Factor analysis and principal component analysis
Textbook, strumenti didattici
pp. 244, 1a edizione 2013 (Codice editore 1120.23)
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Within the vast archipelago of data analysis tools, factor analysis and principal component analysis are among the islands more frequently visited by human scientists. This book is devoted to those who wish to exercise full intellectual control over the tools they employ, while acquiring the ability to critically appraise the results obtained in relation to the objectives of their research projects.
Presentazione del volume
Within the vast archipelago of data-analysis tools, factor analy-sis and principal component analysis are among the islands more frequently visited by human scientists. Their success is due both to the century-old status they have reached, and to the fact that they are easy to apply nowadays, thanks, in particular, to the availability of dedicated data analysis software packages. Today even the most inexperienced student can avail of this user-friendly software, entrusting it with full responsibility for the numerous operations the techniques themselves require. This modus operandi produces results of scarce substantial interest and dubious scientific quality.
This book is devoted to those who wish to exercise full intellectual control over the tools they employ, while acquiring the ability to critically appraise the results obtained in relation to the objectives of their research projects.
Giovanni Di Franco is professor of social-research Methodology at Rome's State Sapienza University. He is the author of: Analisi delle corrispondenze e altre tecniche multivariate per variabili categoriali (2006), L'analisi dei dati con SPSS (2009), Il campionamento nelle scienze umane (2010), Dalla matrice dei dati all'analisi trivariata (2011), Tecniche e modelli di analisi multivariata (2011). He directs the La Cassetta degli attrezzi series published by FrancoAngeli.
Alberto Marradi, once full professor of Methodology of the social sciences at the University of Florence, now directs a master's course in Methodology at the University of Buenos Aires. He also directs the Methodology of the Human Sciences series on behalf of the Italian association of sociology's methodological section. He has acted as vice-president of the International Sociological Association's Methodological Research Committee. He is the author of: Concetti e metodo nella ricerca sociale (1984), L'analisi monovariata (1993), Linee guida per l'analisi bivariata dei dati nelle scienze sociali (1997).
Franco Rositi, Presentazione editoriale
Factor analysis and principal component analysis: nature and functions
(A asscilfication of the goals of factor analysis and principal component analysis)
A century of factor analysis and principal component analysis
(Prologue: British statisticians; Act one: British psychologists; Act two: Chicago psychologists; Act three: back to statisticians)
Matrix algebra: basic concepts
(Vectors; Vector operations: addition, subtraction, multiplication; Linear combinations. Linear dependence or independence; Matrices; Matrix operations: addition, subtraction, multiplication; The product of a scalar by a matrix; Determinants and rank of a matrix; Square matrix inversion; Systems of linear equations; The charateristic roots of a matrix: eigenvalues and eigenvectors)
Matrix algebra applied to correlation matrices in order to extract components
( From correlation coefficients to component loadings; From component loadings to component score coefficients; Extracting principal components: an example)
Differences beetwen factor analysis and principal component analysis
(The echnt ical debate; Various techniques for factor extraction; A test of differences between extraction techniques)
How to refine a single dimension and construct an index
(Refining a single dimension from a set of survey variables; Refining a single dimension from a set of ecological variables; Constructing an index)
Exploring the dimensions of a set of variables
(How a multiple pca is applied using individual data; How a multiple pca is normally performed using ecological data; Inconveniences linked to the usual method of proceeding)
An alternative approach: two-stage pca
(Identifying components and refining them; Refining the components through an iterative process; Summing up: elaborating a two-stage pca)
Tutti i campi devono essere compilati.