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
