Modeling and Multivariate Methods - SAS

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456 Correlations and Multivariate Techniques Chapter 17 Computations and Statistical Details computes Kendall’s τ b where: Note the following: • The sgn(z) is equal to 1 if z>0, 0 if z=0, and –1 if z
Chapter 17 Correlations and Multivariate Techniques 457 Computations and Statistical Details Inverse Correlation Matrix The inverse correlation matrix provides useful multivariate information. The diagonal elements of the inverse correlation matrix, sometimes called the variance inflation factors (VIF), are a function of how closely the variable is a linear function of the other variables. Specifically, if the correlation matrix is denoted R and the inverse correlation matrix is denoted R -1 , the diagonal element is denoted r ii and is computed as where R i 2 is the coefficient of variation from the model regressing the i th explanatory variable on the other explanatory variables. Thus, a large r ii indicates that the ith variable is highly correlated with any number of the other variables. Distance Measures The Outlier Distance plot shows the Mahalanobis distance of each point from the multivariate mean (centroid). The Mahalanobis distance takes into account the correlation structure of the data as well as the individual scales. For each value, the distance is denoted d i and is computed as where: r ii 1 = VIF i = --------------- 2 1 – R i d i = ( Y i – Y)'S – 1 ( Y i – Y) Y i is the data for the i th row Y is the row of means S is the estimated covariance matrix for the data The reference line (Mason and Young, 2002) drawn on the Mahalanobis Distance plot is computed as AxF × nvars where A is related to the number of observations and number of variables, nvars is the number of variables, and the computation for F in formula editor notation is: F Quantile(0.95, nvars, n–nvars–1, centered at 0). If a variable is an exact linear combination of other variables, then the correlation matrix is singular and the row and the column for that variable are zeroed out. The generalized inverse that results is still valid for forming the distances. The T 2 distance is just the square of the Mahalanobis distance, so T 2 i = d 2 i . The upper control limit on the T 2 is ( n – 1) 2 UCL = ------------------ β n a; p 2 -- ;------------------- n – p – 1 2 where n = number of observations
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Version 10 Modeling and Multivariat
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INDIRECT OR CONSEQUENTIAL DAMAGES O
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6 Emphasis Options for Standard Lea
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8 Models with Crossed, Interaction,
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10 8 Analyzing Screening Designs Us
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12 Examining the Residuals . . . .
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14 Response Frequencies . . . . . .
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16 19 Analyzing Principal Component
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18 Interpreting the Profiles . . .
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20 Discriminant Analysis . . . . .
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Contents Book Conventions. . . . .
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24 Learn about JMP Chapter 1 Book C
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26 Learn about JMP Chapter 1 Book C
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28 Learn about JMP Chapter 1 Additi
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30 Learn about JMP Chapter 1 Additi
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Contents Launch the Fit Model Platf
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Contents Example Using Standard Lea
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56 Fitting Standard Least Squares M
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136 Fitting Stepwise Regression Mod
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Contents Example of a Multiple Resp
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158 Fitting Multiple Response Model
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Contents Overview of Generalized Li
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180 Fitting Generalized Linear Mode
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200 Performing Logistic Regression
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Contents Overview of the Screening
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232 Analyzing Screening Designs Cha
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Contents Introduction to the Nonlin
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244 Performing Nonlinear Regression
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Contents Overview of Neural Network
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280 Creating Neural Networks Chapte
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Contents Launching the Platform. .
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296 Modeling Relationships With Gau
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Contents Overview of the Loglinear
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306 Fitting Dispersion Effects with
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Contents Introduction to Partitioni
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318 Recursively Partitioning Data C
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Contents Launch the Platform . . .
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354 Performing Time Series Analysis
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Contents The Categorical Platform .
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386 Performing Categorical Response
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Contents Introduction to Choice Mod
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404 Performing Choice Modeling Chap
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Contents Overview of the Partial Le
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508 Fitting Partial Least Squares M
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Contents Introduction to Item Respo
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Contents Surface Plots . . . . . .
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538 Plotting Surfaces Chapter 23 La
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548 Plotting Surfaces Chapter 23 Pl
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Contents Introduction to Profiling
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556 Visualizing, Optimizing, and Si
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640 References Becker, R.A. and Cle
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646 References Matsumoto, M. and Ni
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648 References Rawlings, J.O. (1988
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650 References Umetrics (1995), Mul
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Contents The Response Models . . .
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654 Statistical Details Appendix A
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690 Index Birth Death Subset.jmp 46
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692 Index Ellipses Transparency 451
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694 Index test for curvature 46 Kru
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696 Index Customizing 267 Nonlinear
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698 Index reliability analysis 453-
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700 Index Stable 363 Stable Inverti
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702 Index
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Modeling and Multivariate Methods - SAS

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