Observations and loadings vectors

In the Plot/List tab dialogs the vectors found in the Items box with data type Observations and loadings are row vectors with the same “shape” as an observation, i.e., with one row per variable.

See the table for the vectors available and their description in alphabetical order. The rightmost column displays the plot/list/spreadsheet where the vector is available, when applicable, in bold text if the vector is displayed by default.

Vector

Description

Displayed

Batch VIP

?

The Batch Variable Importance plot (Batch VIP) is ?available for batch level models and displays the overall importance of the ?variable on the final quality of the batch. With phases, the plot displays the ?importance of a variable by phase. With a PLS model, the Batch VIP displays the ?plot for one y-variable at a time, with a column per variable and per selected ?phase.

Note: The Batch VIP is only available for scores batch ?level datasets.

Batch | Variable ?importance plot

c

For every dimension in the PLS model there is a c vector. ?It contains the Y loading weights used to linearly combine the Y's to form the Y ?score vector u. This means the c vector actually expresses the correlation ?between the Y's and the X score vector t.

Home | Loadings

c(corr)

Y loading weight c scaled as a correlation coefficient ?between Y and u.

Home | Loadings

Analyze | Biplot

ccv

Y loading weight c for a selected model dimension, ?computed from the selected cross validation round.

?

ccvSE

Jack-knife standard error of the Y loading weight c ?computed from the rounds of cross validation.

?

co

Orthogonal Y loading weights co combine the Y variables ?(first dimension) or the Y residuals (subsequent dimensions) to form the scores ?Uo.

These orthogonal Y loading weights are selected so as to ?minimize the correlation between Uo and T, thereby indirectly between Uo and X. ?Available for OPLS and O2PLS models.

?

cocv

Orthogonal Y loading weights co from the Y-part of the ?model, for a selected model dimension, computed from the selected ?cross-validation round. Available for OPLS and O2PLS models.

?

Coeff

PLS/OPLS/O2PLS regression coefficients corresponding to ?the unscaled and uncentered X and Y. This vector is Cumulative over all ?components up to the selected one.

Home | Coefficients

CoeffC

PLS/OPLS/O2PLS regression coefficients corresponding to ?the unscaled but centered X and unscaled Y. This vector is Cumulative over all ?components up to the selected one.

Home | Coefficients

CoeffCS

?

PLS/OPLS/O2PLS regression coefficients corresponding to ?centered and scaled X, and scaled (but uncentered) Y. This vector is Cumulative ?over all components up to the selected one.

Home | ?Coefficients

CoeffCScv

PLS/OPLS/O2PLS regression coefficients corresponding to ?the centered and scaled X and the scaled (but uncentered) Y computed from the ?selected cross validation round.

?

CoeffCScvSE

Jack-knife standard error of the coefficients CoeffCS ?computed from all rounds of cross validation.

?

CoeffMLR

PLS/OPLS/O2PLS regression coefficients corresponding to ?the scaled and centered X but unscaled and uncentered Y. This vector is ?Cumulative over all components up to the selected one.

Home | Coefficients

CoeffRot

Rotated PLS/OPLS/O2PLS regression coefficients ?corresponding to the unscaled and uncentered X and Y. This vector is Cumulative ?over all components up to the selected one.

Home | Coefficients

?

MPowX

The modeling power?of variable X is the fraction of its ?standard deviation explained by the model after the specified ?component.

?

Num

Index number: 1, 2, 3 etc.

?

ObsDS

Observation in the dataset, selected in the Data ?box, in original units.

?

ObsPS

Observation in the current predictionset, in original ?units. There is only one current predictionset at a time although many can be ?specified.

?

p

Loadings of the X-part of the model.

With a PCA model, the loadings are the coefficients with ?which the X variables are combined to form the X scores, t.

The loading, p, for a selected PCA dimension, represent ?the importance of the X variables in that dimension.

With a PLS model, p expresses the importance of the ?variables in approximating X in the selected component.

Home | ?Loadings

p(corr)

?

X loading p scaled as a correlation coefficient between X ?and t.

Home | Loadings

Analyze | Biplot

pc

X loading p and Y loading weight c combined to one ?vector.

Home | Loadings

pc(corr)

X loading p and Y loading weight c scaled as correlation ?coefficients between X and t (p) and Y and u (c), and combined to one ?vector.

Home | Loadings

Analyze | Biplot

pccvSE

Jack-knife standard error of the combined X loading p and ?Y loading weight c computed from all rounds of cross validation.

?

pcv

X loading p for a selected model dimension, computed from ?the selected cross validation round.

