Datahat

Purpose

Calculates the model estimate and residuals of the data.

Synopsis

xhat = datahat(model);

[xhat,resids] = datahat(model,data);

Description

Given a standard model structure (model), DATAHAT computes the model estimate of the data (xhat). For example, if (model) is a PCA model of a matrix X_cal such that X_cal = TP^T + E, then X_hat = TP^T i.e., X_cal = TP^T + E = X_hat + E).

If optional input (data) is supplied then DATAHAT computes the model estimate of (data) that is output in (xhat). For the PCA model of matrix X_cal, and (data) is a data matrix X_new then X_hat = X_newPP^T = T_newP^T. The output (resids) is a matrix with the corresponding residuals E = X_new-X_newPP^T = X_new(I-PP^T). If (data) is X_cal then X_hat = TP^T and resids is E = X_cal(I-PP^T).

Note that preprocessing in (model) will be performed before the residuals are calculated. If data is not provided, only (xhat) of the calibration data is available.

Note that DATAHAT works with almost all standard model structures.

See Also

analysis, npls, parafac, parafac2, qconcalc, residuallimit, tconcalc, tsqmtx, tsqqmtx, tucker, varcap, varcapy