What pieces of limit order book information matter in explaining order choice by patient and impatient traders?

In this paper, we extend the existing empirical evidence on the relationship between the state of the limit order book (LOB) and order choice. Our contribution is twofold: first, we propose a sequential ordered probit (SOP) model which allows studying patient and impatient traders' choices separately; second, we consider two pieces of LOB information, the best quotes and the book beyond the best quotes. We find that both pieces of LOB information explain the degree of patience of an incoming trader and, afterwards, its order choice. Nonetheless, the best quotes concentrate most of the explanatory power of the LOB. The shape of the book beyond the best quotes is crucial in explaining the aggressiveness of patient (limit order) traders, while impatient (market order) traders base their decisions primarily on the best quotes. Patient traders' choices depend more on the state of the LOB on the same side of the market, while impatient traders mostly look at the state of the LOB on the opposite side. The aggressiveness of both types of traders augments with the inside spread. However, patient (impatient) traders submit more (less) aggressive limit (market) orders when the depth of the own (opposite) best quote and the length of the own (opposite) side of the book increase. We also find that higher depth away from the best ask (bid) quote may signal that this quote is 'too low (high)', causing incoming impatient buyers (sellers) to be more aggressive and incoming patient sellers (buyers) to be more conservative.