在贝叶斯信息标准中的有效样本大小,用于在两级嵌套模型中对特定水平的固定和随机效应的选择
Sun-Joo Cho1, Hao Wu1, Matthew Naveiras2
1Vanderbilt University, Nashville, Tennessee, USA.
概括
新贝叶斯信息标准 (BIC) 公式用于多层模型,解决现有方法的差异. 这些增强的BIC标准为复杂的层次数据结构提供了优越的模型选择.
科学领域:
- 统计 统计 统计 统计
- 多层次建模多层次建模
- 计量经济学 计量经济学
背景情况:
- 现有的贝叶斯信息标准 (BIC) 在多层模型的统计软件中的实现不一致.
- 差异源于多级模型的BIC惩罚术语中样本大小规范的变化.
- 对于正确应用BIC来选择具有特定水平固定和随机效应的模型存在不确定性.
研究的目的:
- 在双层嵌套多层模型中选择固定和随机效应的准确BIC惩罚条款.
- 提出新的BIC版本,标记为BIC_A和BIC_B,分别解决全等级和冗余随机效应.
- 评估新的BIC标准的性能与现有的多层次模型选择方法相比.
主要方法:
- 在两级嵌套设计中,针对特定级别的固定和随机效应的BIC惩罚条款的导出.
- 对BIC_A.的惩罚项分解为集群级和参数级组件.
- 对于具有冗余随机效应的场景,BIC_B的导出.
- 数字和模拟研究以验证衍生式和比较性能.
主要成果:
- 对BIC_A和BIC_B的公式被推导出,并根据经验值进行验证.
- BIC_A将罚款分解为每个集群的平均样本大小和总参数乘以集群的数量.
- 模拟研究表明,新的BIC标准 (BIC_A或BIC_B) 优于使用总样本大小或集群数量的标准BIC版本.
- 拟议的BIC标准在各种多层次条件下至少与现有方法一样有效.
结论:
- 衍生的BIC公式 (BIC_A和BIC_B) 为多级模型选择提供了更准确和可靠的方法.
- 新的BIC标准被推为复杂的层次数据的优越全球选择标准.
- 使用教科书中的示例数据集来说明新的BIC的实际应用.
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