Abstract
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.
Highlights
Data Availability Statement: Two data sets were used
The purpose of this paper is to address the log regression model from Eq (1) in the case where the error is additive and the explanatory variables are observed with error and to specifcially show how it can be applied to reduce bias in parameter estimation in accelerating testing models
We fit the resulting simulated data using the 4 methods described in Section 3.1: the ISO/ IEC 10995 procedure of calculating the median for each treatment and fitting a linear model to the log medians (MED), taking the log of the data and fitting a linear model (LL), using Theorem 1 to weight the treatment groups and account for additive error εi,j (IRLS), and using the Iteratively Re-weighted Least Squares (IRLS) method while accounting for measurement error (IRLS-ME)
Summary
Data Availability Statement: Two data sets were used. The first is founding the international standard for accelerated testing, which is available for purchase online: ISO/IEC 10995:2011. The purpose of this paper is to address the log regression model from Eq (1) in the case where the error is additive and the explanatory variables are observed with error and to specifcially show how it can be applied to reduce bias in parameter estimation in accelerating testing models. The proposed methodology will convert a log regression model with measurement error into a weighted regression model using a Taylor series expansion around the error terms, which can be estimated using iterative re-weighting methods The advantage of this approach is that it reduces bias in parameter estimates by accounting for correct sources of error while remaining relatively simple compared to other techniques of fitting non-linear models in the presence of measurement error.
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