论文标题
迭代重新加权最小二乘法估计多句和多choric相关系数
Iteratively Reweighte Least Squares Method for Estimating Polyserial and Polychoric Correlation Coefficients
论文作者
论文摘要
在本文中提出了一种迭代重新加权的最小二乘法（IRL）方法，用于估计多阶段和多声相关系数。它迭代地计算了一系列加权线性回归模型，该模型适合条件期望值。对于多层相关系数，潜在预测因子的条件期望是从观察到的顺序分类变量得出的，并且使用加权最小二乘法获得回归系数。在估计多choric相关系数时，响应变量和预测变量的条件预期会依次更新。估计器的标准误差是根据数据摘要而不是整个数据获得的Delta方法获得的。有条件的单变量正态分布被利用，并且在拟议的算法中对单个积分进行数值评估，与基于传统最大可能性（ML）方法中的双变量正态分布进行数值计算的双积分计算。这使新算法在估计多阶段和多choric相关系数方面非常快。进行了彻底的仿真研究，以将所提出方法的性能与经典ML方法进行比较。实际数据分析说明了新方法在计算速度中的优势。
An iteratively reweighted least squares (IRLS) method is proposed for estimating polyserial and polychoric correlation coefficients in this paper. It iteratively calculates the slopes in a series of weighted linear regression models fitting on conditional expected values. For polyserial correlation coefficient, conditional expectations of the latent predictor is derived from the observed ordinal categorical variable, and the regression coefficient is obtained using weighted least squares method. In estimating polychoric correlation coefficient, conditional expectations of the response variable and the predictor are updated in turns. Standard errors of the estimators are obtained using the delta method based on data summaries instead of the whole data. Conditional univariate normal distribution is exploited and a single integral is numerically evaluated in the proposed algorithm, comparing to the double integral computed numerically based on the bivariate normal distribution in the traditional maximum likelihood (ML) approaches. This renders the new algorithm very fast in estimating both polyserial and polychoric correlation coefficients. Thorough simulation studies are conducted to compare the performances of the proposed method with the classical ML methods. Real data analyses illustrate the advantage of the new method in computation speed.
