Multiple Imputations Technique in Missing Data Analysis : a Bayesian Approach using Conjugate Prior

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Opara, A.I
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Missing data occur when data items which should be observed are not included in the data set and this problem presents difficulties for both producersand users of statistical information. Design-based approaches and Ad Hoc techniques were early measures taken to reduce bias of estimates caused by missing data in sample surveys but these measures do not lead to valid statistical inference. Consequently, model-based missing data methods were researched extensively in the 1970’s and 1980’s because of their capacity for inference validity. Rubin (1987) multiple imputation (MI) was one outstanding of such methods. The method imputes missing components of linear regression model, with missingness in the response vector Y, by estimating the posterior distributionsofmodel parameters and drawing values of parameters from these posterior distributions to determine the conditional distribution of the missing data given the observed data. Non-informative prior distribution which is a scaled inverse chi-squared distribution was used in the Bayesian estimation process of Rubin’s approach. Considerable research has been done on models which are outside Rubin’s model framework such as semi-parametric and quantile regression models. This study contributes to research on MI by using joint normal inverse gamma prior distribution to accommodate available conjugate information in the model. Data for model implementation consist of three measurements taken from two groups (samples) of palmate trees planted by Moor Plantation – an agricultural research Institute, in one of their experimental farms. The Plant Height (〖PH〗_i), Stem Middle (〖SM〗_i) and Girth Bottom (〖GB〗_i) were measured simultaneously for a regression model with PH as the response variable and with missing data. Both simulated and real life data showed that estimates of linear modelparameters, based on multiple imputation with informative conjugate prior (MICP), has better precision than Rubin’s method. Informative conjugate prior can lead to biased estimates; therefore the study determined that if prior data represent random selection from the same population as observed data, such prior does not lead to bias in estimation. The study also showed empirically that MICP converges faster than Rubin’s MI.
A Thesis Submitted to the School of Postgraduate Studies, University of Lagos
Design-based approaches , Linear regression model , Statistical information , Regression models , Research Subject Categories::MATHEMATICS::Algebra, geometry and mathematical analysis::Mathematical analysis
Opara, A.I (2016). Multiple Imputations Technique in Missing Data Analysis : a Bayesian Approach using Conjugate Prior. A Thesis Submitted to University of Lagos School of Postgraduate Studies Phd Thesis and Dissertation, 119pp.