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Abstract:
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Quantile regression is a method of estimating conditional quantiles of the response variable. An advantage of this method is the direct evaluation of the differences among conditional quantiles. Binary quantile regression is a quantile regression for binary responses. In this method, the binary response is determined by whether a continuous latent variable is greater than a threshold value or not, and we apply quantile regression to latent variables. However, binary quantile regression assumes that the response is one-dimensional (i.e., scalar). Thus, this method is not applied to data that have vector binary responses, such as Electronic Commerce purchase data. To tackle this issue, we extend binary quantile regression to apply it to vector binary responses. In this method, we assume that the vector binary response variable can be represented by one continuous latent variable and many threshold values. We employ the Gibbs Sampling and the Metropolis-Heisting algorithms for parameter estimation. The performance of the proposed method is evaluated through numerical experiments. We apply the proposed method to real-world data to compare the estimated quantiles with other quantiles.
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