| Budget Amount *help |
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1999: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1998: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Research Abstract |
In this study, methods for data that have categorical responses are investigated. Especially, analytical methods to deal with over-dispersion are developed and investigated in order to evaluate covariate effects for such data sets.
To incorporate the over-dispersion that cannot be explained by models based on multinomial distribution, we considered Dirichlet-multinomial distribution. Methods which model the relations of indices of association with/without ordered information, such as multinomial logits, cumulative logits, continuation ratio logits, adjacent category logits, complimentary log-log and stereo type model, and linear predictors constructed from the covariates are considered. Fundamental approaches for the work are the maximum likelihood methods based on the distributional extension of the multinomial distribution, such as Dirichlet-multinomial distribution and its extension, generalized estimation equations for the mean-variance structure of the distribution, and computer intensive methods such as the Jackknife method.
We developed analysis systems for such data and analyzed several actual published data. With these analyses, effects of the over-dispersion and modeling of the order information, as wen as differences based on the approach were made clear. The limitations for the Dirichlet-multinomial distribution, especially to handle under-dispersion, were also detected.
In order to study performance of the developed methods, some simulation studies were conducted as well. With these simulation studies, we concluded that the methods were in good agreement in terms of biases and variance estimates of the mean structure parameters in the case where the baseline distributions of the data were Dirichlet-multinomial, and that the method based on Jackknife had comparable abilities to incorporate the effects of over-dispersion.
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