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===Purpose=== | ===Purpose=== | ||
Calculates the model estimate and residuals of the data. | Calculates the model estimate and residuals of the data. | ||
===Synopsis=== | ===Synopsis=== | ||
:xhat = datahat(model); | :xhat = datahat(model); | ||
:[xhat,resids] = datahat(model,''data''); | :[xhat,resids] = datahat(model,''data''); | ||
:[xhat,resids] = datahat(loadings,''data''); | |||
===Description=== | ===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'''<sub>cal</sub> such that '''X'''<sub>cal</sub> = '''TP'''<sup>T</sup> + '''E''', then '''X'''<sub>hat</sub> = '''TP'''<sup>T</sup> | |||
If optional input ''data'' is supplied then DATAHAT computes the model estimate of ''data'' | 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: | ||
Note that preprocessing in model will be performed before the residuals are calculated. If data is not provided, only xhat is available. | : '''X'''<sub>cal</sub> such that '''X'''<sub>cal</sub> = '''TP'''<sup>T</sup> + '''E''', then '''X'''<sub>hat</sub> = '''TP'''<sup>T</sup> | ||
Note that DATAHAT works with almost all standard model structures. | that is: | ||
:'''X'''<sub>cal</sub> = '''TP'''<sup>T</sup> + '''E''' = '''X'''<sub>hat</sub> + '''E'''. | |||
If optional input (''data'') is supplied then DATAHAT computes the model estimate of (''data'') which will be output in (xhat). For the PCA model of matrix '''X'''<sub>cal</sub>, and (''data'') is a data matrix '''X'''<sub>new</sub> then: | |||
:'''X'''<sub>hat</sub> = '''X'''<sub>new</sub>'''PP'''<sup>T</sup> = '''T'''<sub>new</sub>'''P'''<sup>T</sup> | |||
and the output (resids) is a matrix with the corresponding residuals: | |||
:'''E''' = '''X'''<sub>new</sub>-'''X'''<sub>new</sub>'''PP'''<sup>T</sup> = '''X'''<sub>new</sub>('''I'''-'''PP'''<sup>T</sup>) | |||
If (''data'') is '''X'''<sub>cal</sub> then: | |||
:'''X'''<sub>hat</sub> = '''TP'''<sup>T</sup> | |||
and resids is: | |||
:'''E''' = '''X'''<sub>cal</sub>('''I'''-'''PP'''<sup>T</sup>). | |||
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 or a cell-array of loadings can be supplied in place of model (for use with multiway models only). | |||
===See Also=== | ===See Also=== | ||
[[analysis]], [[parafac]] | [[analysis]], [[npls]], [[parafac]], [[parafac2]], [[qconcalc]], [[residuallimit]], [[tconcalc]], [[tsqmtx]], [[tsqqmtx]], [[tucker]], [[varcap]], [[varcapy]] | ||
Latest revision as of 13:05, 22 February 2013
Purpose
Calculates the model estimate and residuals of the data.
Synopsis
- xhat = datahat(model);
- [xhat,resids] = datahat(model,data);
- [xhat,resids] = datahat(loadings,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:
- Xcal such that Xcal = TPT + E, then Xhat = TPT
that is:
- Xcal = TPT + E = Xhat + E.
If optional input (data) is supplied then DATAHAT computes the model estimate of (data) which will be output in (xhat). For the PCA model of matrix Xcal, and (data) is a data matrix Xnew then:
- Xhat = XnewPPT = TnewPT
and the output (resids) is a matrix with the corresponding residuals:
- E = Xnew-XnewPPT = Xnew(I-PPT)
If (data) is Xcal then:
- Xhat = TPT
and resids is:
- E = Xcal(I-PPT).
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 or a cell-array of loadings can be supplied in place of model (for use with multiway models only).
See Also
analysis, npls, parafac, parafac2, qconcalc, residuallimit, tconcalc, tsqmtx, tsqqmtx, tucker, varcap, varcapy