Estimable 2fis for regular (fractional) factorial 2-level designs
Not all combinations of inputs are compatible with each other. You may avoid unnecessary work by reading the advice below. In case of violating the restrictions below, the specification of estimable 2fis will take precedence over other specifications (you will be warned, if this happens; on re-opening the dialog, you will then have the chance to adjust the settings).
Blocked designs (number of blocks larger than 1 on the “Base Settings” tab) and specification of an estimable model are not compatible with each other in the current version of the software. Thus, you have to decide on using blocks OR specifying estimable 2-factor interactions. (Nevertheless, 2 or 4 blocks can be specified as detailed in the section “Brief statistical background” below.
Generators or a specific design (radio buttons on the “Base Settings” tab) can neither be specified together with estimable 2-factor interactions.
Finally, it is neither possible to simultaneously specify hard-to-change factors on the “Factor Details” tab and estimable 2-factor interactions.
This tab allows to specify 2-factor interactions (2fis) that are of special interest and must be estimable from the experiment. Per default, it is assumed that the design must be at least of resolution IV.
There are two different approaches to estimability: If it can realistically be assumed that all the 2fis that are not of special interest are negligible, it is sufficient to request that the specified 2fis are clear of aliasing with EACH OTHER. Otherwise, i.e. if one is not prepared to assume that all the unselected 2fis are negligible, it is more appropriate to request that the specified 2fis are clear of aliasing with ANY 2fis (both with each other and the other 2fis). Even under this approach, the design need not be resolution V, since the unselected 2fis may be aliased with each other.
If a design with certain interactions to be estimable is to be run in more
than four blocks, there is currently no automated way to produce it,
as it is not permitted to specify a number of blocks together
with selecting 2fis to be estimable. A blocked design with 2 or 4 blocks can be
obtained by explicitly including one (2 blocks) or two (4 blocks) blocking factors.
For the case of 4 blocks, it is important to include the interaction between
the two blocking factors into the selected interactions.
For the case of 2 blocks only, the blocking factor is treated like the
other factors, i.e. if its interactions with other factors are not among the selected ones,
they may be aliased with other 2fis (and even with main effects,
if resolution III is permitted in exceptional situations), which is usually
considered adequate.
The design is created with function FrF2 from package FrF2.
The special functionality for estimable 2fis is described here.
Users who are not familiar with the terminology around regular fractional factorial designs (e.g.
the concept of resolution) can browse the DoEGlossary.
The radio button switches off the request for specific interactions to be estimable or requests one of the two implemented modes that have been discussed above.
is per default IV and can be set to III by checking the box. Usually, the default is more appropriate.
In case of the manual selection radio button choice,
move selected 2-factor interactions between
the available list (those are not selected) and the selected list by
selecting them with the mouse (multiple selections possible) and
moving them with the arrow buttons.
For some classical structures (compromise designs by Addelman (1962) or Ke, Tang and Wu (2005),
cf. also estimable.2fis),
it is more comfortable, and in case of distinct designs
(bottom radio button for mode of requesting estimable interactions) also often much faster,
to use the pre-specified strucures for two groups of factors; the type of structure
can be selected from the drop-down, and the factors can be moved between the two groups
using the arrow buttons (each factor must belong to one of the groups).
If the bottom radio button for the mode of requesting estimable 2fis is chosen, the search for a design can take a long time. In this case, it is possible to increase (or decrease) the search time after which the search is stopped even if no appropriate design was identified. Searches with extensive requests can easily time out, especially if they are not implemented using the pre-specified group structure. Expert users may be able to utilize the structure of their problem for finding an appropriate design, using the command-line language rather than the menus.
Ulrike Groemping
See also FrF2 for the function that does the calculations and
estimable for the statistical detail of the “Estimable Model”
functionality within this function.