Multivariable Modeling and Multivariate Analysis for the Behavioral Sciences

Data, Measurement, and Models

Introduction

Types of Study

Types of Measurement

Missing Values

The Role of Models in the Analysis of Data

Determining Sample Size

Significance Tests, p-Values, and Confidence Intervals

Looking at Data

Introduction

Simple Graphics—Pie Charts, Bar Charts, Histograms, and Boxplots

The Scatterplot and Beyond

Scatterplot Matrices

Conditioning Plots and Trellis Graphics

Graphical Deception

Simple Linear and Locally Weighted Regression

Introduction

Simple Linear Regression

Regression Diagnostics

Locally Weighted Regression

Multiple Linear Regression

Introduction

An Example of Multiple Linear Regression

Choosing the Most Parsimonious Model When Applying Multiple Linear Regression

Regression Diagnostics

The Equivalence of Analysis of Variance and Multiple Linear Regression, and An

Introduction to the Generalized Linear Model

Introduction

The Equivalence of Multiple Regression and ANOVA

The Generalized Linear Model

Logistic Regression

Introduction

Odds and Odds Ratios

Logistic Regression

Applying Logistic Regression to the GHQ Data

Selecting the Most Parsimonious Logistic Regression Model

Survival Analysis

Introduction

The Survival Function

The Hazard Function

Cox’s Proportional Hazards Model

Linear Mixed Models for Longitudinal Data

Introduction

Linear Mixed Effects Models for Longitudinal Data

How Do Rats Grow?

Computerized Delivery of Cognitive Behavioral Therapy—Beat the Blues

The Problem of Dropouts in Longitudinal Studies

Multivariate Data and Multivariate Analysis

Introduction

The Initial Analysis of Multivariate Data

The Multivariate Normal Probability Density Function

Principal Components Analysis

Introduction

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 Component Scores

Some Examples of the Application of PCA

Using PCA to Select a Subset of the Variables

Factor Analysis

Introduction

The Factor Analysis Model

Estimating the Parameters in the Factor Analysis Model

Estimating the Numbers of Factors

Fitting the Factor Analysis Model: An Example

Rotation of Factors

Estimating Factor Scores

Exploratory Factor Analysis and PCA Compared

Confirmatory Factor Analysis

Cluster Analysis

Introduction

Cluster Analysis

Agglomerative Hierarchical Clustering

k-Means Clustering

Model-Based Clustering

Grouped Multivariate Data

Introduction

Two-Group Multivariate Data

More Than Two Groups

References

Appendix: Solutions to Selected Exercises

Index

A Summary and Exercises appear at the end of each chapter.