A.6 Interactions and continuous design

In order to take interactions into account, the extended coding matrix $mA$ will be obtained by adding several columns to the ordinary coding matrix $ma$. Successive calls to LISTING 13 will achieve this result by acting upon a temporary matrix ($maa$).

When all columns are added, LISTING 14 is called to obtain the extended model ($mX$) and its VRF.

Another possibility is the following. We can consider that modalities are no more the levels taken by discrete factors, but are rather the values taken by continuous factors. When using such a model, a factor is coded by only a variable (preferably reduced, i.e. centered and weighted). In LISTING 9, options 'xy+yz' (products without squares), 'xx+xy' (products including squares) and 'lenteur' (using inverses) are proposed.

The last two options (full quadratic) are dealed by LISTING 15, which computes a functional model ($fun$) that allows a quadratic research of the optimum.

This research is undertaken in LISTING 16, using the Scilab quapro command. Thereafter, the 3D response surface can be drawn and a report issued.