1. Multivariate Data Analysis
Stats 848.3
Multivariate Data Analysis

2. Instructor:
W.H.Laverty
Office:
235 McLean Hall
Phone:
Lectures:
M W F 12:30pm - 1:20pm
Arts 106
Evaluation:
Assignments,Tests - 40%
Final Examination - 60%

3. Course Outline

4. I Introduction
A brief introduction to multivariate problems

5. II. Analysis of Multivariate Categorical Data
chi-squared tests; log-linear model
multidimensional contingency tables
fixed margin and logit models
causal (path) analysis for categorical variables

6. III. Analysis of Correlation Structure
Bivariate correlation
Partial correlation
multiple correlation
canonical correlation

7. IV. Multivariate Linear Regression Analysis
path analysis

8. V. Multivariate Analysis of Variance and Covariance
MANOVA and MANOCOVA for factorial experiments
Profile analysis and repeated measures designs

9. VI. Advanced Analysis of Correlation Structure
Principal Components
Factor analysis

10. VII. Classification and Grouping Techniques
Discriminant analysis
Cluster analysis

11. Introduction

12. Multivariate Data
We have collected data for each case in the sample or population on not just one variable but on several variables – X1, X2, … Xp
This is likely the situation – very rarely do you collect data on a single variable.
The variables maybe
Discrete (Categorical)
Continuous (Numerical)
The variables may be
Dependent (Response variables)
Independent (Predictor variables)

13. A chart illustrating Statistical Procedures
Independent variables
Dependent Variables
Categorical
Continuous
Continuous & Categorical
Multiway frequency Analysis
(Log Linear Model)
Discriminant Analysis
ANOVA (single dep var)
MANOVA (Mult dep var)
MULTIPLE REGRESSION
(single dep variable)
MULTIVARIATE
(multiple dependent variable)
ANACOVA
(single dep var)
MANACOVA
(Mult dep var) ??

14. Multivariate Techniques
Multivariate Techniques can be classified as follows:
Techniques that are direct analogues of univariate procedures.
There are univariate techniques that are then generalized to the multivariate situarion
e. g. The two independent sample t test, generalized to Hotelling’s T2 test
ANOVA (Analysis of Variance) generalized to MANOVA (Multivariate Analysis of Variance)

15. Techniques that are purely multivariate procedures.
Correlation, Partial correlation, Multiple correlation, Canonical Correlation
Principle component Analysis, Factor Analysis
These are techniques for studying complicated correlation structure amongst a collection of variables

16. Techniques for which a univariate procedures could exist but these techniques become much more interesting in the multivariate setting.
Cluster Analysis and Classification
Here we try to identify subpopulations from the data
Discriminant Analysis
In Discriminant Analysis, we attempt to use a collection of variables to identify the unknown population for which a case is a member

17. A survey was given to 132 students Male=35, Female=97
An Example:
A survey was given to 132 students
Male=35,
Female=97
They rated, on a Likert scale
1 to 5
their agreement with each of 40 statements.
All statements are related to the Meaning of Life

18. Questions and Statements

19. Statements - continued

22. Cluster Analysis of n = 132 university students using responses from Meaning of Life questionnaire (40 questions)

23. Discriminant Analysis of n = 132 university students into the three identified populations