一个概括的Hosmer-Lemeshow适合性测试,用于一系列概括的线性模型
Nikola Surjanovic1, Richard A Lockhart2, Thomas M Loughin2
1Department of Statistics, University of British Columbia, Vancouver, BC Canada.
概括
一个针对一般化线性模型 (GLM) 的新适合性测试扩展了Hosmer-Lemeshow测试. 这种新的方法在各种GLM类中提供可靠的性能,增强了统计学家的模型验证.
科学领域:
- 统计 统计 统计 统计
- 统计建模 统计建模
- 计算统计学 计算统计学
背景情况:
- 通用线性模型 (GLMs) 得到广泛应用,但正式的适用性测试 (GOF) 并不是所有GLM类的普遍可用.
- 现有的GOF测试,如Hosmer-Lemeshow (HL) 测试,主要用于特定的GLM类型,限制了全面的模型评估.
研究的目的:
- 开发和验证一种新的适合性测试,适用于广泛的通用线性模型.
- 创建Hosmer-Lemeshow测试的概括版本,保持统计严谨性和广泛适用性.
主要方法:
- 开发了一种新的适合性测试统计,将Hosmer-Lemeshow统计适用于更广泛的GLM应用.
- 使用斯图特和朱的方法 (2002) 严格推导出了非对称正确的抽样分布.
- 证明了测试的一致性,并通过模拟评估其性能,将其与现有的GOF测试进行比较.
主要成果:
- 拟议的通用HL测试在各种模拟场景中证明了具有竞争力或可比的统计能力.
- 确定了一个特定的环境,其中对波桑回归的HL测试的天真应用未能保持其大小.
- 新的测试被证明是强大的和可靠的跨不同的GLM类.
结论:
- 开发的通用化适合性测试为评估各种通用线性模型的整体适合性提供了有价值的工具.
- 该测试为现有方法提供了更普遍适用的替代方案,解决了目前GOF测试实践的局限性.
- 一般化HL测试易于实施和解释,公开可用的R包有助于其采用.
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