Summary
Contents
Subject index
Quantitative Psychology is arguably one of the oldest disciplines within the field of psychology and nearly all psychologists are exposed to quantitative psychology in some form. While textbooks in statistics, research methods, and psychological measurement exist, none offer a unified treatment of quantitative psychology. The SAGE Handbook of Quantitative Methods in Psychology does just that. Each chapter covers a methodological topic with equal attention paid to established theory and the challenges facing methodologists as they address new research questions using that particular methodology. The reader will come away from each chapter with a greater understanding of the methodology being addressed as well as an understanding of the directions for future developments within that methodological area.
Drawing on a global scholarship the Handbook is divided into seven parts:
Part I: Measurement Theory: Begins with a chapter on classical test theory, followed by the common factor analysis model as a model for psychological measurement. The models for continuous latent variables in item response theory are covered next, followed by a chapter on discrete latent variable models as represented in latent class analysis.
Part II: Structural equation models: Addresses topics in general structural equation modeling, modeling mean structures, multiple-group models, nonlinear structural equation models, mixture models, and multilevel structural equation models.
Part III: Longitudinal models: Covers the analysis of longitudinal data via mixed modeling, repeated measures ANOVA, growth modeling, time series analysis, and event history analysis.
Part IV: Data analysis: Includes chapters on regression models, categorical data analysis, multilevel or hierarchical models, resampling methods, robust data analysis, meta-analysis, Bayesian data analysis, and cluster analysis.
Part V: Design and inference: Addresses issues in the inference of causal relations from experimental and non-experimental research, along with the design of true experiments and quasi-experiments, and the problem of missing data due to various influences such as attrition or non-compliance.
Part VI: Scaling methods: Covers metric and non-metric scaling methods as developed in multidimensional scaling, followed by consideration of the scaling of discrete measures as found in dual scaling and correspondence analysis. Models for preference data such as those found in random utility theory are covered next.
Part VII: Specialized methods: Covers specific topics including the analysis of social network data, the analysis of neuro-imaging data, and functional data analysis.
This volume is an excellent reference and resource for advanced students, academics, and professionals studying or using quantitative psychological methods in their research.
Multilevel Analysis: An Overview and Some Contemporary Issues
Multilevel Analysis: An Overview and Some Contemporary Issues
Human behavior occurs in context, and that context often matters in understanding and interpreting behavior. Multilevel models provide tools for statistical analysis in the presence of clustered or hierarchical data structures, as are common in the social sciences, and can be used to study (or alternatively control for) such structures. Examples of hierarchical structures include data in which students are nested within schools, patients are nested within clinics, or employees are nested within organizations. Multilevel models are also commonly referred to as hierarchical linear models or mixed effects models (Goldstein, 2003; Hox, 2002; Raudenbush and Bryk, 2002; Snijders and Bosker, 1999). The multilevel approach allows researchers to examine hypothesized relationships that incorporate many different ‘units of analysis’ in a statistically appropriate way, thus permitting more accurate modeling of complex systems. In many applications, the variability and dependency associated with nesting are not a nuisance but of primary interest. For such conditions, multilevel modeling approaches can be used for identifying and quantifying sources of variability related to context.
Given the increasingly important role that multilevel models play in analyzing hierarchical data structures, issues related to their estimation and interpretation have received much recent attention. Such issues are naturally intricate owing to the greater complexity of the models. This chapter discusses fundamental concepts and issues in multilevel data analysis as well as recent advances. Multilevel models are powerful and flexible analytic tools, yet are also complicated and require that a number of critical assumptions be satisfied to be properly used. Along these lines, this chapter considers procedures and strategies for model building, specification tests, diagnostics, re-specification, and alternative estimation methods when relevant assumptions are violated. The final section surveys some recent extensions of multilevel modeling techniques.
Introduction
Why multilevel analysis?
Ordinary linear models, such as single-level regression models, are sometimes used to analyze variables from different levels in a hierarchy. This can lead to a number of critical problems when the data are clustered. One set of problems relates to identifying an appropriate unit of analysis. On the one hand, if data are aggregated to higher or macro level units (e.g., schools), much of the variability at the lower or micro level (e.g., students) can be lost, and the statistical analysis loses power. On the other hand, if data are disaggregated to the lower level, then the observations are falsely treated as independent even though observations from the same higher level units tend to be more alike. Ignoring the dependencies among observations within cluster generally leads to standard errors that are underestimated, thus leading to spuriously significant results. This well-known phenomenon in statistics is often examined in the form of design effects (Kish, 1965; 1987).
A second set of problems relates to effect interpretation. Single-level analysis frequently leads to erroneous conclusions about relationships among variables in the data, especially when the data are drawn from a heterogeneous population. Extending inferences to the wrong level yields interpretational errors known as the ecological fallacy, atomistic fallacy, or Simpson's paradox. The ecological fallacy, also known as the Robinson effect, occurs when an effect that in reality exists at a higher level is ascribed to a lower level. As an example, Robinson (1950) showed that whereas the correlation between the percentage of African Americans and the illiteracy level in a geographic region is 0.95, using this correlation to infer a strong relationship between race and literacy would be incorrect as the individual-level correlation is only 0.20. The atomistic fallacy is just the reverse, namely the attribution of an effect at a lower level to the higher level units. Related to these fallacies is Simpson's paradox, which occurs when the heterogeneity of a population is ignored and inferences are made as if the population is homogeneous. For additional examples, see Hox (2002: 3) and Snijders and Bosker (1999: 14).
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