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This volume presents contributions on handling data in which the postulate of independence in the data matrix is violated. When this postulate is violated and when the methods assuming independence are still applied, the estimated parameters are likely to be biased, and statistical decisions are very likely to be incorrect. Problems associated with dependence in data have been known for a long time, and led to the development of tailored methods for the analysis of dependent data in various areas of statistical analysis. These methods include, for example, methods for the analysis of longitudinal data, corrections for dependency, and corrections for degrees of freedom. This volume contains the following five sections: growth curve modeling, directional dependence, dyadic data modeling, item response modeling (IRT), and other methods for the analysis of dependent data (e.g., approaches for modeling cross-section dependence, multidimensional scaling techniques, and mixed models). Researchers and graduate students in the social and behavioral sciences, education, econometrics, and medicine will find this up-to-date overview of modern statistical approaches for dealing with problems related to dependent data particularly useful.
Most biologists use nonlinear regression more than any other statistical technique, but there are very few places to learn about curve-fitting. This book, by the author of the very successful Intuitive Biostatistics, addresses this relatively focused need of an extraordinarily broad range of scientists.
Learn How to Use Growth Curve Analysis with Your Time Course Data An increasingly prominent statistical tool in the behavioral sciences, multilevel regression offers a statistical framework for analyzing longitudinal or time course data. It also provides a way to quantify and analyze individual differences, such as developmental and neuropsychological, in the context of a model of the overall group effects. To harness the practical aspects of this useful tool, behavioral science researchers need a concise, accessible resource that explains how to implement these analysis methods. Growth Curve Analysis and Visualization Using R provides a practical, easy-to-understand guide to carrying out multilevel regression/growth curve analysis (GCA) of time course or longitudinal data in the behavioral sciences, particularly cognitive science, cognitive neuroscience, and psychology. With a minimum of statistical theory and technical jargon, the author focuses on the concrete issue of applying GCA to behavioral science data and individual differences. The book begins with discussing problems encountered when analyzing time course data, how to visualize time course data using the ggplot2 package, and how to format data for GCA and plotting. It then presents a conceptual overview of GCA and the core analysis syntax using the lme4 package and demonstrates how to plot model fits. The book describes how to deal with change over time that is not linear, how to structure random effects, how GCA and regression use categorical predictors, and how to conduct multiple simultaneous comparisons among different levels of a factor. It also compares the advantages and disadvantages of approaches to implementing logistic and quasi-logistic GCA and discusses how to use GCA to analyze individual differences as both fixed and random effects. The final chapter presents the code for all of the key examples along with samples demonstrating how to report GCA results. Throughout the book, R code illustrates how to implement the analyses and generate the graphs. Each chapter ends with exercises to test your understanding. The example datasets, code for solutions to the exercises, and supplemental code and examples are available on the author’s website.
This book provides a brief, easy-to-read guide to implementing hierarchical linear modeling using three leading software platforms, followed by a set of original how-to applications articles following a standardard instructional format. The "guide" portion consists of five chapters by the editor, providing an overview of HLM, discussion of methodological assumptions, and parallel worked model examples in SPSS, SAS, and HLM software. The "applications" portion consists of ten contributions in which authors provide step by step presentations of how HLM is implemented and reported for introductory to intermediate applications.
Growth models are among the core methods for analyzing how and when people change. Discussing both structural equation and multilevel modeling approaches, this book leads readers step by step through applying each model to longitudinal data to answer particular research questions. It demonstrates cutting-edge ways to describe linear and nonlinear change patterns, examine within-person and between-person differences in change, study change in latent variables, identify leading and lagging indicators of change, evaluate co-occurring patterns of change across multiple variables, and more. User-friendly features include real data examples, code (for Mplus or NLMIXED in SAS, and OpenMx or nlme in R), discussion of the output, and interpretation of each model's results. User-Friendly Features *Real, worked-through longitudinal data examples serving as illustrations in each chapter. *Script boxes that provide code for fitting the models to example data and facilitate application to the reader's own data. *"Important Considerations" sections offering caveats, warnings, and recommendations for the use of specific models. *Companion website supplying datasets and syntax for the book's examples, along with additional code in SAS/R for linear mixed-effects modeling.
- Coherent and unified treatment of nonlinear regression with R. - Example-based approach. - Wide area of application.
Nonlinear measurement data arise in a wide variety of biological and biomedical applications, such as longitudinal clinical trials, studies of drug kinetics and growth, and the analysis of assay and laboratory data. Nonlinear Models for Repeated Measurement Data provides the first unified development of methods and models for data of this type, with a detailed treatment of inference for the nonlinear mixed effects and its extensions. A particular strength of the book is the inclusion of several detailed case studies from the areas of population pharmacokinetics and pharmacodynamics, immunoassay and bioassay development and the analysis of growth curves.
Integrates the latest theory, methodology and applications related to the design and analysis of repeated measurement. The text covers a broad range of topics, including the analysis of repeated measures design, general crossover designs, and linear and nonlinear regression models. It also contains a 3.5 IBM compatible disk, with software to implem
Features recent trends and advances in the theory and techniques used to accurately measure and model growth Growth Curve Modeling: Theory and Applications features an accessible introduction to growth curve modeling and addresses how to monitor the change in variables over time since there is no “one size fits all” approach to growth measurement. A review of the requisite mathematics for growth modeling and the statistical techniques needed for estimating growth models are provided, and an overview of popular growth curves, such as linear, logarithmic, reciprocal, logistic, Gompertz, Weibull, negative exponential, and log-logistic, among others, is included. In addition, the book discusses key application areas including economic, plant, population, forest, and firm growth and is suitable as a resource for assessing recent growth modeling trends in the medical field. SAS® is utilized throughout to analyze and model growth curves, aiding readers in estimating specialized growth rates and curves. Including derivations of virtually all of the major growth curves and models, Growth Curve Modeling: Theory and Applications also features: • Statistical distribution analysis as it pertains to growth modeling • Trend estimations • Dynamic site equations obtained from growth models • Nonlinear regression • Yield-density curves • Nonlinear mixed effects models for repeated measurements data Growth Curve Modeling: Theory and Applications is an excellent resource for statisticians, public health analysts, biologists, botanists, economists, and demographers who require a modern review of statistical methods for modeling growth curves and analyzing longitudinal data. The book is also useful for upper-undergraduate and graduate courses on growth modeling.
By focusing primarily on the application of structural equation modeling (SEM) techniques in example cases and situations, this book provides an understanding and working knowledge of advanced SEM techniques with a minimum of mathematical derivations. The book was written for a broad audience crossing many disciplines, assumes an understanding of graduate level multivariate statistics, including an introduction to SEM.