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Analyzing count data with measurement error
Author(s) -
Hamada Michael S.,
Casleton Emily M.,
Osthus Dave,
Weaver Brian P.,
Steiner Stefan H.
Publication year - 2022
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.3078
Subject(s) - statistics , observational error , inference , log normal distribution , count data , statistical inference , regression analysis , mathematics , population , regression , econometrics , computer science , artificial intelligence , poisson distribution , demography , sociology
In this article, we analyze observed count data such as the number of defects in a steel product where the observed counts are the true counts measured with errors. We account for the measurement error by using a measurement error model based on a latent lognormal (LLN) distribution. We consider making inference about a single population (e.g., from samples of a production lot) and a regression model (e.g., from runs of a designed experiment), where the measurement system properties are known, that is, the parameters of the LLN distribution are known. Then, we consider simultaneous inference for the single population and regression model as well as the measurement system. We demonstrate the proposed methodology with both simulated and real observed counts.