Shimmura Ryosuke, Suzuki Joe
Graduate School of Engineer Science, Osaka University, Toyonaka 560-0043, Japan.
Entropy (Basel). 2023 Dec 31;26(1):44. doi: 10.3390/e26010044.
We develop a method for estimating a simple matrix for a multidimensional item response theory model. Our proposed method allows each test item to correspond to a single latent trait, making the results easier to interpret. It also enables clustering of test items based on their corresponding latent traits. The basic idea of our approach is to use the prenet (product-based elastic net) penalty, as proposed in factor analysis. For optimization, we show that combining stochastic EM algorithms, proximal gradient methods, and coordinate descent methods efficiently yields solutions. Furthermore, our numerical experiments demonstrate its effectiveness, especially in cases where the number of test subjects is small, compared to methods using the existing L1 penalty.
我们开发了一种用于估计多维项目反应理论模型简单矩阵的方法。我们提出的方法允许每个测试项目对应一个单一的潜在特质，使结果更易于解释。它还能够根据测试项目对应的潜在特质对其进行聚类。我们方法的基本思想是使用因子分析中提出的前网（基于乘积的弹性网）惩罚。对于优化，我们表明将随机期望最大化算法、近端梯度方法和坐标下降方法结合起来能够有效地得到解决方案。此外，我们的数值实验证明了其有效性，特别是在测试对象数量较少的情况下，与使用现有L1惩罚的方法相比。
