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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE Contents Multivariate Methods Learn about JMP Documentation and Additional Resources Formatting Conventions JMP Documentation JMP Documentation Library JMP Help Additional Resources for Learning JMP Tutorials Sample Data Tables Learn about Statistical and JSL Terms Learn JMP Tips and Tricks Tooltips JMP User Community JMPer Cable JMP Books by Users The JMP Starter Window Technical Support Introduction to Multivariate Analysis Overview of Multivariate Techniques Correlations and Multivariate Techniques Explore the Multidimensional Behavior of Variables Launch the Multivariate Platform The Multivariate Report Multivariate Platform Options Nonparametric Correlations edited by Y Dodge Fieller, E.C (1954), “Some Problems in Interval Estimation,” Journal of the Royal Statistical Society, Series B, 16, 175–185 Florek, K., Lukaszewicz, J., Perkal, J., and Zubrzycki, S (1951a), “Sur La Liaison et la Division des Points d’un Ensemble Fini,” Colloquium Mathematicae, 2, 282–285 Garthwaite, P (1994), “An Interpretation of Partial Least Squares,” Journal of the American Statistical Association, 89:425, 122–127 Golub, G.H., Kahan, W (1965), “Calculating the singular values and pseudo-inverse of a matrix,” Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis 2:2, 205–224 Golub, G.H and van der Vorst, H.A., (2000), “Eigenvalue Computation in the 20th Century,” Journal of Computational and Applied Mathematics 123, 35-65 Goodman, L.A (1974), “Exploratory Latent Structure Analysis Using Both Identifiable and Unidentifiable Models,” Biometrika 61:2, 215–231 Goodnight, J.H (1978), “Tests of Hypotheses in Fixed Effects Linear Models,” SAS Technical Report R–101, Cary NC: SAS Institute Inc, also in Communications in Statistics (1980), A9 167–180 Goodnight, J.H and W.R Harvey (1978), “Least Square Means in the Fixed Effect General Linear Model,” SAS Technical Report R–103, Cary NC: SAS Institute Inc Hand, D, Mannila, H, and Smyth, P (2001), Principles of Data Mining, MIT Press Harris, C.W and Kaiser, H.F (1964), “Oblique Factor Analytic Solutions by Orthogonal Transformation,” Psychometrika, 32, 363–379 Hartigan, J.A (1981), “Consistence of Single Linkage for High–Density Clusters,” Journal of the American Statistical Association, 76, 388–394 Hastie, T., Tibshirani, R., and Friedman, J.H.(2009), Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition, New York: Springer Science and Business Media Hocking, R.R (1985), The Analysis of Linear Models, Monterey: Brooks–Cole Hoskuldsson, A (1988), “PLS Regression Methods,” Journal of Chemometrics, 2:3, 211–228 Hoeffding, W (1948), “A Non-Parametric Test of Independence”, Annals of Mathematical Statistics, 19, 546–557 Huber, P.J (1964), “Robust Estimation of a Location Parameter,” Annals of Mathematical Statistics, 35:1, 73–101 Huber, Peter J (1973), “Robust Regression: Asymptotics, Conjecture, and Monte Carlo,” Annals of Statistics, Volume 1, Number 5, 799–821 Huber, P.J and Ronchetti, E.M (2009), Robust Statistics, Second Edition, Wiley Jackson, J Edward (2003), A User’s Guide to Principal Components, New Jersey: John Wiley and Sons Jardine, N and Sibson, R (1971), Mathematical Taxonomy, New York: John Wiley and Sons Kohonen, T (1989), Self-Organization and Associative Memory, Springer Series in Information Sciences, Volume Kohonen, T (1990), “The Self-Organizing Map,” Proceedings of the IEEE, 78:9, 14641480 Lindberg, W., Persson, J.