Department of Statistics, Brigham Young University, Provo, UT, United States of America.
Department of Physics, Brigham Young University, Provo, UT, United States of America.
PLoS One. 2018 May 30;13(5):e0197222. doi: 10.1371/journal.pone.0197222. eCollection 2018.
In regression settings, parameter estimates will be biased when the explanatory variables are measured with error. This bias can significantly affect modeling goals. In particular, accelerated lifetime testing involves an extrapolation of the fitted model, and a small amount of bias in parameter estimates may result in a significant increase in the bias of the extrapolated predictions. Additionally, bias may arise when the stochastic component of a log regression model is assumed to be multiplicative when the actual underlying stochastic component is additive. To account for these possible sources of bias, a log regression model with measurement error and additive error is approximated by a weighted regression model which can be estimated using Iteratively Re-weighted Least Squares. Using the reduced Eyring equation in an accelerated testing setting, the model is compared to previously accepted approaches to modeling accelerated testing data with both simulations and real data.
在回归设置中，当解释变量存在测量误差时，参数估计将会存在偏差。这种偏差会显著影响建模目标。特别是，加速寿命测试涉及到拟合模型的外推，而参数估计中的少量偏差可能会导致外推预测的偏差显著增加。此外，当对数回归模型的随机分量被假设为乘法时，而实际的基础随机分量是加法时，也可能会出现偏差。为了考虑这些可能的偏差源，可以通过加权回归模型来近似具有测量误差和加法误差的对数回归模型，该模型可以使用迭代重加权最小二乘法进行估计。在加速测试设置中使用简化的 Eyring 方程，通过模拟和真实数据将该模型与之前接受的建模加速测试数据的方法进行比较。
