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1 Applied Multivariate Analysis Introduction
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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.
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3 Adequate Preparation? ► Basic course in statistical science ► STA 671 ► SAS exposure ► Linear algebra (?)
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4 Begin Reviewing and Reading ► Basic data steps in SAS ► Chapter 1 in AMD ► Chapter 2 in AMD ► We’ll begin with Chapter 4
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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)
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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
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7 In Chromatography one observation
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8 In Neuroimaging one observation
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9 In Social Science Research Education level Your opinion on welfare Your opinion on social security Your opinion on …. one (joint) observation
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10 Distinguishing Midges ► Suppose we are interested in measuring the wing length and the antenna length.
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11 Distinguishing Midges ► What can you do with both variables that you can’t do with just one of them?
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12 Measuring Heads ► Are these data truly two-dimensional? Not the usual regression line ….
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13 Our Approach in STA 677 ► Emphasize Intuition SAS Geometry Interpretations Data Analysis ► De-emphasize Theoretical Theoretical basis Formal Formal proofs
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14 Getting on the Computers Here
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15 Personal SAS License ► ► Lorinda Wang ► ► lorinda@pop.uky.edu ► ► SStars Lab ► ► 213d M I King 0039 ► ► Phone 859 257-2204 ► ► Fax 859 323-1266
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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
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17 Basic Vocabulary ► Variance ► Covariance ► Correlation More than one kind of variability will emerge.
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18 Additional Vocabulary ► Eigenvalues ► Eigenvectors ► Projections ► Matrix Notation
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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?
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20 Discovering Linear Combinations Equal Wts On LTG, LTN LTG is WTD > LTN
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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.
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22 Discovery Exercise ► What did you find and does it make sense? Var(LTN)= 15.37 Var(LTG)= 31.84 Var(707)= 38.11 Var(5085)= 39.19 ► This is no accident. And this is what Principal Components is all about.
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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.
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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.
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25 Coming Up Principal Components Analysis
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