Optimizations for Categorizations of Explanatory Variables in Linear Regression via Generalized Fused Lasso

In linear regression, a non-linear structure can be naturally considered by transforming quantitative explanatory variables to categorical variables. Moreover, smaller categories make estimation more flexible. However, a trade-off between flexibility of estimation and estimation accuracy occurs because the number of parameters increases for smaller categorizations. We propose an estimation method wherein parameters for categories with equal effects are equally estimated via generalized fused Lasso. By such a method, it can be expected that the degrees of freedom for the model decreases, flexibility of estimation and estimation accuracy are maintained, and categories of explanatory variables are optimized. We apply the proposed method to modeling of apartment rents in Tokyo’s 23 wards.