?

pcvSE

Jack-knife standard error of the X loading p computed ?from all rounds of cross validation.

?

po

Orthogonal loading po of the X-part of the OPLS/O2PLS ?model. po expresses the unique variability in X not found in Y, i.e., X ?variation orthogonal to Y, in the selected component. Available for OPLS and ?O2PLS models.

Home | Loadings

Home | Loadings | Orth ?X

po(corr)

Orthogonal loading po of the X-part of the OPLS/O2PLS ?model, scaled as the correlation coefficient between X and to, in the selected ?component. Available for OPLS and O2PLS models.

?

pocv

Orthogonal loading po of the X-part of the OPLS/O2PLS ?model, for a selected model dimension, computed from the selected cross ?validation round. Available for OPLS and O2PLS models.

?

poso

Orthogonal loading po of the X-part and the projection of ?to onto Y, so, combined to one vector. Available for OPLS and O2PLS.

Home | ?Loadings

Home | ?Loadings | Orth X

pq

X loading weight p and Y loading weight q combined to one ?vector. Available for OPLS and O2PLS.

Home | Loadings

Home | Loadings | Pred ?X-Y

q

Loadings of the Y-part of the OPLS/O2PLS model.

q expresses the importance of the variables in ?approximating Y variation correlated to X, in the selected component. Y ?variables with large q (positive or negative) are highly correlated with t (and ?X).

Home | Loadings

Home | Loadings | Pred ?X-Y

qcv

Y loading q for a selected model dimension, computed from ?the selected cross validation round. Available for OPLS and O2PLS ?models.

?

Q2VX, ?Q2VY

Predicted fraction, according to cross validation, of the ?variation of the X (PCA) and Y variables (PLS/OPLS/O2PLS), for the selected ?component.

Home | Summary of ?fit | Component contribution

Q2VXCum, ?Q2VYCum

Cumulative predicted fraction, according to cross ?validation, of the variation of the X variables (PCA model) or the Y variables ?(PLS/OPLS/O2PLS model).

Home | Summary of ?fit

qo

Orthogonal loading qo of the Y-part of the OPLS/O2PLS ?model.

qo expresses the unique variability in Y not found in X, ?i.e., Y variation orthogonal to X, in the selected component.

Home | Loadings | Orth ?Y

qocv

Orthogonal loading qo of the Y-part of the OPLS/O2PLS ?model, for a selected model dimension, computed from the selected cross ?validation round.

?

qor

qo and r combined to one vector. Available for OPLS and ?O2PLS.

Home | Loadings | Orth ?Y

r

R is the projection of uo onto X.

R contains non-zero entries when the score matrix Uo is ?not completely orthogonal to X. The norm of this matrix is usually very small ?but is used to enhance the predictions of X. Available for OPLS and ?O2PLS.

Home | Loadings | Orth ?Y

R2VX

Explained fraction of the variation of the X variables, ?for the selected component.

Home | Summary of ?fit | Component contribution

R2VXAdj

Explained fraction of the variation of the X variables, ?adjusted for degrees of freedom, for the selected component.

Home | Summary of ?fit | Component contribution

R2VXAdjCum

Cumulative explained fraction of the variation of the X ?variables, adjusted for degrees of freedom.

Home | X/Y Overview

R2VXCum

Cumulative explained fraction of the variation of the X ?variables.

Home | X/Y ?Overview

R2VY

Explained fraction of the variation of the Y variables, ?for the selected component.

Home | Summary of ?fit | Component contribution

R2VYAdj

?

Explained fraction of the variation of the Y variables, ?adjusted for degrees of freedom, for the selected component.

Home | Summary of ?fit | Component contribution

R2VYAdjCum

?

Cumulative explained fraction of the variation of the Y ?variables, adjusted for degrees of freedom.

Home | Summary of fit | X/Y ?overview

R2VYCum

Cumulative explained fraction of the variation of the Y ?variables.

Home | Summary of fit | X/Y ?overview

RMSEcv

Root Mean Square Error, computed from the selected cross ?validation round.

Analyze | RMSECV

RMSEE

Root Mean Square Error of the Estimation (the fit) for ?observations in the workset.

?

RMSEP

Root Mean Square Error of the Prediction for observations ?in the predictionset.

Predict | Y PS | Scatter

Predict | Y PS | Line

S2VX

Residual variance of the X variables, after the selected ?component, scaled as specified in the workset.

?

S2VY

Residual variance of the Y variables, after the selected ?component, scaled as specified in the workset.

?

so

So is the projection of to onto Y.

