Jmlimit

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Purpose

Confidence limits for Q residuals via Jackson-Mudholkar.

Synopsis

rescl = jmlimit(pc,s,cl)
cl = jmlimit(pc,s,Q,2);

Description

JMLIMIT estimates confidence limits for Q residuals based on the Jackson-Mudholkar method. See Jackson, J.E., "A User's Guide to Principal Components", John Wiley & Sons, New York, NY (1991), and the discussion in the Chemometrics Tutorial on PCA.

Inputs are the number of PCs used pc, the vector of eigenvalues of the residuals' covariance (s), and the confidence limit (cl) expressed as a fraction (e.g. 0.95). Note that for a PCA model structure, model, that the eigenvalues can be found in model.detail.ssq(:,2).

The output rescl is the confidence limit based on the method of Jackson and Mudholkar. See chilimit for an alternate method of residual limit calculation based on chi squared.

Do inverse calculation with flag=2:

cl = jmlimit(pc,s,Q,2);

where Q is the sum of squares residuals from a model and "2" is a flag indicating the inverse calculation.

Note: The input pc is used to indicate which eigenvalues in s are to be considered as residuals. Only eigenvalues s(j), j>pc, are used as residuals. For example, s is from a PCA model built with ncomp = pc and s = model.detail.ssq(:,2), then call jmlimit(ncomp, s, cl, flag) to get the limit. However, if s represents eigenvalues of the residuals' covariance then call jmlimit(0, s, cl, flag) so as to include the full residuals.

Examples

rescl = jmlimit(2,ssq(:,2),0.95);

For a PCA model contained in the structure model:

rescl = jmlimit(4,model.detail.ssq(:,2),0.99);

See Also

chilimit, analysis, pca, residuallimit