Collaborative Research: Model diagnostics in regression and Tobit regression models with measurement error

合作研究：具有测量误差的回归和 Tobit 回归模型中的模型诊断

• 批准号: 1205271
• 负责人: Hira Koul
• 金额: $ 18.5万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1205271&HistoricalAwards=false
• 关键词: Collaborative; Research; Model; diagnostics; regression

Statistical modeling for relationships between a collection of predictors and a response is often implemented by regression analysis. In the classical regression model, both predictors and response variables are assumed to be directly observable. In measurement error regression models, predictors cannot be observed directly, instead, some surrogates are observed. In Tobit regression models, the response variable is observed only when it is above some threshold. The development of useful and optimal inference procedures in the presence of measurement errors in regression and Tobit regression models is of major concern in theoretical and applied statistics. Despite this need, the study of goodness-of-fit and lack-of-fit tests in the measurement error regression models and Tobit regression models with/without measurement errors has lagged behind. In this project, the investigators analyze goodness-of-fit tests for the distributions of the random components of errors-in-variables and Berkson measurement error regression models, and some nonparametric estimators of regression functions in Tobit regression models with or without these measurement errors. Furthermore, the investigators develop and analyze lack-of-fit and goodness-of-fit tests in Tobit regression models with these measurement errors. The investigators make available some new, useful, and optimal inference procedures in these models with an in-depth understanding of their theoretical properties to a wide professional audience in statistics and related disciplines. This project is at the cutting edge of model checking in the presence of measurement error in predictors in regression and Tobit regression models. It advances and enriches the statistical theory and methodology, thereby helping to fill a significant void and well recognized theoretical gap that exists in statistics. Measurement errors are very prevalent in the health sciences, physical sciences, economics, and the social sciences. For example, when investigating the effect of diet on breast cancer, one of the predictor variables studied for predicting breast cancer is the long-term saturated fat intake which cannot be measured precisely. Instead, the surrogate of a 24 hour diet recall for each patient is often used in this type of investigation. Similarly, the exact amount of radiation a person is exposed to when studying the effect of radiation exposure on humans is often measured with error. In labor studies, when investigating the relationship between women's working status and their background information, such as age, education and working experience, the effect of measurement errors is present in the education variables (such as mother's and father's education experience). Tobit regression models, which are used in these types of studies, often suffer from the measurement error problem. Most empirical studies involving Tobit regression models tend to ignore the measurement errors, which usually leads to biased and inefficient statistical conclusions. The research focus of this project, which helps in assessing the accuracy of a regression model or of a model for the distributions of random components in the presence of measurement errors, helps to develop more accurate statistical inference for these and other similar examples.

回归分析通常实现了预测因子和响应之间关系的统计模型。在经典回归模型中，假定预测因子和响应变量是直接可观察的。在测量误差回归模型中，无法直接观察到预测因子，而是观察到一些替代物。在TOBIT回归模型中，仅当响应变量高于某个阈值时才能观察到。 在回归和TOBIT回归模型存在测量误差的情况下，有用和最佳推理程序的开发在理论和应用统计中是主要关注的。尽管需要，但在测量误差回归模型和TOBIT回归模型中，对拟合优点和缺乏合适的测试的研究落后于/没有测量误差。在该项目中，研究人员分析了拟合优点测试，以分析伯克森误差和伯克森测量误差回归模型的随机组成部分的分布，以及带有或没有这些测量错误的TOBIT回归模型中回归函数的一些非参数估计值。此外，研究人员使用这些测量误差开发和分析了TOBIT回归模型中缺乏合适性和合适性测试。调查人员在这些模型中提供了一些新的，有用和最佳的推理程序，并深入了解其理论属性对统计和相关学科的广泛专业受众。该项目处于模型检查的最前沿，在回归和TOBIT回归模型中的预测因子中存在测量误差。它提高并丰富了统计理论和方法论，从而有助于填补统计中存在的重要空隙和公认的理论差距。在健康科学，物理科学，经济学和社会科学中，测量错误非常普遍。例如，在研究饮食对乳腺癌的影响时，研究乳腺癌的预测变量之一是长期饱和脂肪摄入量，无法精确测量。取而代之的是，在这种类型的研究中，经常使用每位患者的24小时饮食回忆的替代物。同样，在研究辐射暴露对人类的影响时，一个人暴露的辐射量通常会误差测量。 在劳动研究中，在研究妇女的工作状况与其背景信息之间的关系（例如年龄，教育和工作经验）时，教育变量（例如母亲和父亲的教育经验）中存在测量错误的效果。 在这些类型的研究中使用的TOBIT回归模型通常会遇到测量误差问题。大多数涉及TOBIT回归模型的经验研究倾向于忽略测量误差，这通常会导致有偏见和效率低下的统计结论。该项目的研究重点有助于评估回归模型的准确性或在存在测量误差的情况下随机组件分布的模型的准确性，有助于对这些和其他类似示例进行更准确的统计推断。