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Applied Multivariate Analysis. Introduction. 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. Adequate Preparation?.

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## Applied Multivariate Analysis

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**Applied Multivariate Analysis**Introduction**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.**Adequate Preparation?**• Basic course in statistical science • STA 671 • SAS exposure • Linear algebra (?)**Begin Reviewing and Reading**• Basic data steps in SAS • Chapter 1 in AMD • Chapter 2 in AMD • We’ll begin with Chapter 4**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)**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**one observation**In Chromatography**one observation**In Neuroimaging**one (joint) observation**In Social Science Research • Education level • Your opinion on welfare • Your opinion on social security • Your opinion on ….**Distinguishing Midges**• Suppose we are interested in measuring the wing length and the antenna length.**Distinguishing Midges**• What can you do with both variables that you can’t do with just one of them?**Not the usual regression line ….**Measuring Heads • Are these data truly two-dimensional?**Our Approach in STA 677**• De-emphasize • Theoretical basis • Formal proofs • Emphasize • Intuition • SAS • Geometry • Interpretations • Data Analysis**Personal SAS License**• Lorinda Wang • lorinda@pop.uky.edu • SStars Lab • 213d M I King 0039 • Phone 859 257-2204 • Fax 859 323-1266**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**More than one kind of variability will emerge.**Basic Vocabulary • Variance • Covariance • Correlation**Additional Vocabulary**• Eigenvalues • Eigenvectors • Projections • Matrix Notation**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?**Equal Wts**On LTG, LTN LTG is WTD > LTN Discovering Linear Combinations**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.**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.**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.**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.**Coming Up**Principal Components Analysis

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