interest), not on the structure of the data (Bauer & Sterba, 2011). This article provides examples of the types of questions that can be posed with nested data and draws attention to when the analysis would require multilevel modeling (a model-based approach) and when the accommodation of nested data without multilevel models (the design-based approach) is sufficient. Demonstrations using linear modeling and structural equation modeling are used to highlight the options available to researchers for modeling with nested data. Although the article focuses on cross-sectional data, a brief overview of issues that arise with longitudinal data is provided in the Discussion section. RESEARCH QUESTIONS WITH NESTED DATA Many intriguing research questions can be exclusively addressed by multilevel models. Such questions include the following: Are there group differences in average outcomes for individuals (e.g., students or teachers) across clusters (e.g., schools)? If so, are cluster characteristics related to those differences? Are there differences in the relation between individual characteristics and outcomes across clusters? If so, are cluster characteristics related to those differences?
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CHALLENGES FOR MULTILEVEL MODELS OF SCHOOL DISORDER: RESPONSE TO HOFFMANN AND JOHNSON
Criminology, 2000
It is an unusual commentary indeed when critics speculate about data analysis, findings, and conclusions, rather than reanalyzing any of our data (publicly available through the National Archive of Criminal Justice Data).l Hoffmann and Johnson (henceforth, HJ) have presented (in an earlier paper in this issue) an entirely different study with entirely different variables and entirely different hierarchical linear models (HLM). Surprisingly, they come up with much of the same conclusions regarding the dominance of individual-level predictors. Their cross-level interaction terms, uninformed by theory, account for negligible portions of explained variance. They present a rather narrow view of multilevel modeling that leaves important questions regarding theory and study design completely unaddressed. A number of omissions and errors further weaken their arguments.