Bootstrap Inference In Several Classes Of Repeated Measures Data

Repeated measures data models are wildly used in public health, bio-science, economics and many other fields. Compared with classical single measure data models, repeated measures data model are more complicated and hypothesis test and interval estimation of the regression coefficient and variance components are more difficult to construct. Traditional methods were designed to construct hypothesis test or interval estimation either based on strict hypothesis which always contrary to reality, or based on the approximate distribution of test statistics and pivot variable. Thus, those methods are limited in use.Many researches have successfully applied generalized p-values to problems which are difficult to figure out exact test since Tsui and Weerahandi proposal generalized p-values in 1989. And the result are better than traditional methods. With the development of computational capability, bootstrap methods based re-sampling technology are wildly used in complicated hypothesis test and interval estimation problems and shew great power that were even better than generalized p-values.Growth curve model are well studied in many literature especially in hypothesis tests and interval estimation problems using generalized p-values in this model. While there almost no famous literature that use bootstrap approach and compare the Monte Carlo result with generalized p-values. This article are dedicated to compare the performance of hypothesis test and interval estimation of the two methods under the framework of growth curve model. In the single treatment group situation, I construct the parametric bootstrap statistics for one-sided tests of the regression coefficient and variance component and parametric bootstrap pivot variables for the interval estimation problems. In the multiple treatments group situation, I construct parametric bootstrap statistics for the equality test of the regression coefficients vectors. The Monte Carlo results show that the two methods both perform well in test and interval estimation of the regression coefficient in single treatment group situation. While parametric bootstrap approach performs also well but little worse than generalized p-values in interval estimation of the variance component. And in multiple treatment group situation, parametric bootstrap approach are more robust than generalized p-values.