Fractional Factorial Designs in the Analysis of Categorical Data
by Alexander von Eye
In this article, first, fractional factorial designs are reviewed, with an emphasis on Box - Hunter
designs. Based on the Sparsity of Effects Principle, it is argued that, when higher order effects are
indeed unimportant in most hypotheses, fractional designs can be used without loss of information.
Fractional factorial designs can be specified such that the desired level of interactions can be
interpreted. Given a fixed amount of time and financial resources, these designs allow one to include more
factors in a study than completely crossed designs, or to increase the sample. It is then shown that, when
the outcome variables are categorical, the same principles apply. It is also shown that higher order
effects need to be specified when the outcome variables are categorical. Parameter interpretation is
illustrated for a selection of fractional factorial designs. The application of fractional factorial
designs is illustrated in both explanatory and exploratory contexts. In addition, a data set is analyzed
using the fractional and the complete information. It is illustrated that distortion from only using the
fractional information can be minimal.
fractional factorial design; categorical outcome variables; log-linear modeling; Configural
Frequency Analysis; parameter interpretability
Alexander von Eye, firstname.lastname@example.org
Richard G. Graf, email@example.com
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