Nonparametric Analysis of Longitudinal Binary Data: An Application to the Intergroup Prisoner's Dilemma Game
针对群体间囚徒困境博弈的150轮实验数据，提出基于置换检验的非参数方法，用累积投资和标准化累积投资两个新指标分析不同匹配条件下群体的投资差异，并构建置信带识别差异来源。
Abstract The intergroup prisoner's dilemma game was suggested by Bornstein (1992, Journal of Personality and Social Psychology. 7, 597-606) for modelling intergroup conflicts over continuous public goods. We analyse data of an experiment in which the game was played for 150 rounds, under three matching conditions. The objective is to study differences in the investment patterns of players in the different groups. A repeated measures analysis was conducted by Goren and Bornstein (1999, Games and Human Behaviour: Essays in Honor of Amnon Rapoport , pp. 299-314), involving data aggregation and strong distributional assumptions. Here we introduce a nonparametric approach based on permutation tests. Two new measures, the cumulative investment and the normalised cumulative investment, provide additional insight into the differences between groups. The proposed tests are based on the area under the investment curves. They identify an overall difference between the groups as well as pairwise differences. A simultaneous confidence band for the mean difference curve is used to detect the games which account for any pairwise difference.