residuallimit Documentation


PLS_Toolbox Documentation: residuallimit	< rescale	reversebytes >

residuallimit

Purpose

Esitmates confidence limits for sum squared residuals.

Synopsis

[rescl,s] = residuallimit(residuals,cl,options)

rescl = residuallimit(s,cl,options)

options = residuallimit('options');.

Description

Inputs are a matrix of residuals residuals, and the frational confidence limit cl where 0<cl<1 {default = 0.95}. For example, for a PCA model X = TP^T + E, the input residuals is the matrix E which can be calculated using the datahat function. Optional input options is discussed below.

The output is the estimated residual limit rescl. An additional output containing eigenvalues of E s is returned when using the Jackson-Mudholkar algorithm. To improve speed, s can be used in place of residuals in subsequent calls to RESIDUALLIMIT for the same data.

See Jackson (1991) for the details of the calculation.

Options

options = a structure array with the following fields:

name: 'options', name indicating that this is an options structure,

algorithm: [ {'jm'} | 'chi2' | 'auto' ], governs choice of algorithm:

'jm', uses Jackson-Mudholkar method (slower, more robust),

'chi2', uses chi-squared moment method (faster, less robust with outliers), and

'auto' automatically selects based on data size (<300 rows or columns, use 'jm', otherwise, use 'chi2')

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

Examples

For a model model caluclated using the PCA function

rescl = reslim(model.detail.ssq(:,2),0.95);