The use of Bayesian information criterion (BIC) in the model selection procedure is under the assumption that the observations are independent and identically distributed (i.i.d.). However, in practice, we do not always have i.i.d. samples. For example, clustered observations tend to be more similar within the same group, and longitudinal data is collected by measuring the same subject repeatedly. In these scenarios, the assumption in BIC is not satisfied. The concept of effective sample size is brought up and improved BIC is defined by replacing the sample size in the original BIC expression with the effective sample size, which will give us a better theoretical foundation in the circumstance that mixed-effects models involve. Numerical experiment results are also given by comparing the performance of our new BIC with other widely used BICs.
翻译:在模式选择程序中使用贝叶斯信息标准(BIC)的假设是,观测是独立的,分布相同(即d.)。然而,在实践中,我们并不总是有i.d.样本。例如,在同一组内,分组观测往往更加相似,通过反复测量同一主题收集纵向数据。在这些假设中,BIC的假设不令人满意。提出有效样本规模的概念,并改进BIC的定义是用有效样本规模取代原BIC表达方式中的样本规模,这将在混合效应模型涉及的情况下为我们提供更好的理论基础。通过将我们新的BIC与其他广泛使用的BIC的性能进行比较,也得出了数值实验结果。