-A., and Wold, S (1983), “Partial Least-Squares Method for Spectrofluorimetric Analysis of Mixtures of Humic Acid and Ligninsulfonate,” Analytical Chemistry, 55, 643–648 Mardia, K., Kent, J., and Bibby, J (1980), Multivariate Analysis, First Edition, New York: Academic Press Mason, R.L and Young, J.C (2002), Multivariate Statistical Process Control with Industrial Applications, Philadelphia: ASA-SIAM McLachlan, G.J and Krishnan, T (1997), The EM Algorithm and Extensions, New York: John Wiley and Sons McQuitty, L.L (1957), “Elementary Linkage Analysis for Isolating Orthogonal and Oblique Types and Typal Relevancies,” Educational and Psychological Measurement, 17, 207–229 Milligan, G.W (1980), “An Examination of the Effect of Six Types of Error Perturbation on Fifteen Clustering Algorithms,” Psychometrika, 45, 325–342 Nelson, Philip R.C., Taylor, Paul A., MacGregor, John F (1996), “Missing Data Methods in PCA and PLS: Score calculations with incomplete observations,” Chemometrics and Intelligent Laboratory Systems, 35, 45–65 Press, W.H, Teukolsky, S.A., Vetterling, W.T., Flannery, B.P (1998), Numerical Recipes in C: The Art of Scientific Computing, Second Edition, Cambridge, England: Cambridge University Press SAS Institute Inc (1983), “SAS Technical Report A-108: Cubic Clustering Criterion,” Cary, NC: SAS Institute Inc Retrieved December 16, 2015 from https://support.sas.com/documentation/onlinedoc/v82/techreport_a108.pdf SAS Institute Inc (2011), SAS/STAT 9.2 User’s Guide, “The VARCLUS Procedure,” Cary, NC: SAS Institute Inc Retrieved April 15, 2015 from http://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/viewer.htm#varclu SAS Institute Inc (2011), SAS/STAT 9.3 User’s Guide, “The PLS Procedure,” Cary, NC: SAS Institute Inc Retrieved April 15, 2015 from http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug SAS Institute Inc (2011), SAS/STAT 9.3 User’s Guide, “The CANDISC Procedure,” Cary, NC: SAS Institute Inc Retrieved April 15, 2015 from http://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/viewer.htm#statug SAS Institute Inc (2005), SAS/STAT 9.2 User’s Guide, “The FASTCLUS Procedure,” Cary, NC: SAS Institute Inc Retrieved June 21, 2016 from http://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/viewer.htm#statug Schafer, J and Strimmer, K (2005), “A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics”, Statistical Applications in Genetics and Molecular Biology, 4, 1175–1189 Sneath, P.H.A (1957) “The Application of Computers to Taxonomy,” Journal of General Microbiology,17, 201–226 Sokal, R.R and Michener, C.D (1958), “A Statistical Method for Evaluating Systematic Relationships,” University of Kansas Science Bulletin, 38, 1409–1438 Tobias, R.D (1995), “An Introduction to Partial Least Squares Regression,” Proceedings of the Twentieth Annual SAS Users Group International Conference, Cary, NC: SAS Institute Inc Tracy, N.D., Young, J.C., Mason, R.R (1992), “Multivariate Control Charts for Individual Observations,” Journal of Quality Technology, 24, 88–95 Umetrics (1995), Multivariate Analysis (3-day course), Winchester, MA White, K.P., Jr., Kundu, B., and Mastrangelo, C.M., (2008), “Classification of Defect Clusters on Semiconductor Wafers Via the Hough Transform,” IEEE Transactions on Semiconductor Manufacturing, 21:2, 272-278 Wold, (1980), “Soft Modelling: Intermediate between Traditional Model Building and Data Analysis,” Mathematical Statistics (Banach Center Publications, Warsaw), 6, 333–346 Wold, S (1994), “PLS for Multivariate Linear Modeling”, QSAR: Chemometric Methods in Molecular Design Methods and Principles in Medicinal Chemistry Wold, S., Sjostrom, M., and Eriksson, L (2001), “PLS-Regression: A Basic Tool of Chemometrics,” Chemometrics and Intelligent Laboratory Systems, 58:2, 109–130 Wright, S.P and R.G O’Brien (1988), “Power Analysis in an Enhanced GLM Procedure: What it Might Look Like,” SUGI 1988, Proceedings of the Thirteenth Annual Conference, 1097–1102, Cary NC: SAS Institute Inc Index Multivariate Methods Numerics 95% bivariate normal density ellipse 42 A agglomerative clustering 144 algorithms 222 approximate F test 112 Average Linkage 149, 167 B 118 bar chart of correlations 37 Biplot 179, 192 Biplot 3D 179, 193 Biplot Options 179, 193 Biplot Ray Position 96 biplot rays 69 bivariate normal density ellipse 42 By variable 59 Baltic.jmp C calculation details 