Modeling and Multivariate Methods - SAS

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Contents Overview of the Partial Least Squares Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .507 Example of Partial Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .507 Launch the Partial Least Squares Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510 Launch through Multivariate Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510 Launching through Fit Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 Centering and Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 Impute Missing Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 Model Launch Control Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512 The Partial Least Squares Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 Model Fit Options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514 Partial Least Squares Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .520 Statistical Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .520
Chapter 21 Fitting Partial Least Squares Models 507 Overview of the Partial Least Squares Platform Overview of the Partial Least Squares Platform The Partial Least Squares (PLS) platform fits linear models based on linear combinations, called factors, of the explanatory variables (Xs). These factors are obtained in a way that attempts to maximize the covariance between the Xs and the response or responses (Ys). In this way, PLS exploits the correlations between the Xs and the Ys to reveal underlying latent structures. The PLS approach to model fitting is particularly useful when there are more explanatory variables than observations or when the explanatory variables are highly correlated. You can use PLS to fit a single model to several responses simultaneously. (Wold, 1995; Wold et al, 2001, Eriksson et al, 2006). Two model fitting algorithms are available: nonlinear iterative partial least squares (NIPALS) and a “statistically inspired modification of PLS” (SIMPLS) (de Jong, 1993; Boulesteix and Strimmer, 2006). The SIMPLS algorithm was developed with the goal of solving a specific optimality problem. For a single response, both methods give the same model. For multiple responses, there are slight differences. The platform uses the van der Voet T 2 test and cross validation to help you choose the optimal number of factors to extract. • In JMP, the platform uses the leave-one-out method of cross validation. • In JMP Pro, you can choose KFold or random holdback cross validation, or you can specify a validation column. If you prefer, you can also turn off validation. Note that leave-one-out cross validation can be obtained by setting the number of folds in KFold equal to the number of rows. In JMP Pro, in addition to fitting main effects, you can also fit polynomial, interaction, and categorical effects by using the Partial Least Squares personality in Fit Model. Example of Partial Least Squares We consider an example from spectrometric calibration, and area where partial least squares is very effective. Consider the Baltic.jmp data table. The data are reported in Umetrics (1995); the original source is Lindberg, Persson, and Wold (1983). Suppose that you are researching pollution in the Baltic Sea. You would like to use the spectra of samples of sea water to determine the amounts of three compounds that are present in these samples. The three compounds of interest are: lignin sulfonate (ls), which is pulp industry pollution; humic acid (ha), a natural forest product; and an optical whitener from detergent (dt). The amounts of these compounds in each of the samples are the responses, The predictors are spectral emission intensities measured at a range of wavelengths (v1–v27). For the purposes of calibrating the model, samples with known compositions are used. The calibration data consist of 16 samples of known concentrations of lignin sulfonate, humic acid, and detergent, with emission intensities recorded at 27 equidistant wavelengths. Use the Partial Least Squares platform to build a model for predicting the amount of the compounds from the spectral emission intensities. In the following, we describe the steps and show reports for JMP. Because different cross validation options are used in JMP Pro, JMP Pro results for the default Model Launch settings differ from those shown in the figures below. To duplicate the results below in JMP Pro, in the Model Launch window, enter 16 as the
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Version 10 Modeling and Multivariat
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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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Contents Overview of Stepwise Regre
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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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Contents Introduction to Logistic M
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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 Launch the Multivariate Pl
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444 Correlations and Multivariate T
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Page 482 and 483: Contents Principal Components. . .
Page 484 and 485: 484 Analyzing Principal Components
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556 Visualizing, Optimizing, and Si
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Contents Example of Model Compariso
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630 Comparing Model Performance Cha
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640 References Becker, R.A. and Cle
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642 References Draper, N. and Smith
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644 References Hooper, J. H. and Am
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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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