SPARSE LOGISTIC MODELING FOR ORDINAL DATA VIA FUSED LASSO

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  • Kato Shunsuke
    Graduate School of Engineering, Osaka Prefecture University
  • Kawano Shuichi
    Graduate School of Informatics and Engineering, The University of Electro-Communications

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  • Fused Lasso に基づくスパース順序ロジットモデリング
  • Fused Lasso ニ モトズク スパース ジュンジョ ロジットモデリング

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 Ordinal logistic models are widely used in various fields of research. Among ordinal logistic models, this paper adopts continuation ratio logistic models. Since the models are too flexible, the estimates of parameters in the models tend to be unstable. For the reason, it is often assumed that the values of coefficient parameters that same variables have are equal. The assumption is called “equal slope assumption”. Yasukawa & Tsubaki (2003) used the information criterion AIC for determining which the model satisfies equal slope assumption or not. However, as the number of covariates increases, the number of models to be selected increases exponentially. Therefore, model selection procedures with information criteria are realistically impossible.<br> To overcome the problem, we propose a sparse ordinal logistic model (SOL), which is constructed by combining the fused lasso (Tibshirani et al., 2005) with continuation ratio logistic models. Monte Carlo simulations and a real data analysis are performed to investigate the efficiency of SOL.

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