So contains non-zero entries when the score matrix To is ?not completely orthogonal to Y. The norm of this matrix is usually very small ?but is used to enhance the predictions of Y. Available for OPLS and O2PLS ?models.

Home | Loadings | Orth ?X

VarID

Numerical variable identifiers, primary or ?secondary.

All lists displaying variables, for instance Home | Coefficients | List

VIP

Variable Influence on the Projection. It provides the ?influence of every term in the matrix X on all the Y's. Terms with VIP>1 have ?an above average influence on Y. This vector is Cumulative over all components ?up to the selected one.

Home | ?VIP

VIPcv

VIP computed from the selected cross validation ?round.

?

VIPcvSE

Jack-knife standard error of the VIP computed from all ?rounds of cross validation.

?

VIPorth

Orthogonal variable importance for the projection, ?VIPorth, summarizes the importance of the variables explaining the part of X ?orthogonal to Y. Terms with VIP > 1 have an above average influence on the ?model.

?

VIPpred

Predictive variable importance for the projection, ?VIPpred, summarizes the importance of the variables explaining the part of X ?related to Y. Terms with VIP > 1 have an above average influence on the ?model.

?

w

?

X loading weight that combine the X variables (first ?dimension) or the X residuals (subsequent dimensions) to form the scores t. This ?loading weight is selected so as to maximize the correlation between t and u, ?thereby indirectly between t and Y.

X variables with large w's (positive or negative) are ?highly correlated with u (and Y).

Home | Loadings

w*

?

X loading weight that combines the original X variables ?(not their residuals in contrast to w) to form the scores t.

In the first dimension w* is equal to w.

w* is related to the correlation between the X variables ?and the Y scores u.

W* = ?W(P'W)-1

X variables with large w* (positive or negative) are ?highly correlated with u (and Y).

Home | Loadings

w*c

X loading weight w* and Y loading weight c combined to ?one vector.

Home | ?Loadings

w*ccvSE

?

Jack-knife standard error of the combined X loading ?weight w* and Y loading weight c computed from all rounds of cross ?validation.

?

w*cv

X loading weight w*, for a selected model dimension, ?computed from the selected cross validation round.

?

w*cvSE

Jack-knife standard error of the X loading weight w* ?computed from all rounds of cross validation.

?

wcv

X loading weight w, for a selected model dimension, ?computed from the selected cross validation round.

?

wcvSE

Jack-knife standard error of the X loading weight w ?computed from all rounds of cross validation.

?

wo

Orthogonal loading weight wo of the X-part of the ?OPLS/O2PLS model. It combines the X residuals to form the orthogonal X score to. ?This loading weight is selected so as to minimize the correlation between to and ?u, thereby indirectly between to and Y.

?

wocv

Orthogonal loading weight wo of the X-part of the ?OPLS/O2PLS model, for a selected model dimension, computed from the selected ?cross validation round.

?

Xavg

Averages of X variables, in original units. If the ?variable is transformed, the average is in the transformed metric.

?

XObs

X variables for the selected observation in the workset ?in original units. Can be displayed in transformed or scaled units.

?

XObsPred

Reconstructed observations as X=TP’ from the workset. Can ?be displayed in transformed or scaled units.

?

XObsPredPS

Reconstructed observations as X=TP’ from the ?predictionset. Can be displayed in transformed or scaled units.

?

XObsRes

Residuals of observations (X space) in the workset, in ?original units. Can be displayed in transformed or scaled units.

?

XObsResPS

Residuals of observations (X space) in the predictionset, ?in original units. Can be displayed in transformed or scaled units.

?

Xws

Scaling weights of the X variables.

?

YRelatedProfile

Displays the estimated pure profiles of the underlying ?constituents in X under the assumption of additive Y-variables.

Estimation includes a linear transformation of the ?Coefficient matrix, Bp(BpTBp)-1, where Bp is the ?Coefficient matrix using only the predictive components to compute the ?Coefficient matrix (i.e., the components orthogonal to Y are not included in the ?computation of Bp). Available for OPLS and O2PLS models.

Analyze | Y-related ?profiles

Yavg

Averages of Y variables, in original units. If the ?variable is transformed, the average is in the transformed metric.

?

YObs

Y variables for the selected observation in the workset ?in original units. Can be displayed in transformed or scaled units.

?

YObsRes

Residuals of observations (Y space) in the workset, in ?original units. Can be displayed in transformed or scaled units.

?

YObsResPS

Residuals of observations (Y space) in the predictionset, ?in original units. Can be displayed in transformed or scaled units.

?

Yws

Scaling weights of the Y variables.