Departamento de Estatística, Universidade Federal de Pernambuco, Recife, PE, Brazil.
PLoS One. 2021 Jun 28;16(6):e0253349. doi: 10.1371/journal.pone.0253349. eCollection 2021.
Beta regressions are commonly used with responses that assume values in the standard unit interval, such as rates, proportions and concentration indices. Hypothesis testing inferences on the model parameters are typically performed using the likelihood ratio test. It delivers accurate inferences when the sample size is large, but can otherwise lead to unreliable conclusions. It is thus important to develop alternative tests with superior finite sample behavior. We derive the Bartlett correction to the likelihood ratio test under the more general formulation of the beta regression model, i.e. under varying precision. The model contains two submodels, one for the mean response and a separate one for the precision parameter. Our interest lies in performing testing inferences on the parameters that index both submodels. We use three Bartlett-corrected likelihood ratio test statistics that are expected to yield superior performance when the sample size is small. We present Monte Carlo simulation evidence on the finite sample behavior of the Bartlett-corrected tests relative to the standard likelihood ratio test and to two improved tests that are based on an alternative approach. The numerical evidence shows that one of the Bartlett-corrected typically delivers accurate inferences even when the sample is quite small. An empirical application related to behavioral biometrics is presented and discussed.
贝塔回归通常用于响应值假设在标准单位区间内的情况，例如速率、比例和浓度指数。通常使用似然比检验对模型参数进行假设检验推断。当样本量较大时，它可以提供准确的推断，但在其他情况下可能会导致不可靠的结论。因此，开发具有优越有限样本性能的替代检验方法非常重要。我们在更一般的贝塔回归模型（即变化精度）的表述下推导出似然比检验的巴特莱特校正。该模型包含两个子模型，一个用于均值响应，另一个用于精度参数。我们的兴趣在于对同时索引两个子模型的参数进行检验推断。我们使用了三个巴特莱特校正的似然比检验统计量，当样本量较小时，预计它们会有更好的性能。我们提出了蒙特卡罗模拟证据，证明了巴特莱特校正检验相对于标准似然比检验和基于另一种方法的两种改进检验在有限样本行为方面的表现。数值证据表明，即使样本量很小，巴特莱特校正的一种检验通常也能提供准确的推断。我们还提出并讨论了一个与行为生物统计学相关的实证应用。