222 Canonical 3D Plot 93 centroid 43 Centroid Method 150, 167 Cluster Criterion 156 Cluster platform 143 compare methods 144, 170, 184 hierarchical 144–167 introduction 144, 170, 184 k-means 170–193 launch 148 normal mixtures 183–196 Cluster the Correlations 39 Clustering History 156 Color Clusters 156 Color Map 157 Color Map On Correlations 39 Color Map On p-values Color Points 39 97 150, 167 computational details 222 Consider New Levels 93 Constellation Plot 157 contrast M matrix 111 correlation matrix 34 Cronbach’s alpha 44–46 statistical details 51 Complete Linkage D 45 dendrogram 143–144, 153 Dendrogram Scale command 156 Density Ellipse 42 dimensionality 57 Discriminant Analysis, PLS 142 Distance Graph 157 Distance Scale 157 Danger.jmp E E matrix 111 Effect Sizes, Latent Class Analysis 203 eigenvalue decomposition 57, 61 Eigenvectors 63 Ellipse alpha 42 Ellipse Color 43 Ellipses Transparency 42 EM algorithm 170 Even Spacing 157 Expectation Maximization algorithm 170 F factor analysis 57 Factor Analysis platform By variable 59 factor analysis, overview 57 Factor Rotation 69 Fit Line 42 formulas used in JMP calculations 222 G 157 group similar rows see Cluster platform Geometric Spacing H H matrix 111 Hoeffding’s D 41, 48 I Impute Missing Data in PLS 123 Inverse Corr table 36 inverse correlation 36, 49 item reliability 44–46 J Jackknife Distances 44 K 40 Kendall’s tau-b 48 KMeans 170 K-Means Clustering Platform SOMs 180 Kendall’s Tau L L matrix 111 Legend 157 linear combination 57 Loading Plot 68 M M matrix 111 Mahalanobis distance 43, 49 Mark Clusters 156 MDS Plot 204 missing data imputation, PLS 123 missing value 35 missing values 37 Mixture Probabilities 204 multinomial mixture model 198 Multivariate 31, 33 multivariate mean 43 multivariate outliers 43 Multivariate platform 221 principal components 57 N Nonpar Density 43 40 Nonparametric Measures of Association table 40 normal density ellipse 42 Nonparametric Correlations O Other 42 43 Outlier Distance plot 49 Outlier Analysis P 35 Pairwise Correlations table 37 Parallel Coord Plots 179, 193 Partial Corr table 36 partial correlation 36 Partial Least Squares platform validation 122 PCA 57 Pearson correlation 37, 47 PLS 115–140 Statistical Details 138–141 principal components analysis 57 product-moment correlation 37, 47 Pairwise Correlations Q questionnaire analysis 44–46 R reduce dimensions 57 reliability analysis 44–46 also see Survival platform ROC Curve 95 S 97 Cluster Hierarchy 158 Cluster Tree 158 Clusters 158, 179, 193 Density Formula 193 Display Order 158 Distance Matrix 158 Save Canonical Scores Save Save Save Save Save Save Save Formula for Closest Cluster Save Mixture Formulas 193 Save Mixture Probabilities Scatterplot Matrix 41, 94 193 158 scatterplot matrix 34 Score Plot 67 Scree Plot 66 Shaded Ellipses 42 Show Biplot Rays 96 Show Canonical Details 97 42 Dendrogram 156 Show Correlations Show Show Distances to each group 95 94 Histogram 42 Show Group Means Show 96 Normal 50% Contours 96 Points 42, 96 Show Means CL Ellipses Show Show Show Probabilities to each group 93 significance probability 37 Simulate Clusters 193 Single Linkage 150, 167 Solubility.jmp 58 SOMs 180 Spearman’s Rho 48 Spearman’s Rho 40 Standardize Data 152 statistical details 222 Show Within Covariances T T2 Statistic 44 Transposed Parameter Estimates 203 Two way clustering 157 U Univariate 35 W-Z Ward’s 150, 167 95 Table of Contents Contents Learn about JMP 10 17 Documentation and Additional Resources Formatting Conventions JMP Documentation JMP Documentation Library JMP Help Additional Resources for Learning JMP Tutorials Sample Data Tables Learn about Statistical and JSL Terms Learn JMP Tips and Tricks Tooltips JMP User Community JMPer Cable JMP Books by Users The JMP Starter Window Technical Support 17 19 19 20 24 24 25 25 25 26 26 26 26 27 27 27 Introduction to Multivariate Analysis 28 Overview of Multivariate Techniques Correlations and Multivariate