1 Applied Multivariate Analysis Introduction 2 Nature of Multivariate Analysis ► Typically exploratory, not confirmatory ► Often focused on simplification.

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Presentation transcript:

1 Applied Multivariate Analysis Introduction

2 Nature of Multivariate Analysis ► Typically exploratory, not confirmatory ► Often focused on simplification ► Often focused on revealing structure in dimensions that our eyes and imaginations don’t fully support.

3 Adequate Preparation? ► Basic course in statistical science ► STA 671 ► SAS exposure ► Linear algebra (?)

4 Begin Reviewing and Reading ► Basic data steps in SAS ► Chapter 1 in AMD ► Chapter 2 in AMD ► We’ll begin with Chapter 4

5 Potential Topics Covered ► Principal Components Analysis (PCA) ► Factor Analysis (FA) ► Discriminant Analysis (DA) ► Multidimensional Scaling (MDS) ► Cluster Analysis (CA) ► Canonical Correlations Analysis (CCA) ► Multivariate Analysis of Variance (MANOVA)

6 Why Multivariate? ► Typically more than one measurement is taken on a given experimental unit ► Need to consider all the measurements together so that one can understand how they are related ► Need to consider all the measurements together so that one can extract essential structure

7 In Chromatography one observation

8 In Neuroimaging one observation

9 In Social Science Research Education level Your opinion on welfare Your opinion on social security Your opinion on …. one (joint) observation

10 Distinguishing Midges ► Suppose we are interested in measuring the wing length and the antenna length.

11 Distinguishing Midges ► What can you do with both variables that you can’t do with just one of them?

12 Measuring Heads ► Are these data truly two-dimensional? Not the usual regression line ….

13 Our Approach in STA 677 ► Emphasize  Intuition  SAS  Geometry  Interpretations  Data Analysis ► De-emphasize  Theoretical  Theoretical basis  Formal  Formal proofs

14 Getting on the Computers Here

15 Personal SAS License ► ► Lorinda Wang ► ► ► ► SStars Lab ► ► 213d M I King 0039 ► ► Phone ► ► Fax

16 Organizational Details ► Please get the textbook (required) ► Look at Readme.txt on the text CD ► Notes posted on the class website ► Take a look at the syllabus

17 Basic Vocabulary ► Variance ► Covariance ► Correlation More than one kind of variability will emerge.

18 Additional Vocabulary ► Eigenvalues ► Eigenvectors ► Projections ► Matrix Notation

19 Discovering Linear Combinations ► Log on to the computer in front of you and access our course web site. ► Find the data set helmet.xls and open it. ► Compute (.707*LTN)+(.707*LTG) (use Excel) ► What did you just do geometrically?

20 Discovering Linear Combinations Equal Wts On LTG, LTN LTG is WTD > LTN

21 Discovery Exercise Continued ► Find the variance of LTN, LTG (use Excel). ► Find the variance of (.707*LTN)+(.707*LTG) --- equal weights. ► Find the variance of (.50*LTN)+(.85*LTG) --- unequal weights with LTG weighted more.

22 Discovery Exercise ► What did you find and does it make sense?  Var(LTN)=  Var(LTG)=  Var(707)=  Var(5085)= ► This is no accident. And this is what Principal Components is all about.

23 Encounter With SAS ► Save the helmet file to your hard disk. ► Exit Excel and start up SAS. ► Watch the demonstration on how to bring the Excel file into SAS. ► Repeat this yourself.

24 Encounter With SAS ► It is easy to transfer the AMD.txt data to Excel files. If you don’t know how and want to know, just ask. ► So you can always bring your data in as Excel files if you want. ► That is what I’ll do in front of the class.

25 Coming Up Principal Components Analysis