1. Stats 848.3 Multivariate Data Analysis

2. Instructor:W.H.Laverty Office:235 McLean Hall Phone:966-6096 Lectures: M W F 9:30am - 10:20am 242.1 McLean Hall 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 – X 1, X 2, … X p This is likely the situation – very rarely do you collect data on a single variable. The variables maybe 1.Discrete (Categorical) 2.Continuous (Numerical) The variables may be 1.Dependent (Response variables) 2.Independent (Predictor variables)

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

14. Multivariate Techniques Multivariate Techniques can be classified as follows: 1.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 T 2 test ANOVA (Analysis of Variance) generalized to MANOVA (Multivariate Analysis of Variance)

15. 2.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. 3.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. 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