Fractional Factorial Designs in the Analysis of Categorical Data

by Alexander von Eye .

Abstract: 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.

Key Words: fractional factorial design; categorical outcome variables; log-linear modeling; Configural Frequency Analysis; parameter interpretability

Author:
Alexander von Eye, voneye@msu.edu

Editor: Richard G. Graf, rgraf@sunstroke.sdsu.edu

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