Goodness of Fit Statistics for Log-linear Transition Modelwith Categorical Longitudinal Data

• Main Authors: Zong-Yi Wu, 吳宗益
• Other Authors: Chao, W.-H.
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/48680861660954629215

碩士 === 國立東華大學 === 應用數學系 === 97 === After fitting a regression moldel to the data at hand, it is a common practice to check the model using appropriate goodness of fit statistics. Quite a few statistics have been proposed in the literature for assessing the goodness of fit of a Markov based regression model in the categorical time series or longitudinal data setting. For example, Fokianos (2002) proposed using the family of power divergence statistics SD_lambda for assessing the goodness of fit of categorical time series models, and proved that the statistics are asymptotically normally distributed when the fitted model is correct. In addition, Chang (2004) applied the W statistic of his adviser, Professor Chao, in his data analysis to assessing the goodness of fit of the log-linear transition model, a Markov based regression model in continuous time. Professor Chao conjectured that the W statistic has an asymptotically chi-squared distribution when the fitted model is true. Through simulation studies, we explore in the thesis if the SD_lambda and W statistics are appropriate in assessing the goodness of fit of log-linear transition model, and investigate their performance in size and power. The results of the simulation indicate that when the fitted model is correct and sample size is large enough, W approximates very well to chi-squared distribution as conjectured, but SD_lambda approximates to normal distribution only when the lambda lies between -1 to 0. Furthermore, statistics W and those SD_lambda for -1 < lambda ≦ 0 were found to have good performance in simulated type I error rate and power; and in general W has a better performance in power than SD_lambda for these lambda.