TCSCP

Transforms coefficients from a second order response surface model generated from squares and crossproducts of centered variables to a model using uncentered variables.

Required Arguments

XMEAN — Vector of length NVAR containing the means of the variables. (Input)

SCPM — Vector of length NVAR(NVAR + 1)/2 containing the means of the generated square and crossproduct variables. (Input)

 

Elements	Description
1 to NVAR	Squared variable means
NVAR+ 1 to NVAR * (NVAR + 1)/2	Crossproduct variable means

BC — Vector of length NVAR * (NVAR + 3)/2 + 1 containing the coefficients for the centered variables. (Input)
Here, the fitted model is

 

where zj = xj ‑ XMEAN(j) and mjk = j * NVAR ‑ j(j ‑ 1)/2 + k ‑ j. These regression coefficients can come from a regression using variables generated by routine GCSCP with the option ICEN = 1.

B — Vector of length NVAR * (NVAR + 3)/2 + 1 containing the coefficients of the uncentered variables. (Output)
Here, the model uses the original x variables, i.e.,

 

Optional Arguments

NVAR — Number of variables. (Input)
Default: NVAR = size (XMEAN,1).

FORTRAN 90 Interface

Generic: CALL TCSCP (XMEAN, SCPM, BC, B [, …])

Specific: The specific interface names are S_TCSCP and D_TCSCP.

FORTRAN 77 Interface

Single: CALL TCSCP (NVAR, XMEAN, SCPM, BC, B)

Double: The double precision name is DTCSCP.

Description

Routine TCSCP transforms coefficients from a second-order response surface model fitted using squares and crossproducts of centered variables into a model using the original uncentered variables. Let xij be the i-th setting of the j-th variable (i = 1, 2, …, n; j = 1, 2, …, m). Denote the means (stored in XMEAN) by

 

The settings of the j-th centered variable are given by

 

The settings of the j-th squared variable are given by

 

where

 

(stored in (m + j)-th column of SCPM) is the mean of the j-th squared variable. The settings of the jk crossproduct variable are given by

 

where

 

(stored in the

 

location of SCPM) is the mean of the jk-th (j < k) crossproduct variable. The fitted model is

 

TCSCP transforms the

 

to regression coefficients for the original independent variables. The fitted transformed model is

 

where

 

 

Comments

Crossproduct variables are ordered as follows: (1, 2), (1, 3), …, (1, NVAR), (2, 3), (2, 4), …, (2, NVAR), …, (NVAR ‑ 1, NVAR).

Example

This example transforms coefficients from a second-order response surface model with three independent variables fitted using squares and crossproducts of centered variables into a model using the original uncentered variables.

 

USE TCSCP_INT

USE WRRRN_INT

 

IMPLICIT NONE

INTEGER NVAR

PARAMETER (NVAR=3)

!

REAL B(NVAR*(NVAR+3)/2+1), BC(NVAR*(NVAR+3)/2+1), &

SCPM(NVAR*(NVAR+1)/2), XMEAN(NVAR)

!

DATA XMEAN/10.0, 11.0, 6.0/

DATA SCPM/12.0, 5.0, 2.0, 3.0, 7.0, 1.0/

DATA BC/1.0, 2.0, 3.0, 0.0, 5.0, 0.0, 7.0, 0.0, 9.0, 10.0/

!

CALL TCSCP (XMEAN, SCPM, BC, B)

!

CALL WRRRN ('B', B, 1, NVAR*(NVAR+3)/2+1, 1)

!

END

Output

 

B

1 2 3 4 5 6 7 8

1753.0 -152.0 -57.0 -284.0 5.0 0.0 7.0 0.0

 

9 10

9.0 10.0