Factor Analysis and Dimension Reduction in R: A Social Scientist's Toolkit

Factor Analysis and Dimension Reduction in R provides a comprehensive coverage of dimension reduction procedures, including principal components analysis (PCA) and principal factor analysis (PFA), with model performance metrics. It also covers higher-order factor models, bifactor models, mixed data models, and more. The book features worked examples, data assumptions, residual and outlier analysis, and visualization of factor results. It is suitable for graduate-level and optional module courses for social scientists, as well as quantitative methods and multivariate statistics courses.

Format: Paperback / softback
Length: 564 pages
Publication date: 12 December 2022
Publisher: Taylor & Francis Ltd

Factor Analysis and Dimension Reduction in R offers comprehensive coverage of a wide array of dimension reduction techniques, along with model performance metrics, to facilitate informed decision-making. While factor analysis, particularly in its forms of principal components analysis (PCA) or principal factor analysis (PFA), is widely recognized among social scientists, it's important to understand that factor analysis is a subset of the broader family of dimension reduction methods. This book aims to expand the toolkit available to social scientists by presenting a diverse range of solutions for factor analysis problems.

The book begins by introducing the fundamentals of factor analysis and its applications in social science research. It covers both orthogonal and oblique rotation methods for factor analysis, including higher-order factor models, bifactor models, models based on binary and ordinal data, mixed data models, generalized low-rank models, cluster analysis with generalized linear random matrix (GLRM), models involving supplemental variables or observations, Bayesian factor analysis, regularized factor analysis, testing for unidimensionality, and prediction with factor scores.

The second half of the book delves into various other dimension reduction procedures. These include kernel PCA, factor analysis with multidimensional scaling, locally linear embedding models, Laplacian eigenmaps, diffusion maps, force directed methods, t-distributed stochastic neighbor embedding, independent component analysis (ICA), dimensionality reduction via regression (DRR), non-negative matrix factorization (NNMF), Isomap, Autoencoder, uniform manifold approximation and projection (UMAP) models, neural network models, and longitudinal factor analysis models.

To aid in understanding and applying these techniques, the book includes numerous worked examples with replicable R code. Each example demonstrates the step-by-step process of applying the relevant dimension reduction method to a real-world dataset, allowing readers to gain hands-on experience with the techniques.

Furthermore, the book provides detailed explanations of the theoretical concepts and algorithms underlying each dimension reduction method. This clarity helps readers to understand the underlying principles and assumptions of the techniques, enabling them to make informed decisions about which method to use for their specific research questions.

In addition to its comprehensive coverage of dimension reduction techniques, the book also includes a special chapter dedicated to metrics for comparing model performance. This chapter discusses various performance metrics commonly used in factor analysis and other dimension reduction methods, such as the adjusted R-squared, root mean squared error (RMSE), mean absolute error (MAE), and coefficient of determination (R2). By understanding these metrics, researchers can evaluate the effectiveness of different dimension reduction techniques and choose the most suitable method for their data analysis.

Overall, Factor Analysis and Dimension Reduction in R is an essential resource for social scientists interested in exploring and analyzing complex data sets. With its extensive coverage, worked examples, and detailed explanations, this book empowers researchers to uncover meaningful patterns and insights from their data, leading to more informed decision-making and scientific progress.

Weight: 1080g
Dimension: 246 x 174 (mm)
ISBN-13: 9781032246697