Model effects
When a certain model is estimable, we can obtain statistical quality indicators that gives us information on the power to estimate each effect in the model, the variance inflation factor of each estimate in the model, or the relative error of estimation of each individual effect.
The power to detect an active effect.
Calculated for different values of Signal-to-noise ratio and significance level ($\alpha$). For detailed information on how the power is calculated, please click here.
Variance inflation factor
Variance inflation factor (VIF) is a measure of how much the variance of the estimate of an individual effect is inflated due to aliasing or multicollinearity with other effects. The expression for VIF is given as:
$VIF = \frac{1}{1-R^2}$
where $R^2$ is the coefficient of determination of a model where the dependent variable is the selected effect and the independent variables are all the other terms in the model selected. A VIF value of 1 ($R^2 = 0$) indicates that there is no aliasing between the selected effect and all other effects included in the model. Ideally this number should be small ($<10$).
Relative error of estimation
The Relative error of estimation (REE) is the standard error of the estimate of an effect relative to the standard error of the model. This is given by the expression:
$REE = \sqrt{(\mathbf{X’X})^{-1}_{ii}}$ ,
where $\mathbf{X}$ is the selected model matrix and $(\mathbf{X’X})^{-1}_{ii}$ is the $i^{th}$ diagonal element of the variance covariance matrix $(\mathbf{X’X})^{-1}$ . The actual standard error of an estimate of an effect can be calculated by multiplying this expression with the standard error from the model.
All the three characterizations (POWER, VIF, REE) can be calculated for the following models:
- ME – All main effects model
- MEIE – All main effects + all two-factor interactions model
- MESOE – All main effects + all second order effects (two-factor interactions and quadratic effects) model.
- MEQE – Main effects + all quadratic effects model.
Additional notes:
Some model options may not appear for the chosen design. This happens when the said model cannot be fit with the design selected.
The powers and REE for the blocking effect is only displayed when blocking option is selected (Under – ‘Define your experiment’) and the intrablock correlation coefficient is set to Extreme (For more information, refer to ‘power page’).
The VIF and REE calculations are independent from the specified value of Signal-to-noise ratio and significance level $\alpha$.