Dimension Reduction for Multinomial Models Via a Kolmogorov-Smirnov Measure (KSM)

Due to advances in technology and data collection techniques, the number of measurements often exceeds the number of samples in ecological datasets. As such, standard models that attempt to assess the relationship between variables and a response are inapplicable and require a reduction in the number of dimensions to be estimable. Several filtering methods exist to accomplish this, including Indicator Species Analyses and Sure Information Screening, but these techniques often have questionable asymptotic properties or are not readily applicable to data with multinomial responses. As such, we propose and validate a new metric called the Kolmogorov-Smirnov Measure (KSM) to be used for filtering variables. In the paper, we develop the KSM, investigate its asymptotic properties, and compare it to group equalized Indicator Species Values through simulation studies and application to a well-known biological dataset.