Partial analysis of high-way factorial designs

Assessing factorial invariance of two-way rating designs using three-way methods

Assessing the factorial invariance of two-way rating designs such as ratings of concepts on several scales by different groups can be carried out with three-way models such as the Parafac and Tucker models. By their definitions these models are double-metric factorially invariant. The differences between these models lie in their handling of the links between the concept and scale spaces. These...

Model-Robust Factorial Designs

Multistratum Fractional Factorial Designs

Recent work on multistratum fractional factorial designs is set in a general and unified framework, and a criterion for selecting multistratum fractional factorial designs that takes stratum variances into account is proposed. Application of the general theory is illustrated on designs of experiments with multiple processing stages, including split-lot designs, blocked strip-plot designs, and p...

Equivalence of Fractional Factorial Designs

Two designs for a fractional factorial experiment are equivalent if one can be obtained from the other by reordering the treatment combinations, relabeling the factors and relabeling the factor levels. Designs can be viewed as sets of points in pdimensional space, where p is the number of factors. It is shown that, in this setting, two designs are equivalent if the Hamming distances between the...

Generation of Fractional Factorial Designs

The joint use of counting functions, Hilbert basis and Markov basis allows to define a procedure to generate all the fractions that satisfy a given set of constraints in terms of orthogonality. The general case of mixed level designs, without restrictions on the number of levels of each factor (like primes or power of primes) is studied. This new methodology has been experimented on some signif...