Census Data, Dimensions, Distances - Lecture Slides | STAT 530, Exams of Statistics

Download Census Data, Dimensions, Distances - Lecture Slides | STAT 530 and more Exams Statistics in PDF only on Docsity! 1 STAT 530/J530 B.Habing Univ. of S.C. 1 STAT 530/J530 October 28th, 2008 Instructor: Brian Habing Department of Statistics LeConte 203 Telephone: 803-777-3578 E-mail: habing@stat.sc.edu STAT 530/J530 B.Habing Univ. of S.C. 2 Census Data STAT 530/J530 B.Habing Univ. of S.C. 3 How Many Dimensions? Classical Multidimensional Scaling Tries to Minimize: And aim for between under 0.1. Dim 2 3 4 15 Stress 0.64 0.56 0.48 0.09 ( ) ∑ ∑ < < − = ji ij ji ijij d dd Stress 2 22 ˆ 2 STAT 530/J530 B.Habing Univ. of S.C. 4 Other Distances? For interval valued data - Maximum distance: Manhattan Distance: ||max jkikkij xxd −= ∑ −= k jkikij xxd || STAT 530/J530 B.Habing Univ. of S.C. 5 Other Distances? For presence absence data - Matching Index: Ochiai Index: Dice Index: Jaccard Index: ndad /)( += ))((/ cabaad ++= )2/(2 cbaad ++= )/( cbaad ++= STAT 530/J530 B.Habing Univ. of S.C. 6 Non-metric Multidimensional Scaling Sammon Mapping minimizes: Isometric Scaling ( ) ∑∑ < < − ji ij ijij ji ij d dd d 2ˆ1 ( ) ∑ < − ji ij ijij d ddf 2 2 ˆ ˆ)(