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===Purpose=== | ===Purpose=== | ||
Continuum regression for multivariate y. | Continuum regression for multivariate y. | ||
===Synopsis=== | ===Synopsis=== | ||
:b = cr(x,y,lv,powers) | :b = cr(x,y,lv,powers) | ||
===Description=== | ===Description=== | ||
CR develops continuum regression models for a matrix of predictor variables (x | |||
For a | CR develops continuum regression models for a matrix of predictor variables X-block, (x), and vector or matrix of predicted variables Y-block, (y). Models are calculated for 1 to (lv) latent variables for each value of the continuum parameter specified in the row vector (powers). | ||
CR uses the de Jong, Wise & Ricker method for continuum regression (S. de Jong, B. M. Wise and N. L. Ricker, "Canonical Partial Least Squares and Continuum Power Regression," ''J. Chemo.'', '''15''', 85-100, 2001). It is a | |||
The algorithm used here is usually stable up to a continuum parameter of about 6 | The output is the matrix of regression vectors (b). For a Y-block with ''Ny'' variables, X-block with ''Nx'' variables, ''Lv'' latent variables (lv) and ''Np'' powers [size of (powers) is 1 by ''Np''], the output (b) is size ''Lv''*''Ny''*''Np'' by ''Nx''. The first block in (b) corresponds to the first power in powers and is ''Lv''*''Ny'' by ''Nx'' with the first row corresponding to a 1 latent variable model for the first Y variable. | ||
CR uses the de Jong, Wise & Ricker method for continuum regression (S. de Jong, B.M. Wise and N.L. Ricker, "Canonical Partial Least Squares and Continuum Power Regression," ''J. Chemo.'', '''15''', 85-100, 2001). It is a faster implementation of the Wise and Ricker method used in the previous POWERPLS. Note that results are identical for both methods for univariate Y, but not for multivariate Y, where the results from CR are typically slightly better. | |||
The algorithm used here is usually stable up to a continuum parameter of about 6 to 8, sometimes as high as 10 depending upon the problem. At powers this high, however, the models have essentially converged to the PCR solution. No instabilities at small powers have been noted. | |||
===See Also=== | ===See Also=== | ||
[[crcvrnd]], [[pcr]], [[pls]] | [[crcvrnd]], [[pcr]], [[pls]] | ||
Latest revision as of 15:12, 7 October 2008
Purpose
Continuum regression for multivariate y.
Synopsis
- b = cr(x,y,lv,powers)
Description
CR develops continuum regression models for a matrix of predictor variables X-block, (x), and vector or matrix of predicted variables Y-block, (y). Models are calculated for 1 to (lv) latent variables for each value of the continuum parameter specified in the row vector (powers).
The output is the matrix of regression vectors (b). For a Y-block with Ny variables, X-block with Nx variables, Lv latent variables (lv) and Np powers [size of (powers) is 1 by Np], the output (b) is size Lv*Ny*Np by Nx. The first block in (b) corresponds to the first power in powers and is Lv*Ny by Nx with the first row corresponding to a 1 latent variable model for the first Y variable.
CR uses the de Jong, Wise & Ricker method for continuum regression (S. de Jong, B.M. Wise and N.L. Ricker, "Canonical Partial Least Squares and Continuum Power Regression," J. Chemo., 15, 85-100, 2001). It is a faster implementation of the Wise and Ricker method used in the previous POWERPLS. Note that results are identical for both methods for univariate Y, but not for multivariate Y, where the results from CR are typically slightly better.
The algorithm used here is usually stable up to a continuum parameter of about 6 to 8, sometimes as high as 10 depending upon the problem. At powers this high, however, the models have essentially converged to the PCR solution. No instabilities at small powers have been noted.