Techniques Explore the Multidimensional Behavior of Variables Launch the Multivariate Platform The Multivariate Report Multivariate Platform Options Nonparametric Correlations Scatterplot Matrix Outlier Analysis Mahalanobis Distance Jackknife Distances T2 Statistic Saving Distances and Values Item Reliability Impute Missing Data Example of Item Reliability 28 30 30 32 33 34 38 39 41 42 42 42 42 43 43 43 Computations and Statistical Details Estimation Methods REML Robust Pearson Product-Moment Correlation Nonparametric Measures of Association Spearman’s ρ (rho) Coefficients Kendall’s τb Coefficients Hoeffding’s D Statistic Inverse Correlation Matrix Distance Measures Mahalanobis Distance Measures Jackknife Distance Measures T2 Distance Measures Cronbach’s Alpha Principal Components Reduce the Dimensionality of Your Data Overview of Principal Component Analysis Example of Principal Component Analysis Launch the Principal Components Platform Missing Data Principal Components Report Principal Components Report Options Statistical Details Estimation Methods REML Wide Sparse DModX Calculation Discriminant Analysis Predict Classifications Based on Continuous Variables Discriminant Analysis Overview Example of Discriminant Analysis Discriminant Launch Window Stepwise Variable Selection Updating the F Ratio and Prob>F Statistics 44 44 44 45 45 45 46 46 47 47 48 48 48 49 49 51 51 53 53 54 57 57 58 67 67 67 67 68 68 70 70 72 72 73 75 76 76 Buttons Columns Stepwise Example Discriminant Methods Regularized, Compromise Method Shrink Covariances The Discriminant Analysis Report Principal Components Canonical Plot and Canonical Structure Canonical Structure Canonical Plot Modifying the Canonical Plot Classification into Three or More Categories Classification into Two Categories Discriminant Scores Score Summaries Entropy RSquare Discriminant Analysis Options Score Options Canonical Options Show Canonical Details Show Canonical Structure Example of a Canonical 3D Plot Specify Priors Consider New Levels Save Discrim Matrices Scatterplot Matrix Validation in JMP and JMP Pro Technical Details Description of the Wide Linear Algorithm Saved Formulas Linear Discriminant Method Quadratic Discriminant Method Regularized Discriminant Method Wide Linear Discriminant Method Multivariate Tests Approximate F-Tests Between Groups Covariance Matrix 76 77 78 79 81 82 82 83 84 84 84 86 86 87 87 89 90 91 93 95 96 98 99 100 101 101 101 102 103 103 103 104 105 106 107 110 111 111 Partial Least Squares Models Develop Models Using Correlations between Ys and Xs Overview of the Partial Least Squares Platform Example of Partial Least Squares Launch the Partial Least Squares Platform Centering and Scaling Standardize X Model Launch Control Panel Partial Least Squares Report Model Comparison Summary and Method = Root Mean PRESS Plot Root Mean PRESS Calculation of Q2 Calculation of R2X and R2Y When Validation Is Used Model Fit Report Partial Least Squares Options Model Fit Options Variable Importance Plot VIP vs Coefficients Plots Save Columns Statistical Details Partial Least Squares NIPALS SIMPLS van der Voet T2 T2 Plot Confidence Ellipses for X Score Scatterplot Matrix Standard Error of Prediction and Confidence Limits Standard Error of Prediction Formula Mean Confidence Limit Formula Indiv Confidence Limit Formula Standardized Scores and Loadings Standardized Scores Standardized Loadings PLS Discriminant Analysis (PLS-DA) Hierarchical Cluster 113 113 116 117 120 123 123 123 125 125 126 129 129 130 130 131 131 132 134 135 135 138 138 138 139 139 140 140 141 141 142 142 142 143 143 143 144 Group Observations Using a Tree of Clusters Hierarchical Cluster Overview 144 146 Overview of Platforms for Clustering Observations Example of Clustering Launch the Hierarchical Cluster Platform Clustering Method Method for Distance Calculation Data Structure Not Enough Nonmissing Data Alert Transformations to Y, Columns Variables Hierarchical