Description Details Author(s) References See Also Examples

Implements the LS-PLS (least squares - partial least squares) method described in for instance J<c3><b8>rgensen, K., Segtnan, V. H., Thyholt, K., N<c3><a6>s, T. (2004) "A Comparison of Methods for Analysing Regression Models with Both Spectral and Designed Variables" Journal of Chemometrics, 18(10), 451–464, <doi:10.1002/cem.890>.

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LS-PLS (least squares–partial least squares) models are written on the form

*Y = X β + T1
gamma1 + … + Tk gammak + E,*

where the terms *Ti* are one or more matrices *Zij*
separated by a colon (:), i.e., *Zi1:Zi2:...:Zil*. Multi-response models are
possible, in wich case *Y* should be a matrix.

The model is fitted from left to right. First *Y* is fitted to
*X* using least squares (LS) regression and the residuals
calculated.
For each *i*, the matrices *Zi1*, ..., *Zil*
are orthogonalised against the variables used in the regression sofar
(when *i = 1*, this means *X*).
The residuals from the LS regression are used as the response in PLS
regressions with the orthogonalised matrices as predictors (one PLS
regression for each matrix), and the desired number of PLS components
from each matrix are included among the LS prediction variables.
The LS regression is then refit with the new variables, and new
residuals calculated.

The function to fit LS-PLS models is `lspls`

. A typical
usage to fit the model

*Y = Xβ + Z gamma + V1:V2 eta + W theta + E*

would be

1 2 |

The first argument is the formula describing the model.
`X`

is fit first, using LS. Then PLS scores from `Z`

(orthogonalised) are added. Then PLS scores from `V1`

and
`V2`

are added (simultaneously), and finally PLS scores from
`W`

. The next argument, `ncomp`

, specifies the number of
components to use from each PLS: 3 `Z`

score vectors, 2 `V1`

score vectors, 1 `V2`

score vector and 2 `W`

score vectors.
Finally, `mydata`

should be a data frame with matrices `y`

,
`X`

, `Z`

, `V1`

, `V2`

and `W`

(for
single-response models, `y`

can be a vector).

Currently, score plots and loading plots of fitted models are
implemented. `plot(mod, "scores")`

gives score plots for each PLS
regression, and `plot(mod, "loadings")`

gives loading plots.

There is a `predict`

method to predict response or score values
from new data

1 | ```
predict(mod, newdata = mynewdata)
``` |

(This predicts response values. Use `type = "scores"`

to get
scores.) Also, the standard functions `resid`

and `fitted`

can be used to extract the residuals and fitted values.

In order to determine the number of components to use from each matrix, one can use cross-validation:

1 2 |

In `lsplsCv`

, `ncomp`

gives the maximal number of components to
test. The argument `segments`

specifies the number of segments to
use. One can specify the type of segments to use (random (default),
consequtive or interleaved) with the argument `segment.type`

.
Alternatively, one can supply the segments explicitly with
`segments`

. See `lsplsCv`

for details.

One can plot cross-validated RMSEP values with `plot(cvmod)`

.
(Similarly, `plot(cvmod, "MSEP")`

plots MSEP values.) This makes
it easier to determine the optimal number of components for each PLS.
See `plot.lsplsCv`

for details. To calculate the RMSEP or
MSEP values explicitly, one can use the function `RMSEP`

or
`MSEP`

.

Bj<c3><b8>rn-Helge Mevik [aut, cre]

Maintainer: Bj<c3><b8>rn-Helge Mevik <b-h@mevik.net>

Jørgensen, K., Segtnan, V. H., Thyholt, K., Næs, T. (2004) A
Comparison of Methods for Analysing Regression Models with Both
Spectral and Designed Variables.
*Journal of Chemometrics*, **18**(10), 451–464.

Jørgensen, K., Mevik, B.-H., Næs, T. Combining Designed Experiments with Several Blocks of Spectroscopic Data. (Submitted)

Mevik, B.-H., Jørgensen, K., Måge, I., Næs, T. LS-PLS: Combining Categorical Design Variables with Blocks of Spectroscopic Measurements. (Submitted)

`lspls`

, `lsplsCv`

, `plot.lspls`

,
`plot.lsplsCv`

1 | ```
## FIXME
``` |

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