doe_fit_model Function

public function doe_fit_model(nway, x, y, map, alpha) result(rst)

Fits a Taylor series model to the provided data.

$$Y = \beta_{0} + \sum_{i=1}^{n} \beta_{i} X_{i} + \sum_{i=1}^{n-1} \sum_{j=i+1}^{n} \beta_{ij} X_{i} X_{j} + \sum_{i=1}^{n} \beta_{ii} X_{i}^{2} + \sum_{i=1}^{n-2} \sum_{j=i+1}^{n-1} \sum_{k=j+1}^{n} \beta_{ijk} X_{i} X_{j} X_{k} + \sum_{i=1}^{n} \sum_{j=1 \\ j \neq i}^{n} \beta_{iij} X_{i}^{2} X_{j} + \sum_{i=1}^{n} \beta_{iii} X_{i}^{3}$$

The first line of terms (through the squared terms) is included for a two-way model, and the remaining terms are added for a three-way model.
Each unique combination of factors appears exactly once. For example, with two factors, a two-way model is:

$$Y = \beta_{0} + \beta_{1} X_{1} + \beta_{2} X_{2} + \beta_{12} X_{1} X_{2} + \beta_{11} X_{1}^{2} + \beta_{22} X_{2}^{2}$$

The coefficients are ordered as: constant, main effects, cross terms (i < j, lexicographic), squared terms, and (three-way only) triple cross terms (i < j < k), X_i**2 * X_j terms (i, then j, with i /= j), and cubed terms.

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=int32),	intent(in)			::	nway	The number of interaction levels.
real(kind=real64),	intent(in),		dimension(:,:)	::	x	The M-by-N matrix containing the M values of each of the N factors used to produce the results.
real(kind=real64),	intent(in),		dimension(:)	::	y	An M-element array containing the results from the M experiments.
logical,	intent(in),	optional,	target, dimension(:)	::	map	An optional array of the same size as beta that can be used to eliminate a parameter from the model (false), or keep a parameter in the model (true). If not supplied, all parameters will be assumed to be part of the model as if the array were filled with all true values.
real(kind=real64),	intent(in),	optional		::	alpha	The significance level at which to evaluate the confidence intervals. The default value is 0.05 such that a 95% confidence interval is calculated.

Return Value type(doe_model)

The resulting model.