Applied Multivariate Analysis Introduction 1 Nature of Multivariate

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Applied Multivariate Analysis Introduction 1

Applied Multivariate Analysis Introduction 1

Nature of Multivariate Analysis ► Typically exploratory, not confirmatory ► Often focused on simplification

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. 2

Adequate Preparation? ► Basic course in statistical science ► STA 671 ► SAS exposure

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

Begin Reviewing and Reading ► Basic data steps in SAS ► Chapter 1 in

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

Potential Topics Covered ► Principal Components Analysis (PCA) ► Factor Analysis (FA) ► Discriminant

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) 5

Why Multivariate? ► Typically more than one measurement is taken on a given experimental

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 6

In Chromatography one observation 7

In Chromatography one observation 7

In Neuroimaging one observation 8

In Neuroimaging one observation 8

In Social Science Research • Education level • Your opinion on welfare • Your

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

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

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

Distinguishing Midges ► What can you do with both variables that you can’t do

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

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

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

Our Approach in STA 677 ► Emphasize § Intuition § SAS § Geometry §

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

Getting on the Computers Here 14

Getting on the Computers Here 14

Personal SAS License ► Lorinda Wang ► lorinda@pop. uky. edu ► SStars Lab ►

Personal SAS License ► Lorinda Wang ► [email protected] uky. edu ► SStars Lab ► 213 d M I King 0039 ► Phone 859 257 -2204 ► Fax 859 323 -1266 15

Organizational Details ► Please get the textbook (required) ► Look at Readme. txt on

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 16

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

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

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

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

Discovering Linear Combinations ► Log on to the computer in front of you and

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 ► What (. 707*LTN)+(. 707*LTG) (use Excel) did you just do geometrically? 19

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

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

Discovery Exercise Continued ► Find the variance of LTN, LTG (use Excel). ► Find

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. 21

Discovery Exercise ► What did you find and § Var(LTN)= 15. 37 § Var(LTG)=

Discovery Exercise ► What did you find and § Var(LTN)= 15. 37 § Var(LTG)= 31. 84 § Var(707)= 38. 11 § Var(5085)= 39. 19 does it make sense? ► This is no accident. And this is what Principal Components is all about. 22

Encounter With SAS ► Save ► Exit the helmet file to your hard disk.

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

Encounter With SAS ► It is easy to transfer the AMD. txt data to

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. 24

Coming Up Principal Components Analysis 25

Coming Up Principal Components Analysis 25