Modeling for Categorical Data and Handling Over-dispersion via Computer Intensive Methods

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Possibilities and performances of the use of computer intensive methods for handling over-dispersion are studied when we analyze effects of covariates on multi (including more than three) category response data. We set up a system to generate Dirichlet-multinominal random numbers based on the uniform random numbers given by a physical random number generator, using beta-binomial decomposition of the Dirichlet-multinominal distribution. Using this system, we carried out simulation studies for examining effects of handling over-dispersion regarding covariate effect evaluation in the categorical data analysis. Especially we focus on elucidating effectiveness of computer intensive methods such as bootstrap and jackknife methods, compared to the alternatives like multinomial maximum likelihood method (ML), Dirichlet-multinominal ML or generalized estimating equations (GEE) based on their moments up to 2nd order. The simulation results showed the computer intensive methods were comparable to the Dirichlet-multinominal ML, even in the case where the latter is the optimum for the study setting. Furthermore, it is indicated that the computer intensive methods are robust to the departure of the postulated models from the true structure.Based on these simulation results, we applied above methods to some real data and we found that there was a case where the Dirichlet-multinominal ML failed to fit the data while the GEE and the computer intensive methods were able to fit the data successfully.Since the calculations of the computational intensive methods themselves are costly, the simulation studies to evaluate their performances require substantial amount of computational burden. We therefore investigated efficient use of computational resources to ease this problem with simultaneous use of several computers via distributed parallel processing methods. This issue needs to be explored further.