doe_model_diagnostics Function

public function doe_model_diagnostics(mdl, x, y) result(diag)

Computes model diagnostics and goodness-of-fit metrics.

With $m$ observations, $p$ model parameters, observed responses $y_i$, model predictions $\hat{y}_i$, and mean response $\bar{y}$, the following quantities are computed.

$$SS_{res} = \sum_{i=1}^{m} (y_i - \hat{y}_i)^{2}$$ $$SS_{tot} = \sum_{i=1}^{m} (y_i - \bar{y})^{2}$$ $$R^{2} = 1 - \frac{SS_{res}}{SS_{tot}}$$ $$R^{2}_{adj} = 1 - \frac{SS_{res} / (m - p)}{SS_{tot} / (m - 1)}$$ $$RMSE = \sqrt{\frac{SS_{res}}{m}}$$ $$s = \sqrt{\frac{SS_{res}}{m - p}}$$ $$F = \frac{(SS_{tot} - SS_{res}) / (p - 1)}{SS_{res} / (m - p)}$$

Degenerate cases are handled as follows: $R^{2}$ is zero if $SS_{tot} = 0$; the adjusted $R^{2}$ and residual standard error are zero if $m \le p$; and the F-statistic is zero (with a p-value of 1) if $p = 1$ or $m \le p$. The p-value is the upper tail of the F-distribution with $(p - 1, m - p)$ degrees of freedom.

Arguments

Type	Intent	Optional	Attributes		Name
class(doe_model),	intent(in)			::	mdl	The fitted DOE model.
real(kind=real64),	intent(in),		dimension(:,:)	::	x	The M-by-N matrix containing the M values of each of the N factors used in model fitting.
real(kind=real64),	intent(in),		dimension(:)	::	y	The M-element array containing the observed responses. This array must have the same number of rows as x.

Return Value type(doe_diagnostics)

A doe_diagnostics object containing the R-squared, adjusted R-squared, RMSE, residual standard error, F-statistic, mean response, observation count, and parameter count.