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Arbitrariness of models for augmented and coarse data, with emphasis on incomplete data and random effects models

机译:扩充和粗略数据模型的任意性,重点在于不完整数据和随机效应模型

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摘要

Statistical models often extend beyond the data available. First, in coarse data, what is actually observed is less detailed than what might be, owing to incompleteness, censoring, grouping, or a combination thereof. Second, in augmented data, the observed data are hypothetically supplemented with random effects, latent variables/classes, or component membership in mixture distributions. The two settings together will be referred to as enriched data. Reasons for modelling enriched data encompass mathematical and computational convenience, advantages in interpretation, and substantive plausibility. Models for enriched data combine evidence coming from empirical data with unverifiable model components, resting entirely on assumptions. This has acute consequences for enriched data, but knowledge about this issue is somewhat scattered. We provide a unified framework for enriched data and show, generally and with focus on incomplete-data models and random-effects models on the other hand, that to any given model an entire class of models can be assigned, with all of its members producing the same fit to the observed data but arbitrary regarding the unobservable parts of the enriched data. The concepts developed are illustrated using a clinical trial in toenail dermatophyte onychomycosis and a developmental toxicity study conducted in mice.
机译:统计模型通常超出可用数据的范围。首先,在粗略数据中,由于不完整,检查,分组或其组合,实际观察到的内容比可能的详细程度要少。第二,在扩充数据中,假设数据在混合分布中被随机效应,潜在变量/类别或成分隶属关系所补充。这两个设置一起称为丰富数据。对丰富数据进行建模的原因包括数学和计算上的便利性,解释上的优势以及真实性。丰富数据的模型将来自经验数据的证据与无法验证的模型成分结合在一起,完全基于假设。这对于丰富的数据会产生严重的后果,但是有关此问题的知识有些分散。我们提供了一个用于丰富数据的统一框架,并且通常以不完整数据模型和随机效应模型为重点,向我们展示了可以给任何给定模型分配一整类模型,并由其所有成员生成同样适用于观察到的数据,但是对于丰富数据中不可观察到的部分是任意的。脚趾甲皮肤癣菌病的临床试验和在小鼠中进行的发育毒性研究说明了开发的概念。

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