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.