This paper discusses estimation and limited information goodness-of-fit test statistics in factor models for binary data using pairwise likelihood estimation and sampling weights. The paper extends the applicability of pairwise likelihood estimation for factor models with binary data to accommodate complex sampling designs. Additionally, it introduces two key limited information test statistics: the Pearson chi-squared test and the Wald test. To enhance computational efficiency, the paper introduces modifications to both test statistics. The performance of the estimation and the proposed test statistics under simple random sampling and unequal probability sampling is evaluated using simulated data.

翻译：本文讨论了在复杂抽样设计下，利用成对似然估计和抽样权重，针对二元数据的因子模型进行估计以及有限信息拟合优度检验的统计量。本文扩展了成对似然估计在二元数据因子模型中的适用性，使其能够适应复杂的抽样设计。此外，本文引入了两种关键的有限信息检验统计量：皮尔逊卡方检验和沃尔德检验。为了提高计算效率，本文对这两种检验统计量均提出了改进方案。通过模拟数据，评估了在简单随机抽样和不等概率抽样下，估计方法及所提检验统计量的性能。