# Pcr

## Contents

### Purpose

Principal Components Regression: multivariate inverse least squares regression.

### Synopsis

- model = pcr(x,y,ncomp,
*options*) %identifies model (calibration step) - pred = pcr(x,model,
*options*) %applies model to a new X-block - valid = pcr(x,y,model,
*options*) %applies model to a new X-block, with corresponding new Y values - pcr % Launches an Analysis window with PCR as the selected method.

### Description

PCR calculates a single principal components regression model using the given number of components `ncomp` to predict `y` from measurements `x`, OR applies an existing PCR model to a new set of data `x`

To make predictions, the inputs are `x` the new predictor x-block (2-way array class "double" or "dataset"), and `model` the PCR model. The output `pred` is a structure, similar to `model`, that contains scores, predictions, etc. for the new data.

If new y-block measurements are also available for the new data, then the inputs are `x` the new x-block (2-way array class "double" or "dataset"), `y` the new y-block (2-way array class "double" or "dataset"), and `model` the PCR model to apply. The output `valid` is a structure, similar to `model`, that contains scores, predictions, and additional y-block statistics etc. for the new data.

In prediction and validation modes, the same model structure is used but predictions are provided in the `model.detail.pred` field.

Note: Calling **pcr** with no inputs starts the graphical user interface (GUI) for this analysis method.

#### Inputs

**x**= X-block data (2-way array or DataSet Object)**y**= Y-block data (2-way array or DataSet Object)**ncomp**= number of components to to be calculated (positive integer scalar).

#### Optional Inputs

**options**discussed below

#### Outputs

The output is a standard model structure with the following fields (see Standard Model Structure):

**modeltype**: 'PCR',**datasource**: structure array with information about input data,**date**: date of creation,**time**: time of creation,**info**: additional model information,**reg**: regression vector,**loads**: cell array with model loadings for each mode/dimension,**pred**: 2 element cell array containing model predictions for each input block (when options.blockdetail='normal' x-block predictions are not saved and this will be an empty array), and the y-block predictions.**tsqs**: cell array with T^{2}values for each mode,**ssqresiduals**: cell array with sum of squares residuals for each mode,**description**: cell array with text description of model, and**detail**: sub-structure with additional model details and results.

### Options

*options* = a structure array with the following fields:

**display**: [ 'off' | {'on'} ], governs level of display to command window,

**plots**: [ 'none' | {'final'} ], governs level of plotting,

**outputversion**: [ 2 | {3} ], governs output format (discussed below),

**preprocessing**: {[] []}, two element cell array containing preprocessing structures (see PREPROCESS) defining preprocessing to use on the x- and y-blocks (first and second elements respectively),

**algorithm**: [ {'svd'} | ' robustpcr' | ' correlationpcr' | 'frpcr' ], governs which algorithm to use.- 'svd' = standard singular value decomposition algorithm.
- 'robustpcr' = robust algorithm with automatic outlier detection.
- 'correlationpcr' = standard PCR with re-ordering of factors in order of y-variance captured.
- 'frpcr' = full-ratio PCR (a.k.a. optimized scaling) with automatic sample scale correction. Note that with FRPCR, models generally perform better without mean-centering on the x-block.

**blockdetails**: [ 'compact' | {'standard'} | 'all' ] level of detail (predictions, raw residuals, and calibration data) included in the model.

- ‘Standard’ = the predictions and raw residuals for the X-block as well as the X-block itself are not stored in the model to reduce its size in memory. Specifically, these fields in the model object are left empty: 'model.pred{1}', 'model.detail.res{1}', 'model.detail.data{1}'.
- ‘Compact’ = for this function, 'compact' is identical to 'standard'.
- 'All' = keep predictions, raw residuals for both X- & Y-blocks as well as the X- & Y-blocks themselves.

**confidencelimit**: [ {'0.95'} ], confidence level for Q and T2 limits. A value of zero (0) disables calculation of confidence limits,

**roptions**: structure of options to pass to**rpcr**(robust PCR engine from the Libra Toolbox). Only used when algorithm is 'robustpcr',

**alpha**: [ {0.75} ], (1-alpha) measures the number of outliers the algorithm should resist. Any value between 0.5 and 1 may be specified. These options are only used when algorithm is 'robustpcr'.

**intadjust**: [ {0} ], if equal to one, the intercept adjustment for the LTS-regression will be calculated. See**ltsregres**for details (Libra Toolbox).

The default options can be retreived using: options = pcr('options');.

#### OUTPUTVERSION

By default (options.outputversion = 3) the output of the function is a standard model structure model. If options.outputversion = 2, the output format is:

- [b,ssq,t,p] = pcr(x,y,ncomp,
*options*)

where the outputs are

**b**= matrix of regression vectors or matrices for each number of principal components up to ncomp,

**ssq**= the sum of squares information,

**t**= x-block scores, and

**p**= x-block loadings.

Note: The regression matrices are ordered in **b** such that each *Ny* (number of y-block variables) rows correspond to the regression matrix for that particular number of principal components.

### See Also

analysis, crossval, frpcr, mlr, modelstruct, pca, pls, preprocess, ridge