Influence analysis is an important component of data analysis, and the local influence approach has been widely applied to many statistical models to identify influential observations and assess minor model perturbations since the pioneering work of Cook (1986). The approach is often adopted to develop influence analysis procedures for factor analysis models with ranking data. However, as this well-known approach is based on the observed data likelihood, which involves multidimensional integrals, directly applying it to develop influence analysis procedures for the factor analysis models with ranking data is difficult. To address this difficulty, a Monte Carlo expectation and maximization algorithm (MCEM) is used to obtain the maximum-likelihood estimate of the model parameters, and measures for influence analysis on the basis of the conditional expectation of the complete data log likelihood at the E-step of the MCEM algorithm are then obtained. Very little additional computation is needed to compute the influence measures, because it is possible to make use of the by-products of the estimation procedure. Influence measures that are based on several typical perturbation schemes are discussed in detail, and the proposed method is illustrated with two real examples and an artificial example.

中文翻译：

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具有排名数据的因素分析模型的影响分析。

影响分析是数据分析的重要组成部分，自Cook（1986）的开创性工作以来，局部影响方法已广泛应用于许多统计模型，以识别有影响的观察结果并评估较小的模型扰动。通常采用此方法来开发具有排名数据的因素分析模型的影响分析程序。但是，由于这种众所周知的方法是基于观察到的数据似然性（涉及多维积分），因此很难将其直接用于开发具有排序数据的因子分析模型的影响分析程序。为了解决这一难题，使用了蒙特卡洛期望和最大化算法（MCEM）来获得模型参数的最大似然估计，然后在MCEM算法的E步中基于完整数据对数似然的条件期望，获得了影响分析的措施。由于可以利用估算程序的副产品，因此很少需要进行额外的计算来计算影响量。详细讨论了基于几种典型摄动方案的影响措施，并以两个实际示例和一个人工示例对所提出的方法进行了说明。