This study presents a scalable Bayesian estimation algorithm for sparse estimation in exploratory item factor analysis based on a classical Bayesian estimation method, namely Bayesian joint modal estimation (BJME). BJME estimates the model parameters and factor scores that maximize the complete-data joint posterior density. The algorithm's scalability is achieved through an alternating optimization scheme that iteratively updates model parameters and latent variables. Simulation studies show that the proposed algorithm has high computational efficiency and accuracy in variable selection over latent factors and the recovery of the model parameters. Moreover, we conducted a real data analysis using large-scale data from a psychological assessment that targeted the Big Five personality traits. This result indicates that the proposed algorithm achieves computationally efficient parameter estimation and extracts the interpretable factor loading structure.

翻译：本研究提出了一种基于经典贝叶斯估计方法——贝叶斯联合众数估计（BJME）的可扩展贝叶斯估计算法，用于探索性项目因子分析中的稀疏估计。BJME通过最大化完整数据联合后验密度来估计模型参数和因子得分。该算法的可扩展性通过交替优化方案实现，该方案迭代更新模型参数与潜变量。仿真研究表明，本算法在潜因子上进行变量选择以及恢复模型参数方面具有较高的计算效率和准确性。此外，我们利用针对大五人格特质的大规模心理学评估数据进行了真实数据分析。结果表明，本算法能够实现计算高效的参数估计，并提取可解释的因子载荷结构。