Bayesian Analysis of Multivariate Longitudinal Ordinal Data Using Multiple Multivariate Probit Models
Issue:
Volume 12, Issue 1, January 2023
Pages:
1-12
Received:
1 March 2023
Accepted:
17 March 2023
Published:
28 March 2023
Abstract: Multivariate longitudinal ordinal data are often involved in longitudinal studies with each individual having more than one longitudinal ordinal measure. However, due to complicated correlation structures within each individual and no explicit likelihood functions, analyzing multivariate longitudinal ordinal data is quite challenging. In this paper, Markov chain Monte Carlo (MCMC) sampling methods are developed to analyze multivariate longitudinal ordinal data by extending multivariate probit (MVP) models for univariate longitudinal ordinal data to multiple multivariate probit models (MMVP) for multivariate longitudinal ordinal data. The identifiable MVP models require the covariance matrix of the latent multivariate normal variables underlying the longitudinal ordinal variables to be a correlation matrix, thus a Metropolis-Hastings (MH) algorithm is usually necessitated, which brings a rigorous task to develop efficient MCMC sampling methods. In contrast to the identifiable MVP models, the non-identifiable MVP models can be constructed to circumvent a MH algorithm to sample a correlation matrix by a Gibbs sampling to sample a covariance matrix, and hence improve the mixing and convergence of the MCMC components. Therefore, both the identifiable MMVP models and the non-identifiable MMVP models for multivariate longitudinal ordinal data are presented, and their corresponding MCMC sampling methods are developed. The performances of these methods are illustrated through simulation studies and an application using data from the Russia Longitudinal Monitoring Survey-Higher School of Economics (RLMS-HSE).
Abstract: Multivariate longitudinal ordinal data are often involved in longitudinal studies with each individual having more than one longitudinal ordinal measure. However, due to complicated correlation structures within each individual and no explicit likelihood functions, analyzing multivariate longitudinal ordinal data is quite challenging. In this paper...
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Properties and Construction Method for Symmetric Balanced Incomplete Block Design with λ=1
Troon John Benedict,
Onyango Fredrick,
Karanjah Anthony
Issue:
Volume 12, Issue 1, January 2023
Pages:
13-17
Received:
13 April 2023
Accepted:
27 April 2023
Published:
10 May 2023
Abstract: Symmetric Balanced Incomplete Block Designs with λ=1 is a common class of BIBDs which are mostly used in incomplete experimental block design set up because of their simplicity in set up and also in analysis. Over the years since development of the BIBDs by Yates in the year 1939. A number of research has been done on the design to establish properties of the design and also to determine the construction methods of the design. In terms of properties, the studies have only been able to establish necessary but not sufficient not sufficient conditions for the existence of the design. For the symmetric BIBDs the studies have also determined the non-existence properties for such designs. However, the sufficient existence property for the design have not been established. In terms of construction, the studies have been able to derive several construction methods for BIBDs. However, these methods have been determined not to be adequate in constructing all the BIBDs which still leave the existence of some BIBDs as unknown. For symmetric BIBDs with λ=1 which are also known as projective planes, the studies have not been able to establish the sufficient properties for existence of this class of BIBDs just like the other classes of symmetric BIBDs. Therefore, this give room for investigating other properties of this class of BIBDs. The present study therefore, aimed at deriving the properties of the design from the known properties of BIBDs and also using the properties to determine the construction technique that would be suitable used in constructing this class of BIBDs. The study used the known properties of symmetric BIBDs to derive new properties of symmetric BIBDs, then restricted it to the case of λ=1. Which aided in derivation of new properties of the design and also the construction method. The study was able to derive three new properties for this class of BIBD and it was also able to show that the class of BIBD would be best constructed using PG(2,S).
Abstract: Symmetric Balanced Incomplete Block Designs with λ=1 is a common class of BIBDs which are mostly used in incomplete experimental block design set up because of their simplicity in set up and also in analysis. Over the years since development of the BIBDs by Yates in the year 1939. A number of research has been done on the design to establish proper...
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