Estimation of Linear models from Coarsened Observations Estimation of Linear models Estimation from Coarsened Observations A Method of Moments Approach
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粗化观测下线性模型的估计：矩方法
- 研究问题
- 当潜在线性变量只能通过有序类别观察时，如何估计多方程模型及误差相关结构，并减少最大似然法涉及的多元积分负担？
- 方法与思路
- 作者利用解释变量与广义残差零相关的矩条件构建 GMM，通过重复使用标准技术估计模型，并将方法用于潜在变量相关系数估计。
- 材料陈述的贡献
- 摘要称，该方法避开大规模多元积分，在多元正态误差下与最大似然法一致；与 Stata cmp 的比较显示估计接近且计算耗时较少。
- 阅读关注点
- 应核对广义残差的定义、类别阈值和误差分布设定，明确与最大似然法一致的含义，并检查矩条件识别、效率及计算比较。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或期刊接收。摘要部分维度描述残缺，且未说明等价条件细节与计算比较的具体规模。
原文摘要
In the last few decades, the study of ordinal data in which the variable of interest is not exactly observed but only known to be in a specific ordinal category has become important. In Psychometrics such variables are analysed under the heading of item response models (IRM). In Econometrics, subjective well-being (SWB) and self-assessed health (SAH) studies, and in marketing research, Ordered Probit, Ordered Logit, and Interval Regression models are common research platforms. To emphasize that the problem is not specific to a specific discipline we will use the neutral term coarsened observation. For single-equation models estimation of the latent linear model by Maximum Likelihood (ML) is routine. But, for higher -dimensional multivariate models it is computationally cumbersome as estimation requires the evaluation of multivariate normal distribution functions on a large scale. Our proposed alternative estimation method, based on the Generalized Method of Moments (GMM), circumvents this multivariate integration problem. The method is based on the assumed zero correlations between explanatory variables and generalized residuals. This is more general than ML but coincides with ML if the error distribution is multivariate normal. It can be implemented by repeated application of standard techniques. GMM provides a simpler and faster approach than the usual ML approach. It is applicable to multiple -equation models with -dimensional error correlation matrices and response categories for the equation. It also yields a simple method to estimate polyserial and polychoric correlations. Comparison of our method with the outcomes of the Stata ML procedure cmp yields estimates that are not statistically different, while estimation by our method requires only a fraction of the computing time.