An Introduction to Applied Multivariate Analysis with R

Transcription

1 ~ Snrinuer Brian Everitt Torsten Hathorn An Introduction to Applied Multivariate Analysis with R

2 > Preface vii 1 Multivariate Data and Multivariate Analysis Introduction A brief history of the development of multivariate analysis Types of variables and the possible problem of missing values Missing values Some multivariate data sets Covariances, correlations, and distances Covariances Correlations Distances The multivariate normal density function Summary Exercises Looking at Multivariate Data: Visualisation Introduction The scatterplot The bivariate boxplot The convex hull of bivariate data The chi-plot The bubble and other glyph plots The scatterplot matrix Enhancing the scatterplot with estimated bivariate densities Kernel density estimators Three-dimensional plots Trellis graphics Stalactite plots Summary Exercises

3 xii 3 Principal Components Analysis Introduction Principal components analysis (PCA) Finding the sample principal components Should principal components be extracted from the covariance or the correlation matrix? Principal components of bivariate data with correlation coefficient r Rescaling the principal components How the principal components predict the observed covariance matrix Choosing the number of components Calculating principal components scores Some examples of the application of principal components analysis Head lengths of first and second sons Olympic heptathlon results Air pollution in US cities The biplot Sample size for principal components analysis Canonical correlation analysis Head measurements Health and personality Summary Exercises Multidimensional Scaling Introduction Models for proximity data Spatial models for proximities: Multidimensional scaling Classical multidimensional scaling Classical multidimensional scaling: Technical- details Examples of classical multidimensional scaling Non-metric multidimensional scaling House of Representatives voting Judgements of World War II leaders Correspondence analysis Teenage relationships Summary Exercises Exploratory Factor Analysis Introduction A simple example of a factor analysis model The k-factor analysis model

4 p xiii 5.4 Scale invariance of the k-factor model Estimating the parameters in the k-factor analysis model Principal factor analysis Maximum likelihood factor analysis Estimating the number of factors Factor rotation Estimating factor scores Two examples of exploratory factor analysis Expectations of life Drug use by American college students Factor analysis and principal components analysis compared Summary Exercises Cluster Analysis Introduction Cluster analysis Agglomerative hierarchical clustering Clustering jet fighters K-means clustering Clustering the states of the USA on the basis of their crime rate profiles Clustering Romano-British pottery Model-based clustering Finite mixture densities Maximum likelihood estimation in a finite mixture density with multivariate normal components Displaying clustering solutions graphically Summary Exercises Confirmatory Factor Analysis and Structural Equation Models Introduction Estimation, identification, and assessing fit for confirmatory factor and structural equation models Estimation Identification Assessing the fit of a model Confirmatory factor analysis models Ability and aspiration A confirmatory factor analysis model for drug use Structural equation models Stability of alienation Summary

5 . xiv 7.6 Exercises The Analysis of Repeated Measures Data Introduction Linear mixed-effects models for repeated measures data Random intercept and random intercept and slope models for the timber slippage data Applying the random intercept and the random intercept and slope models to the timber slippage data Fitting random-effect models to the glucose challenge data Prediction of random effects Dropouts in longitudinal data Summary Exercises References Index