| Summary: | 碩士 === 國立東華大學 === 應用數學系 === 99 === For categorical time series and longitudinal data, quite a few statistics had been proposed in the literature for assessing the goodness of fit of the regression model in consideration. For example, Fokianos (2002) proposed using the ungrouped form of power divergence statistics SD_λ to assess the goodness of fit of some categorical time series regression models, and proved that the SD_λ statistics are asymptotically normally distributed when the fitted model is the true model. Wu (2009) studied and compared the performance of %Fokianos' SD_λ statistics and the W statistic of Chang (2004) in assessing the goodness of fit of the log-linear transition model, a continuous time Markov based regression model, in longitudinal data setting. Through simulation studies, he found that the null distribution of W statistic approximates very well to the chi-square distribution as conjectured. Moreover, he found that both SD_λ and W statistics have satisfactory type-I error rate and W statistic is more powerful than SD_λ. Although Fokianos (2002) had studied the performance of SD_λ statistics in categorical time series data setting, the regression model he considered is limited to marginal regression models. In this thesis, we will investigate the performance of SD_λ and W statistics, through simulation studies, in assessing the goodness of fit of more general regression models such as autoregressive regression models. The result of our simulation indicates that SD_λ for - 0.8≦λ≦0 and W statistics both have satisfactory type-I error rate, and their asymptotic null distributions approximate very well to the normal distribution and chi-squared distribution, respectively. In addition, we find that W statistic is more powerful than SD_λ statistics at some scenarios we considered.
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