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covsel_mlr

variable selection using covsel, then multiple linear regression (MLR)

Calling sequence

model=covsel_mlr(x,y,split,lv,(centred))

Arguments

x, y:

the calibration dataset; dimensions (n x q) and (n x k) or Div structures

warning: when x is not square and of full rank, the MLR is computed with the Moore-Penrose pseudo-inverse of xx'

split:

parameter for the cross-validation:

- an integer: number of random blocs

- two integers [a b]: a random blocks ; b repetitions of the cross-validation

- a vector of dimension n attributing each observation to a block (numbers 1,2,...k for k blocks): blocks given by the vector

- a matrix (n x b ) of column-vectors of dimension n attributing each observation to a block (numbers 1,2,...k for k blocs): blocks given by each vector, b repetitions of the cross-validation

- 'vnbxx': venitian blinds, xx blocks; ex: 'vnb10' for 10 blocks

- 'jckxx': Jack knife, xx blocks; ex: 'jck8' for 8 blocks

lv:

the number of x-variables to be selected

(centred):

1=centred (by default); 0=not centred

model.err:

the standard errors of calibration aand cross-validation

model.err.d is a matrix (2 x lv x k); the lines are the rmsec and the rmsecv respectively

model.ypredcv:

the predicted values of y after cross-validation

model.ypredcv.d is a matrix of dimensions (n x q x k)

model.b:

the b-vector or vector of the regression coefficients

model.b.d is a matrix of dimensions (q x lv x k)

model.x_mean, model.y_mean:

means of x and y , a vector (q x 1) and a vector (k x 1)

x_ref:

model.x_ref

y_ref:

model.y_ref

model.center:

centering option applied; 1=centred; 0=not centred

model.method:

the method name; here: 'covsel_mlr'

model.var_selected:

the selected x-variables determined with all the y-variables, line (k+1), then ordered for each of the k y-variables, (lines 1 to k)

model.var_selected.d is of dimensions ((k+1) x lv )

Examples

[model]=covsel_mlr(x,y,50,20)
[model]=covsel_mlr(x,y,50,20,0)

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