Bayesian approach to errors-in-variables in count data regression models / Nur Aainaa Rozliman
In most practical applications, data sets are often contaminated with error or mismeasured covariates. When these errors-in-variables or measurement errors are not corrected, they will cause misleading statistical inferences and analysis. Therefore, we will focus on addressing errors-in-variables...
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| Format: | Thesis |
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2018
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| Online Access: | http://studentsrepo.um.edu.my/9536/ http://studentsrepo.um.edu.my/9536/1/Nur_Aainaa_Rozilman.pdf http://studentsrepo.um.edu.my/9536/9/aainaa.pdf |
| Summary: | In most practical applications, data sets are often contaminated with error or mismeasured
covariates. When these errors-in-variables or measurement errors are not corrected,
they will cause misleading statistical inferences and analysis. Therefore, we will focus
on addressing errors-in-variables problems in count data regression models, specifically
Poisson regression and negative binomial regression models. To remain useful in realistic
situations, we utilize the Bayesian approach where the variance is estimated instead
of assumed as known. We relax the distributional assumption of the exposure model by
intentionally misspecifying the model with a flexible distribution. Following this, we shall
also compare the performance between two different flexible distributions in modelling
the exposure, namely the flexible generalized skew-normal distribution and flexible skewgeneralized
normal distribution. We also conduct simulation studies on synthetic data sets
using Markov Chain Monte Carlo simulation techniques to investigate the performance of
the flexible Bayesian approach. The results of our findings show that the flexible Bayesian
approach is able to estimate the values of the true regression parameters consistently and
accurately with a significant bias reduction. |
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