Cluster Report Dendrogram Report Distance Graph Illustration of Dendrogram and Distance Graph Clustering History Report Hierarchical Cluster Options Additional Examples of the Hierarchical Clustering Platform Example of a Distance Matrix Example of Wafer Defect Classification Using Spatial Measures Statistical Details Spatial Measures Choose Spatial Components Window Spatial Measures Reports Distance Method Formulas 146 148 150 151 151 152 154 154 156 156 156 157 158 158 163 163 165 167 167 167 168 169 K Means Cluster Group Observations Using Distances K Means Cluster Platform Overview Overview of Platforms for Clustering Observations Example of K Means Cluster Launch the K Means Cluster Platform Iterative Clustering Report Iterative Clustering Options Iterative Clustering Control Panel K Means NCluster= Report Cluster Comparison Report K Means NCluster= Report K Means NCluster= Report Options 171 171 173 173 174 177 178 179 179 181 182 182 182 Self Organizing Map Self Organizing Map Control Panel Self Organizing Map Report 184 184 185 Description of SOM Algorithm 185 Normal Mixtures Group Observations Using Probabilities Normal Mixtures Clustering Platform Overview Overview of Platforms for Clustering Observations Example of Normal Mixtures Clustering Launch the Normal Mixtures Clustering Platform Options Iterative Clustering Report Iterative Clustering Options Iterative Clustering Control Panel Normal Mixtures NCluster= Report Cluster Comparison Report Normal Mixtures NCluster= Report Normal Mixtures NCluster= Report Options Robust Normal Mixtures Robust Normal Mixtures Control Panel Robust Normal Mixture Reports Statistical Details for the Normal Mixtures Method Additional Details for Robust Normal Mixtures Latent Class Analysis Group Observations of Categorical Variables Latent Class Analysis Platform Overview Example of Latent Class Analysis Launch the Latent Class Analysis Platform The Latent Class Analysis Report Latent Class Model for Clusters Report Latent Class Analysis Platform Options Latent Class Analysis Options Latent Class Model Options Additional Example of the Latent Class Analysis Platform Plot Probabilities of Cluster Membership Statistical Details for the Latent Class Analysis Platform Cluster Variables 187 187 189 189 190 192 193 193 194 194 197 197 197 197 199 200 200 201 201 203 203 205 205 208 208 209 211 211 212 212 212 214 216 Group Similar Variables into Representative Groups Cluster Variables Platform Overview Example of the Cluster Variables Platform 216 218 218 Launch the Cluster Variables Platform The Cluster Variables Report Color Map on Correlations Cluster Summary Cluster Members Standardized Components Cluster Variables Platform Options Additional Examples of the Cluster Variables Platform Example of Color Map on Correlations Example of Cluster Variables Platform for Dimension Reduction Cluster Variables Fit Models Statistical Details for the Cluster Variables Platform Variable Clustering Algorithm 219 220 220 221 221 222 222 223 223 224 224 225 227 227 Statistical Details Multivariate Methods Wide Linear Methods and the Singular Value Decomposition The Singular Value Decomposition The SVD and the Covariance Matrix The SVD and the Inverse Covariance Matrix Calculating the SVD References Index Multivariate Methods 229 229 231 231 232 232 233 234 238 238 ... to Multivariate Analysis Overview of Multivariate Techniques Correlations and Multivariate Techniques Explore the Multidimensional Behavior of Variables Launch the Multivariate Platform The Multivariate. .. Experiments Guide Multivariate Methods Read about techniques for analyzing several variables simultaneously Describes these Analyze > Multivariate Methods menu platforms: • Multivariate • Principal... manual is as follows: SAS Institute Inc 2017 JMP® 13 Multivariate Methods, Second Edition Cary, NC: SAS Institute Inc JMPđ 13 Multivariate Methods, Second Edition Copyright â 2017, SAS Institute