Bayesian Influence Assessment in the Growth Curve Model with Unstructured Covariance |
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Authors: | Jian-Xin Pan Wing-Kam Fung |
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Affiliation: | (1) Statistics Department, IACR-Rothamsted, Harpenden, Herts, AL5 2JQ, U.K.;(2) Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China |
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Abstract: | From a Bayesian point of view, in this paper we discuss the influence of a subset of observations on the posterior distributions of parameters in a growth curve model with unstructured covariance. The measure used to assess the influence is based on a Bayesian entropy, namely Kullback-Leibler divergence (KLD). Several new properties of the Bayesian entropy are studied, and analytically closed forms of the KLD measurement both for the matrix-variate normal distribution and the Wishart distribution are established. In the growth curve model, the KLD measurements for all combinations of the parameters are also studied. For illustration, a practical data set is analyzed using the proposed approach, which shows that the diagnostics measurements are useful in practice. |
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Keywords: | Bayesian analysis case-deletion method growth curve model Kullback-Leibler divergence statistical diagnostics |
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