  This paper concerns a method of selecting a subset of features for a
sequential logit model. Tanaka and Nakagawa (2014) proposed a mixed integer
quadratic optimization formulation for solving the problem based on a quadratic
approximation of the logistic loss function. However, since there is a
significant gap between the logistic loss function and its quadratic
approximation, their formulation may fail to find a good subset of features. To
overcome this drawback, we apply a piecewise-linear approximation to the
logistic loss function. Accordingly, we frame the feature subset selection
problem of minimizing an information criterion as a mixed integer linear
optimization problem. The computational results demonstrate that our
piecewise-linear approximation approach found a better subset of features than
the quadratic approximation approach.
