标题： 从粗化观测值估计线性模型 线性模型估计 从粗化观测值估计 矩量法 显示英文标题

标题： Estimation of Linear models from Coarsened Observations Estimation of Linear models Estimation from Coarsened Observations A Method of Moments Approach

摘要： 在过去的几十年里，研究那些感兴趣的变量不是精确观测到的，而是只知道处于特定顺序类别中的顺序数据变得非常重要。在心理测量学中，这些变量是在项目反应模型（IRM）的标题下进行分析的。在计量经济学中，主观幸福感（SWB）和自评健康（SAH）研究，以及在市场营销研究中，有序概率模型、有序对数模型和区间回归模型是常见的研究平台。为了强调这个问题并不特定于某一学科，我们将使用中性术语“粗化观测”。对于单方程模型，通过最大似然（ML）估计潜在线性模型是常规操作。但对于高维多变量模型，计算上比较繁琐，因为估计需要大规模评估多元正态分布函数。我们提出的替代估计方法基于广义矩方法（GMM），避免了这种多变量积分问题。该方法基于解释变量与广义残差之间假设的零相关性。这比ML更一般，但如果误差分布是多元正态，则与ML一致。可以通过重复应用标准技术来实现。GMM比通常的ML方法更简单、更快。它适用于具有多维误差相关矩阵和方程响应类别的多方程模型。它还提供了一种简单的方法来估计多序列相关和多列相关。将我们的方法与Stata ML过程cmp的结果进行比较，得到的估计值在统计上没有差异，而用我们的方法进行估计只需要很少的计算时间。 显示英文摘要

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.