Local differential privacy is a quantitative privacy metric based on indistinguishability, and the increasing complexity of recent attacks on privacy information has fostered its adoption. WALDP is a recently proposed local differential privacy mechanism, which reduces the amount of noise using dimension reduction. We focus on this mechanism and propose another dimension reduction method DR.OR using odds ratios. It is possible to maintain the original concept, i.e., data generality, by using DR.OR as a subroutine of WALDP. Previous study focused only on support vector machines (SVMs), but we also evaluated WALDP for the logistic regression and the deep neural network, and showed that WALDP achieves high accuracy as well. In particular, the proposed DR.OR boasts high accuracy, especially for logistic regression, which has a strong relationship with odds ratios. This suggests that further performance improvements can be expected by selecting a dimension reduction method in consideration of the learning model.