Overview of the Partial Least Squares Platform
In contrast to ordinary least squares, PLS can be used when the predictors outnumber the observations. PLS is used widely in modeling high-dimensional data in areas such as spectroscopy, chemometrics, genomics, psychology, education, economics, political science, and environmental science.
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. See Garthwaite (1994), Wold (1994), Wold et al. (2001), Eriksson et al. (2006), and Cox and Gaudard (2013).
Two model fitting algorithms are available: nonlinear iterative partial least squares (NIPALS) and a “statistically inspired modification of PLS” (SIMPLS). For more information about NIPALS, see Wold (1980). For more information about SIMPLS, see De Jong (1993). For a description of both methods, see Boulesteix and Strimmer (2007). 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.
In JMP, the PLS platform is accessible only through Analyze > Multivariate Methods > Partial Least Squares. In JMP Pro, you can also access the Partial Least Squares personality through Analyze > Fit Model.
In JMP Pro, you can do the following:
• Conduct PLS-DA (PLS discriminant analysis) by fitting responses with a nominal modeling type, using the Partial Least Squares personality in Fit Model.
• Fit polynomial, interaction, and categorical effects, using the Partial Least Squares personality in Fit Model.
• Select among several methods for validation and cross validation.
• Impute missing data.
• Obtain bootstrap estimates of the distributions of various statistics. Right-click in the report of interest. For more information about bootstrap estimates, see Basic Analysis.
Partial Least Squares uses the van der Voet T2 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. You can also choose not to use validation.
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In JMP Pro, you can choose KFold, Leave-One-Out, or random holdback cross validation, or you can specify a validation column. You can also choose not to use validation.