Comprehensive and comprehensible, this classic covers the basic and advanced topics essential for using factor analysis as a scientific tool in psychology, education, sociology, and related areas. Emphasizing the usefulness of the techniques, it presents sufficient mathematical background for understanding and sufficient discussion of applications for effective use. This includes not only theory but also the empirical evaluations of the importance of mathematical distinctions for applied scientific analysis.
This book holds up very well after 35 years, and is readable and useful today. Most data scientists have encountered the idea of principal component analysis, so I'll explain factor analysis relative to it. Factor analysis considerably extends PCA, by allowing factors which are correlated with each other (and then higher-order factors based on these correlated factors). It also allows for the possbility of explaining only communal variance (that captured by at least two variables) instead of all variance. The third extension is that in factor analysis, the factors or components may be post-rotated after they are extracted and truncated, to re-align them better with the original variables. This book explains all of these techniques and gives considerable empirical wisdom on which should be used when.
One caveat I will offer is that this book is useful only for exploratory factor analysis. Although there is a chapter on confirmatory factor analysis (testing a clearly defined hypothesis about the structure), it is too brief and does not sufficiently explain how the analysis is actually conducted.
This classic book is hard to reach now so being able to access a reissue of it is really helpful. I got this book to puzzle my way through explaining the theoretical underpinnings for decisions that turned out to work statistically. At the time I did the statistics I was following recommendations in a journal, but it wasn`t until I read Gorsuch`s book that I could understand why the method I followed worked so well. Some sections of this book are very technical (i.e. math-dense) and difficult to understand, but the theoretical discussions are enlightening.