Computer-Aided Multivariate Analysis

Increasingly, researchers need to perform multivariate statistical analyses on their data. Unfortunately, a lack of mathematical training prevents many from taking advantage of these advanced techniques, in part, because books focus on the theory and neglect to explain how to perform and interpret multivariate analyses on real-life data. For years, Afifi and Clark's Computer-Aided Multivariate Analysis has been a welcome exception-helping researchers choose the appropriate analyses for their data, carry them out, and interpret the results. Only a limited knowledge of statistics is assumed, and geometrical and graphical explanations are used to explain what the analyses do. However, the basic model is always given, and assumptions are discussed. Reflecting the increased emphasis on computers, the Third Edition includes three additional statistical packages written for the personal computer. The authors also discuss data entry, database management, data screening, data transformations, as well as multivariate data analysis. Another new chapter focuses on log-linear analysis of multi-way frequency tables. Students in a wide range of fields-ranging from psychology, sociology, and physical sciences to public health and biomedical science-will find Computer-Aided Multivariate Analysis especially informative and enlightening.

PREPARATION FOR ANALYSIS
What is Multivariate Analysis?
How is Multivariate Analysis Defined?
Examples of Studies in Which Multivariate Analysis is Useful
Multivariate Analyses Discussed in this Book
Organization and Content of this Book
Characterizing Data for Future Analyses
Variables: Their Definition, Classification, and Use
Defining Statistical Variables
How Variables are Classified: Stevens's Classification System
Examples of Classifying Variables
Other Characteristics of Data
Preparing for Data Analysis
Processing the Data so they Can Be Analyzed
Choice of Computer for Statistical Analysis
Choice of a Statistical Package
Techniques for Data Entry
Data Management for Statistics
Data Example: Los Angeles Depression Study
Data Screening and Data Transformation
Making Transformations and Assessing Normality and Independence
Common Transformations
Assessing the Need for and Selecting a Transformation
Assessing Independence
Selecting Appropriate Analyses
Which Analyses?
Why Selection of Analyses is Often Difficult
Appropriate Statistical Measures Under Stevens's Classification
Appropriate Multivariate Analyses Under Stevens's Classification
APPLIED REGRESSION ANALYSIS
Simple Linear Regression and Correlation
Using Linear Regression and Correlation to Examine the Relationship Between Two Variables
When are Regression and Correlation Used?
Data Example
Description of Methods of Regression: fixed-X Case
Description of Methods of Regression and Correlation: variable-X Case
Further Examination of Computer Output
Robustness and Transformations for Regression Analysis
Other Options in Computer Programs
Special Applications of Regression
Discussion of Computer Programs
What to Watch Out For
Multiple Regression and Correlation
Using Multiple Linear Regression to Examine the Relationship Between One Dependent Variable and Multiple Independent Variables
When are Multiple Regression and Correlation Used?
Data Example
Description of Techniques: Fixed-X Case
Description of Techniques: Variable-X Case
How to Interpret the Results: Fixed-X Case
How to Interpret the Results: Variable-X Case
Residual Analysis and Transformations
Other Options in Computer Programs
Discussion of Computer Programs
What to Watch Out For
Variable Selection in Regression Analysis
Using Variable Selection Techniques in Multiple Regression Analysis
When are Variable Selection Methods Used?
Data Example
Criteria for Variable Selection
A General F Test
Stepwise Regression
Subset Regression
Discussion of Computer Programs
Discussion and Extensions
What to Watch Out For
Special Regression Topics
Special Topics in Regression Analysis
Missing Values in Regression Analysis
Dummy Variables
Constraints on Parameters
Methods for Obtaining a Regression Equation When Multicollinearity is Present
Ridge Regression
MULTIVARIATE ANALYSIS
Canonical Correlation Analysis
Using Canonical Correlation Analysis to Analyze Two Sets of Variables
When is Canonical Correlation Analysis Used?
Data Example
Basic Concepts of Canonical Correlation
Other Topics Related to Canonical Correlation
Discussion of Computer Programs
What to Watch Out For
Discriminant Analysis
Using Discriminant Analysis to Classify Cases
When is Discriminant Analysis Used?
Data Example
Basic Concepts of Classification
Theoretical background
Interpretation
Adjusting the Value of the Dividing Point
How Good is the Discriminant Function?
Testing for the Contributions of Classification Variables
Variable Selection
Classification Into More than Two Groups
Use of Canonical Correlation in Discriminant Function Analysis
Discussion of Computer Programs
What to Watch Out For
Logistic Regression
Using Logistic Regression to Analyze a Dichotomous Outcome Variable
When is Logistic Regression Used?
Data Example
Basic Concepts of Logistic Regression
Interpretation: Categorical Variables
Interpretation: Continuous and Mixed Variables
Refining and Evaluating Logistic Regression Analysis
Applications of Logistic Regression
Discussion of Computer Programs
What to Watch Out For
Regression Analysis Using Survival Data
Using Survival Analysis to Analyze Time-to-Event Data
When is Survival Analysis Used?
Data Examples
Survival Functions
Common Distributions Used in Survival Analysis
The Log-Linear Regression Model
The Cox Proportional Hazards Regression Model
Some Comparisons of the Log-Linear, Cox, and Logistic Regression Models
Discussion of Computer Programs
What to Watch Out For
Principal Components Analysis
Using Principal Components Analysis to Understand Intercorrelations
When is Principal Components Analysis Used?
Data Example
Basic Concepts of Principal Components Analysis
Interpretation
Use of Principal Components Analysis in Regression and Other Applications
Discussion of Computer Programs
What to Watch Out For
Factor Analysis
Using Factor Analysis to Examine the Relationship Among P Variables
When is Factor Analysis Used?
Data Example
Basic Concepts of Factor Analysis
Initial Factor Extraction: Principal Components Analysis
Initial Factor Extraction: Iterated Principal Components
Factor Rotations
Assigning Factor Scores to Individuals
An Application of Factor Analysis to the Depression Data
Discussion of Computer Programs
What to Watch Out For
Cluster Analysis
Using Cluster Analysis to Group cases
When is Cluster Analysis Used?
Data Example
Basic Concepts: Initial Analysis and Distance Measures
Analytical Clustering Techniques
Cluster Analysis for Financial Data Set
Discussion of Computer Programs
What to Watch Out For
Log-Linear Analysis
Using Log-Linear Models to Analyze Categorical Data
When is Log-Linear Analysis Used
Data Example
Notation and Sample Considerations
tests of Hypotheses and Models for Two-Way Tables
Example of a Two-Way Table
Models for Multiway Tables
Tests of Hypotheses for Multiway Tables: Exploratory Model Building
Tests of Hypotheses: Specific Models
Sample Size Issues
The Logit Model
Discussion of Computer Programs
What to Watch Out For
Appendix A: Lung Function Data
Appendix B: Lung Cancer Survival Data