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 Pro, you can do the following:|
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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 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.