Semiparametric Logistic Regression Of Longitudinal Data And Improved Transformed Deviance Statistics

In this thesis we mainly investigate the parameter estimation and the goodness-of-fit test for the logistic models with longitudinal binary data. The longitudinal data refers to the data promoted with time. The biggest characteristic of longitudinal data is that it combines section data with time series data. Semiparametric logistic model combines many good properties of both parametric model and non-parametric model. It not only uses the information in the data effectively, but also better analyzes actual problems bringing useful information into the model. We also use the Newton-Raphson method to estimate the parameters.Deviance is a common goodness-of-fit test statistics. However, due to the small sample size, the deviance D cannot be approximated by its asymptotic distribution Xn-p-^n this case, if we still use the statistics D, the results may be very bad. In this paper we introduce the Bartlett transform D and extend it to the longitudinal data.From the Monte-Carlo simulation study, we see that using semipara-metric logistic model, estimates of parameters can effectively converge to the true values of parameters. Using the improved statistic D, the prob-ability of both the first and second type of error is lower than the D statistics. It shows that the improved statistic has a better performance.