Technological innovations have revolutionized the process of scientific research and knowledge discovery in health studies and allow researchers to easily collect intensive longitudinal data that have many closely spaced measurement occasions. The collection of intensive longitudinal data holds much promise for better understanding the emergence and clinical course of a wide range of both physical health and mental health conditions. In theory, intensive longitudinal data can provide answers to important questions in health studies. However, statistical methodology designed to capitalize on the richness of intensive longitudinal data currently lags behind these data collection abilities. For instance, it is not immediately clear that what statistical procedures can be applied to intensive longitudinal data to address questions such as: How does the subjective sensation of withdrawal vary over a day or a week? What is the relationship between mood and drug use? Does the relationship change across individual subjects? Does the relationship vary across subgroups if the population is a combination of several subgroups? In this project, we propose three new classes of statistical models for intensive longitudinal data with a continuous response, binary response and count response, respectively. These new models possess many valuable features which make them the most appropriate to use for addressing critical questions in health studies and drug abuse researches. The proposed new models allow populations to be composed of several subgroups, and effects to vary over time and change across individual subjects, and they keep the structure of the error process very flexible. We will propose estimation procedures for the new models, and develop software to implement the proposed procedures. We plan to apply the proposed procedures to test important hypotheses about drug use using empirical data on tobacco, alcohol and marijuana, and address important questions in health studies using empirical data on asthma. We also plan to publish the proposed research in both the statistical and behavioral/social science literature, and make the new procedures widely available to scientists in health studies, by means of software free of charge. Thus, the proposed research will provide scientists in various health-related research areas with tools they need to address central scientific questions using intensive longitudinal data. The proposed procedures will be employed to address central drug use questions using empirical data on tobacco, alcohol and marijuana, which are the most widely used substances within the US and have been linked to a myriad of both short and long-term consequences. The proposed procedures will also be used to test important hypotheses in health studies using empirical data on asthma, which is a major health problem as there are thought to be 10 million people with asthma within the United States. [unreadable] [unreadable] [unreadable]